Precise Higgs-background predictions: Merging NLO QCD and squared quark-loop corrections to four-lepton + 0,1 jet production

Abstract

We present precise predictions for four-lepton plus jets production at the
LHC obtained within the fully automated Sherpa+OpenLoops framework. Off-shell
intermediate vector bosons and related interferences are consistently included
using the complex-mass scheme. Four-lepton plus 0- and 1-jet final states are
described at NLO accuracy, and the precision of the simulation is further
increased by squared quark-loop NNLO contributions in the gg -> 4l, gg -> 4l+g,
gq -> 4l+q, and qq -> 4l+g channels. These NLO and NNLO contributions are
matched to the Sherpa parton shower, and the 0- and 1-jet final states are
consistently merged using the MEPS@NLO technique. Thanks to Sudakov
resummation, the parton shower provides improved predictions and uncertainty
estimates for exclusive observables. This is important when jet vetoes or jet
bins are used to separate four-lepton final states arising from Higgs decays,
diboson production, and top-pair production. Detailed predictions are presented
for the ATLAS and CMS H->WW analyses at 8 TeV in the 0- and 1-jet bins.
Assessing renormalisation-, factorisation- and resummation-scale uncertainties,
which reflect also unknown subleading Sudakov logarithms in jet bins, we find
that residual perturbative uncertainties are as small as a few percent.

Full text

Prepared for submission to JHEP IPPP/13/66
DCPT/13/132
MCNET-13-12
SLAC-PUB-15714
ZU-TH 15/13
LPN13-056
FR-PHENO-2013-007
Precise Higgs-background predictions:
merging NLO QCD and squared quark-loop
corrections to four-lepton + 0,1 jet production
F. Cascioli,aS. Höche,bF. Krauss,cP. Maierhöfer,aS. Pozzorini,aF. Siegertd
aInstitut für Theoretische Physik, Universität Zürich, 8057 Zürich, Switzerland
bSLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
cInstitute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, UK
dPhysikalisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
E-mail: cascioli@physik.uzh.ch, shoeche@slac.stanford.edu,
frank.krauss@durham.ac.uk, philipp@physik.uzh.ch,
pozzorin@physik.uzh.ch, frank.siegert@cern.ch
Abstract: We present precise predictions for four-lepton plus jets production at the LHC
obtained within the fully automated Sherpa+OpenLoops framework. Off-shell intermedi-
ate vector bosons and related interferences are consistently included using the complex-mass
scheme. Four-lepton plus 0- and 1-jet final states are described at NLO accuracy, and the
precision of the simulation is further increased by squared quark-loop NNLO contributions
in the gg →4`,gg →4`+ g,gq→4`+q, and q¯q→4`+ g channels. These NLO and
NNLO contributions are matched to the Sherpa parton shower, and the 0- and 1-jet fi-
nal states are consistently merged using the Meps@Nlo technique. Thanks to Sudakov
resummation, the parton shower provides improved predictions and uncertainty estimates
for exclusive observables. This is important when jet vetoes or jet bins are used to separate
four-lepton final states arising from Higgs decays, diboson production, and top-pair pro-
duction. Detailed predictions are presented for the Atlas and Cms H→WW∗analyses at
8 TeV in the 0- and 1-jet bins. Assessing renormalisation-, factorisation- and resummation-
scale uncertainties, which reflect also unknown subleading Sudakov logarithms in jet bins,
we find that residual perturbative uncertainties are as small as a few percent.
arXiv:1309.0500v2 [hep-ph] 25 Jan 2014

Contents
1 Introduction 1
2 NLO, matching and merging with Sherpa and OpenLoops 5
2.1 Loop amplitudes with OpenLoops and Collier 5
2.2 Matching to parton shower and merging in Sherpa 6
2.3 Merging of squared quark-loop contributions to four-lepton production 9
3 Monte-Carlo simulations 10
3.1 Input parameters and process definition 10
3.2 Fixed-order ingredients of the calculation 10
3.3 Matching to the parton shower, multi-jet NLO merging, and scale variations 12
4 Analysis of inclusive `ν`ν + 0,1jets production 15
4.1 Fixed-order, matched and merged NLO simulations 16
4.2 Squared quark-loop contributions 18
5Atlas and Cms H→WW∗analyses in the 0- and 1-jet bins 23
5.1 Kinematic distributions after pre-selection cuts 24
5.2 Kinematic distributions in control and signal regions 25
5.3 Exclusive 0- and 1-jet bin cross sections in control and signal regions 29
6 Conclusions 34
A Treatment of bottom- and top-quark contributions 36
B Cuts of the Atlas and Cms H→WW∗analyses in 0- and 1-jet bins 38
1 Introduction
Final states involving four leptons played a key role in the discovery of the Higgs boson [1,2]
and will continue to be crucial in the understanding of its properties and coupling structure.
There are two classes of final states of interest, namely those consistent with H→ZZ∗de-
cays yielding four charged leptons and those related to H→WW∗resulting in two charged
leptons and two neutrinos. They have quite different backgrounds, and for the latter, the
dominant and large top-pair production background necessitates the introduction of jet
vetoes to render the signal visible. More precisely, four-lepton final states consistent with
H→WW∗decays are split into exclusive bins with 0, 1 and 2 jets. The separate analysis
of the different jet bins permits to disentangle Higgs production via gluon fusion from the
vector-boson fusion (VBF) production mode. In addition, data-driven determinations of
– 1 –

the H→WW∗background take advantage of the fact that its two leading components—
diboson and top-pair production—deliver final states of different jet multiplicity. While
diboson production represents the leading background in the 0-jet bin, the top-production
component becomes slightly more important in the 1-jet bin and clearly dominant in the
2-jet bin.
Due to the absence of a mass peak and the high background cross section, the experi-
mental analyses suffer from signal-to-background ratios as low as around 10 percent. It is
thus clear that the precision of the employed background-determination techniques, and the
related error estimates, play a crucial role for any Higgs-boson measurement in this channel.
In fact, with the statistics available at the end of the LHC run at 8 TeV, systematic errors
resulting from the background subtraction already dominate the total uncertainty.
In the H→WW∗analyses by Atlas [3] and Cms [4] a data-driven approach is used to
reduce uncertainties in the simulation of the two leading backgrounds. The top-production
contribution is fitted to data in a top-enriched control sample. Using Monte-Carlo tools,
the top background is extrapolated to the signal region and to an independent diboson-
enriched control region. This latter region is used to normalise the diboson background
after subtraction of the top contamination. The diboson background is then extrapolated
to the signal region using Monte-Carlo predictions. While this approach reduces theoretical
uncertainties associated with the background normalisation, the extrapolations between the
various control and signal sub-samples rely on Monte-Carlo modelling of the background
shapes.
Given that the accuracy of present Higgs-boson measurements requires extrapolation
uncertainties at the percent level, it is clear that Monte-Carlo simulations should include all
available correction effects and appropriate error estimates. In this context, due to various
nontrivial features of the H→WW∗analyses, the requirements in terms of theoretical
precision go beyond the mere inclusion of higher-order corrections to inclusive four-lepton
production. First, a reliable modelling of the various jets associated to the four-lepton
final state requires higher-order QCD corrections up to the highest relevant jet multiplicity.
Second, in order to describe potentially large Sudakov logarithms and related uncertainties,
which arise from jet vetoes and exclusive jet bins, fixed-order predictions should be matched
to parton showers or supplemented by appropriate resummations. Third, vector bosons are
produced well below their mass shell in H→WW∗→`ν`ν decays. Theoretical predictions
for background processes should thus account for corresponding off-shell effects, including
non-resonant channels and related interferences.
In this paper we will concentrate on diboson production, which represents about 75
and 40 percent of the H→WW∗→`ν`ν background in the 0- and 1-jet bins, respectively.
While we are especially interested in the Higgs-boson analyses, diboson production plays
an important role also for precision tests of the Standard Model, vector-boson scattering,
searches for anomalous couplings, or as a background in numerous searches.
Higher-order QCD corrections to diboson production at hadron colliders have been
extensively studied in the literature. Next-to-leading order (NLO) corrections to inclusive
W-pair final states [5–10] amount to roughly 50% at the LHC and can be further en-
hanced in the tails of distributions or reduced by jet vetoes. Due to the gluon–(anti)quark
– 2 –

channels, which start contributing to pp →W+W−only at NLO, the size of the correc-
tions largely exceeds estimates based on leading-order (LO) scale variations. The matching
of NLO predictions for WW production to parton showers was first studied in Ref. [11]
using the MC@NLO method [11], while the POWHEG matching [12] for WW, WZ and
ZZ production, including spin-correlated leptonic decays with non-resonant contributions,
was presented in Ref. [13]. Similar predictions for ZZ production based on the MC@NLO
method can be found in Ref. [14].
The NLO corrections to pp →W+W−jwere presented in Refs. [15–17], including
spin-correlated leptonic decays and off-shell effects associated with the Breit–Wigner distri-
butions of the resonant W-bosons. At the 14 TeV LHC with rather inclusive cuts the cor-
rections are slightly above 30%. Also in this case, due to the opening of the gg →W+W−q¯q
channel at NLO, the corrections largely exceed LO scale variations. This means that un-
certainty estimates based on scale variations start to be meaningful only at NLO. The
inclusion of QCD corrections is thus essential in order to improve both, theoretical predic-
tions and error estimates. The matching of NLO pp →W+W−jcalculations to parton
showers remains to be addressed in the literature.
Higher-order QCD effects have been studied in quite some detail also for pp →WWjj
in the VBF- and QCD-production modes. In the VBF case, NLO corrections including
resonant and non-resonant leptonic decays [18] have been matched to parton showers [19].
For QCD-induced W+W−j j production, NLO predictions have been presented by two
independent groups, including spin-correlated leptonic decays as Breit–Wigner resonances
[20] or in narrow-width approximation [21]. Depending on the scale choice and the collision
energy, NLO effects at the LHC can range from a few percent to tens of percent [20].
Up to date, only NLO QCD corrections to same-sign WWjj production [22,23] have
been matched to parton showers [24]. Recently, NLO predictions became available also for
pp →W Z jj [25].
While full NNLO corrections to diboson production are not yet available, the finite
and gauge-invariant contribution from squared quark-loop gg →W+W−amplitudes was
studied in detail in Refs. [26–29]. Due to the large gluon flux, such NNLO terms increase
the inclusive W+W−cross section by 3–5% at the LHC. Their relative importance is known
to increase in the H→WW∗analysis. While in presence of tight cuts it can reach up to
30% [26,27], with the cuts currently applied by the LHC experiments it remains around
10% [28,29], which corresponds to about half of the Higgs-boson signal. In spite of the tiny
Higgs-boson width, the interference of the gg →4`continuum with the signal can reach
order 10% of the gg →4`signal-plus-background cross section [27,28]. This interference
contribution arises almost entirely above threshold, i.e. at invariant masses MWW >2MW,
and is strongly suppressed at small dilepton invariant mass as well as in the transverse-mass
region mT.MH[28,30]. In Ref. [29] it was shown that also pp →W+W−jreceives a
significant gg →W+W−gcontribution from squared quark-loop amplitudes, which can
reach 6–9% when Higgs-search cuts are applied.
In this paper we present new precise predictions for four-lepton plus 0- and 1-jet pro-
– 3 –

duction,1obtained within the fully automated Sherpa+OpenLoops framework [32,33].
The OpenLoops [33] algorithm is an automated generator of virtual QCD corrections to
Standard-Model processes, which uses the Collier library [34] for the numerically stable
evaluation of tensor integrals [35,36] and scalar integrals [37]. Thanks to a fully flexible
interface of Sherpa with OpenLoops, the entire generation chain—from process definition
to collider observables—is fully automated and can be steered through Sherpa run cards.
The simulation presented in this paper is the first phenomenological application of
Sherpa+OpenLoops. It comprises all previously known QCD contributions to pp →
4`and pp →4`+ 1j, and extends them in various respects. For both processes, NLO
corrections are matched to the Sherpa parton shower [32] using the fully colour-correct
formulation [38,39] of the Mc@Nlo method [11].2Using the recently developed multi-jet
merging at NLO [40,41], the two Mc@Nlo samples are consistently merged in a single
simulation, which preserves the logarithmic accuracy of the shower and simultaneously
guarantees NLO accuracy in the 0- and 1-jet bins. Also squared quark-loop contributions
to pp →4`+ 0,1jets are included. In addition to the pure gluonic channels, gg →4`and
gg →4`+ g, also the quark-induced qg →4`+q,¯qg →4`+ ¯q, and q¯q→4`+ g channels are
taken into account. Moreover, the various squared quark-loop contributions are matched
to the parton shower and merged in a single sample. To guarantee an exact treatment of
spin correlations and off-shell vector bosons, the complex-mass scheme [42] is used, and all
resonant and non-resonant four-lepton plus jets topologies are taken into account.
Detailed predictions are presented for the case of W-pair plus jets production as a signal,
as well as for the irreducible background to the Atlas and Cms H→WW∗analyses in
the 0- and 1-jet bins. To illustrate the relative importance of the various contributions,
merged NLO predictions are contrasted with an inclusive Mc@Nlo simulation of pp →4`,
with separate NLO results for four-lepton plus 0- and 1-jet production, and with squared
quark-loop contributions. Residual perturbative uncertainties are assessed by means of scale
variations. In addition to the usual renormalisation- and factorisation-scale variations, also
the resummation scale of the Sherpa parton shower is varied. This reflects subleading
Sudakov logarithms beyond the shower approximation, which renders error estimates more
realistic in presence of jet vetoes.
The presented simulation involves various interesting improvements for the H→WW∗
analyses. The NLO matching and merging of pp →4`+ 0,1jets provides NLO accurate
predictions and Sudakov resummation in the first two exclusive jet bins. The inclusion
of pp →4`+ 1jat NLO, which contributes, as a result of merging, both to the 0- and
1-jet bins, guarantees that all q¯q,qg,¯qg and gg channels are open. In this situation scale
variations can be regarded as more realistic estimates of theoretical uncertainties. Matching
and merging render squared quark-loop gg →4`contributions to exclusive jet bins more
reliable. In fact, if not supplemented by shower emissions, the parton-level gg →4`channel
completely misses the Sudakov suppression induced by the jet veto. Matching gg →4`to
1First partial results of this study were anticipated in [31].
2In the following, Mc@Nlo refers to the algorithm of Refs. [38,39], which is an extension of the original
Mc@Nlo method by Frixione and Webber [11]. In particular, we never refer to the Mc@Nlo event
generator.
– 4 –

the parton shower automatically implies fermion-loop processes with initial-state quarks,
like qg→4`+q, which result from q→qgshower splittings. The corresponding quark-
induced matrix elements, which are included for the first time in this study, provide an
improved description of hard jet emission.
Finally we point out that, while the presented simulation deals only with µ+νµe−¯νe+jets
final states, the employed tools allow for a fully automated generation of any other combi-
nation of charged leptons and neutrinos.
The paper is organised as follows. In Section 2we discuss the calculation of one-
loop amplitudes with OpenLoops and Collier as well as NLO matching and merging in
Sherpa. Details of the Monte-Carlo simulations can be found in Section 3. In Section 4
we present results for inclusive WW-signal cuts, with emphasis on squared quark-loop
contributions, merging aspects and jet-veto effects. Section 5is devoted to a detailed dis-
cussion of the H→WW∗analyses at the LHC. Our conclusions are presented in Section 6.
Appendix Adescribes the treatment of bottom- and top-quark contributions, and the
H→WW∗selection cuts are documented in Appendix B.
2 NLO, matching and merging with Sherpa and OpenLoops
This section is devoted to the automation of NLO calculations in Sherpa+OpenLoops
and to methodological aspects of matching and merging of NLO and squared quark-loop
corrections.
2.1 Loop amplitudes with OpenLoops and Collier
For the calculation of virtual corrections we employ OpenLoops [33], a fully automated
generator of Standard-Model scattering amplitudes at one loop. The OpenLoops method
has been designed in order to break various bottlenecks in multi-particle one-loop calcu-
lations. The algorithm is formulated in terms of Feynman diagrams and tensor integrals,
which allows for very high CPU efficiency to be achieved. While this was already known
from 2→4NLO calculations based on algebraic methods [43–46], the idea behind Open-
Loops is to replace algebraic manipulations of Feynman diagrams by a numerical recursion,
which results in order-of-magnitude reductions both in the size of the numerical code and
in the time needed to generate it. Thanks to these improvements, which are accompanied
by a further speedup of loop amplitudes at runtime, OpenLoops is able to address large-
scale problems, such as NLO simulations for classes of processes involving a large number
of multi-leg partonic channels.
The OpenLoops recursion is based on the well known idea that one-loop Feynman dia-
grams can be cut-opened in such a way that the resulting tree-like objects can be generated
with automated tree algorithms. However, rather than relying on conventional tree algo-
rithms, the recursion is formulated in terms of loop-momentum polynomials called “open
loops”. An analogous idea was proposed in Ref. [47] in the framework of Dyson-Schwinger
off-shell recursions. Diagrams involving Nloop propagators are built by reusing compo-
nents from related diagrams with N−1loop propagators in a systematic way. Together
– 5 –

with other techniques to speed up colour and helicity summations [33], this allows to handle
multi-particle processes with up to O(104−105)one-loop diagrams.
The algorithm is completely general, since the kernel of the reduction depends only
on the Feynman rules of the model at hand, and once implemented it is applicable to any
process. Similarly, the so-called R2rational terms [48] are generated as counterterm-like
diagrams from corresponding Feynman rules.
For the numerical evaluation of one-loop tensor integrals, OpenLoops is interfaced
to the Collier library [34], which implements the Denner–Dittmaier reduction meth-
ods [35,36] and the scalar integrals of Ref. [37]. Thanks to a variety of expansions in
Gram determinants and other kinematic quantities [36], the Collier library systemati-
cally avoids spurious singularities in exceptional phase-space regions. This allows for a fast
and numerically stable evaluation of tensor integrals in double precision. Alternatively,
OPP reduction [49] can be used instead of tensor integrals.
The present implementation of OpenLoops can handle one-loop QCD corrections to
any Standard-Model process with up to six particles attached to the loops.3Virtual QCD
corrections are computed exactly, and the full set of Feynman diagrams contributing to
a given process is taken into account by default. For final states involving four leptons,
the complex-mass scheme [42] is used for a consistent description of resonant and non-
resonant vector-boson propagators and their interferences. OpenLoops can also be used
to compute squared one-loop matrix elements, such as the various squared quark-loop
amplitudes considered in this paper. The correctness of one-loop amplitudes generated with
OpenLoops has been tested systematically against an independent in-house generator for
more than one hundred different parton-level processes, and agreement at the level of 12-14
digits on average was found. The first public version of the code will be released in the
course of 2013.
2.2 Matching to parton shower and merging in Sherpa
The combination of fixed-order calculations and resummation is essential for the analysis of
exclusive cross sections. Parton showers implement resummation in a simple, yet effective
way. While formally only correct to leading-logarithmic accuracy, they include a number
of features that are important for a realistic prediction of exclusive jet spectra. Firstly, the
strong coupling factors associated to quark and gluon emissions are evaluated at scales set
by the transverse momenta in the parton branchings. This choice sums higher-logarithmic
corrections, originating in the enhanced probability for soft and collinear radiation. Sec-
ondly, modern parton showers naturally implement local four-momentum conservation in
each individual parton emission, which leads to a realistic description of the kinematics
in multi-particle final states. Thirdly, most parton showers include higher-logarithmic cor-
rections in an effective approximation known as angular ordering. This method yields the
correct jet rates in e+e−annihilation to hadrons [50], as well as the production of Drell–Yan
lepton pairs in hadronic collisions [51].
3Final-state lepton pairs couple to QCD loops only via electroweak vector bosons and should thus be
counted as a single particle.
– 6 –

Cross sections in jet bins as analysed here are strongly sensitive to real radiative correc-
tions, or their suppression. Such corrections are dominated by Sudakov double logarithms
of the jet-veto scale, which can have a large impact both on exclusive cross sections and
related uncertainty estimates. A priori it is not clear if renormalisation- and factorisation-
scale variations provide a meaningful estimate of NLO cross sections in jet bins. In fact
conventional scale variations can turn out to be artificially small as a consequence of acci-
dental cancellations between Sudakov-enhanced logarithms and contributions that do not
depend on the jet veto [52]. In this respect, fixed-order calculations matched to a parton
shower allow for more reliable predictions and error estimates. In particular, factorisation-
and renormalisation-scale uncertainties can be supplemented by independent variations of
the resummation scale, i.e. the scale that enters Sudakov logarithms and corresponds to
the starting point of the parton-shower evolution. Resummation-scale variations reflect the
uncertainties associated with subleading Sudakov logarithms beyond the shower approxi-
mation, and independent variations of the factorisation, renormalisation and resummation
scales provide a more reliable assessment of theoretical errors in presence of jet bins.
The parton shower used for our calculation is based on Catani–Seymour dipole sub-
traction [53]. It was described in detail in Refs. [54,55]. Splitting kernels are given by
the spin-averaged dipole-insertion operators, taken in the large-Nclimit. The momentum
mapping in branching processes is defined by inversion of the kinematics in the dipole-
subtraction scheme. The parameters of the parton shower are given by its infrared cutoff,
by the resummation scale, and by the precise scale at which the strong coupling is evalu-
ated. This latter scale must be proportional to the transverse momentum kTin the splitting
process, but it may be varied using a prefactor, b, of order one. In practice, the explicit form
of kTis dictated by the dipole kinematics, and different prefactors are used for final-state
and initial-state evolution. The resummation scale can be chosen freely in principle, but at
leading order it must be equal to the factorization scale.
The matching of NLO calculations and parton showers in the Mc@Nlo method [11] is
based on the idea that O(αs)expansions of the parton shower can provide local subtraction
terms (called MC counterterms), which cancel all infrared singularities in real-emission
matrix elements. The subtracted result is a finite remainder. When combined with the
parton shower it gives the correct O(αs)distribution of emissions in the radiative phase
space. The total cross section is obtained to NLO accuracy by adding virtual corrections
and integrated MC counterterms to the Born cross section and combining them into a
common seed for the parton shower. The matching procedure effectively restricts the role
of the parton shower to QCD emissions beyond NLO.
This method needs to be modified in processes with more than three coloured particles
at Born level, because of non-factorisable soft-gluon insertions at real-emission level. Spin
correlations further complicate the picture. This problem is solved by using a variant of
the original Mc@Nlo technique [38,39]. Like Sherpa’s parton shower itself, this method
is based on the dipole-subtraction formalism by Catani and Seymour [53], and it is imple-
mented in Sherpa in a fully automated way. It supplements the parton shower with spin
and colour correlations for the first emission and therefore extends it systematically beyond
the large-Ncapproximation.
– 7 –

We combine Mc@Nlo calculations of varying jet multiplicity into inclusive event sam-
ples using the Meps@Nlo method [40,41]. This technique is based on partitioning the
phase space associated to QCD emissions into a soft and a hard regime. The soft region is
filled by the parton shower alone, while the hard region is described in terms of fixed-order
calculations, to which the parton shower has been matched. In case of the Mc@Nlo simu-
lation with the highest jet multiplicity, Nmax, the parton shower is allowed to fill the entire
phase space. The phase-space separation is achieved in terms of a kinematical variable
analogous to the jet criterion in longitudinally-invariant kT-clustering algorithms [56]. We
will denote the separation cut by Qcut. It should be chosen smaller than the minimum jet
transverse momentum. In this manner, the prediction for inter-jet correlations involving
up to Nmax jets is always NLO accurate, and augmented by resummation as implemented
in the parton shower.
The choice of the renormalisation scale in the Meps@Nlo approach is based on the
CKKW technique, a multi-jet merging algorithm for tree-level matrix elements [57]. Each
shower emission is associated with a factor αs(b k2
T), where the scale is dictated by the
resummation. The smooth transition between parton-shower and matrix-element regimes
at the merging scale Qcut requires a similar scale choice also in matrix elements. To this
end, multi-jet events are clustered into a 2→2core process. The clustering algorithm is
defined as an exact inversion of the parton shower, such that clusterings are determined
according to the parton-shower branching probabilities [56]. The coupling factors resulting
from the various QCD emissions are then evaluated at scales µ2=b k2
T, where kTis the
nodal scale of the corresponding branching, while the αK
s(µ2)term associated with the core
process is taken at the usual scale µ=µR. This latter can be chosen freely as in fixed-order
calculations.
In practice, in the Meps@Nlo algorithm all αsterms are first evaluated at the scale
µR, and the CKKW prescription is implemented via weight-correction factors,
αs(b k2
T)
αs(µ2
R)≈1−αs(µ2
R)
2πb0ln b k2
T
µ2
R,(2.1)
for each branching. More precisely, in LO and NLO matrix elements the left- and right-
hand sides of (2.1) are used, respectively. For the hard remainder function in the Mc@Nlo
calculations contributing to the Meps@Nlo result the renormalisation scale is always eval-
uated according to the most likely underlying Born configuration, classified according to
the branching probability in the parton shower.
The fact that the CKKW scale choice adapts to the jet kinematics can improve the
description of jet emission also at high transverse momentum. In this region, where jet emis-
sion is typically associated to CKKW coupling factors αs(p2
T), fixed-order calculations based
on a global renormalisation scale µRinvolve a relative factor αs(µ2
R)/αs(p2
T), which can sig-
nificantly overestimate the jet rate if µRdoes not adapt to the jet transverse momentum
and pTµR. This factor tends to be compensated by NLO corrections, but in Mc@Nlo
simulations with fixed jet multiplicity Nit remains uncompensated for the (N+ 1)-th
jet, whose description relies on real-emission LO matrix elements. Within Meps@Nlo, if
N < Nmax such real-emission matrix elements are confined at transverse momenta below
– 8 –

the merging scale and replaced by an Mc@Nlo simulation with N+ 1 jets above Qcut. In
this way NLO accuracy is ensured for the first Nmax jets, and the problem remains present
only for the subsequent jet. A simple solution consists of including (Nmax + 1)-jet LO
matrix elements in the merging procedure. In this way, also the (Nmax + 1)-th jet receives
a CKKW coupling factor αs(p2
T)above the merging scale. As discussed in Section 3.3, for
the Meps@Nlo simulation of pp →4`+ 0,1jwe adopt a dynamical scale µRthat depends
only on the W-boson transverse energy and does not adapt to extra jet emissions. The
above discussion is thus relevant for the high-pTtail of the second jet, where it’s likely that
µRpT, since the two jets typically recoil against each other and the transverse energy of
the W bosons tends to remain of the order of MW.
In order to guarantee a complete treatment of scale uncertainties, renormalisation-scale
variations in the Meps@Nlo merging approach are performed simultaneously in the fixed-
order calculation and in the parton shower. The same rescaling factors are applied to the
CKKW scales and to the scale µRused in the αsterms associated with the core process.
2.3 Merging of squared quark-loop contributions to four-lepton production
We present here, for the first time, a combination of the squared quark-loop contributions to
pp →4`+ 0,1jusing the ME+PS merging technique of Ref. [56]. At matrix-element level
we consider all squared one-loop amplitudes that involve a closed quark loop. While squared
quark-loop corrections to 4`final states involve only gg initial states, 4`+ 1jproduction
involves, in addition to gg →4`+ g, also qg→4`+q,¯qg→4`+ ¯qand q¯q→4`+ g
contributions. For these quark-initiated channels we require that all final-state leptons are
connected to the quark loop via vector-boson exchange, i.e. we exclude topologies where
vector bosons couple to the external quark line. The inclusion of these quark-initiated
channels is mandatory for a consistent merging of the 4`+ 0,1jsamples. This is due to
the fact that gluon- and quark-initiated channels are intimately connected via q→qgand
g→q¯qparton-shower splittings. Including the qgand ¯qgchannels ensures that all splitting
functions used in the shower are replaced by matrix elements in the hard-jet region. The
finite contribution from the q¯q→4`+ g channel is added for consistency. While the gg-
induced channels have already been discussed in the literature [26–29,58], the squared
quark-loop contributions to the qg-, ¯qg- and q¯q-channels are investigated for the first time
in this paper.
To merge the 4`+ 0,1jfinal states we can use the tree-level techniques of Ref. [56] since
all involved matrix elements are infrared and ultraviolet finite. In particular, the merging
scale Qcut acts as an infrared cutoff that avoids soft and collinear divergences of 4`+ 1j
matrix elements, and the phase-space region below Qcut is filled by gg →4`matrix elements
plus shower emissions. As discussed in Section 3.3, while squared quark-loop corrections
represent NNLO contributions to inclusive 4`+ 0,1jproduction, their intrinsic accuracy is
only leading order. Consequently, as we will see in Sections 4–5, squared quark-loop terms
are more sensitive to renormalisation- and resummation-scale variations as compared to
Meps@Nlo predictions.
– 9 –

3 Monte-Carlo simulations
In the following we discuss input parameters and theoretical ingredients of the Monte-Carlo
simulations presented in Sections 4and 5.
3.1 Input parameters and process definition
The presented results refer to pp →µ+νµe−¯νe+Xat a centre-of-mass energy of 8TeV.
Predictions at NLO and squared quark-loop corrections are evaluated using the five-flavour
CT10 NLO parton distributions [59] with the respective running strong coupling αs. At
LO we employ the CT09MCS PDF set. For the vector-boson masses we use
MW= 80.399 GeV, MZ= 91.1876 GeV,(3.1)
and in order to guarantee NLO accurate W→`ν branching fractions we use NLO input
widths
ΓW= 2.0997 GeV,ΓZ= 2.5097 GeV.(3.2)
The electroweak mixing angle is obtained from the ratio of the complex W- and Z-boson
masses as [42]
cos2θw=M2
W−iΓWMW
M2
Z−iΓZMZ
,(3.3)
and the electromagnetic fine-structure constant is derived from the Fermi constant Gµ=
1.16637 ·10−5GeV−2in the so-called Gµ-scheme, which results in
α−1=π
√2GµM2
W1−M2
W
M2
Z−1
= 132.348905 .(3.4)
Since quark-mixing effects cancel almost completely [17], we set the CKM matrix equal to
one.
Partonic channels with initial- and final-state b quarks are not included in order to
avoid any overlap with t¯
tand tW production. At NLO this separation is nontrivial since
W+W−+ 1jproduction receives pp →W+W−b¯
breal-emission contributions that involve
top-quark resonances. At the same time, W+W−b¯
bfinal states are intimately connected to
the virtual corrections to q¯q→W+W−gvia cancellations of collinear singularities that arise
from g→b¯
bsplittings [17]. This is discussed in detail in Appendix A, where we introduce a
prescription to separate W+W−+jets from single-top and top-pair production processes in
such a way that each contribution is infrared finite and free from large logarithms associated
to g→b¯
bsplittings. This prescription is not unique, and we estimate the related ambiguity
to be of order 1%. It can be eliminated by a consistent matching of W+W−+jets and
W+W−b¯
bproduction as explained in Appendix A.
3.2 Fixed-order ingredients of the calculation
Sample Feynman diagrams contributing to the fixed-order building blocks of the calculation
are shown in Figures 1and 2. For brevity µ+νµe−¯νeconfigurations are often denoted as
`ν`ν or 4`final states in the following. The first figure illustrates NLO QCD corrections to
– 10 –

¯q
qe−
¯νe
νµ
µ+
W−
W+
¯q
qe−
¯νe
νµ
µ+
Z/γ
W−
W+
¯q
qe−
νµ
µ+
¯νe
Z/γ W+
¯q
g¯q
e−
¯νe
νµ
µ+
W−
W+
¯q
g¯q
e−
νµ
µ+
¯νe
g
Z/γ W+
g
g q
e−
¯νe
νµ
µ+
¯q
W−
W+
¯q
qe−
¯νe
νµ
µ+
W−
W+
¯q
g¯q
e−
¯νe
νµ
µ+
W−
W+
¯q
g¯q
e−
νµ
µ+
¯νe
Z/γ W+
Figure 1. Sample Feynman diagrams contributing to pp →µ+νµe−¯νeand pp →µ+νµe−¯νe+ 1j
at NLO.
pp →4`and pp →4`+ 1j, which involve various ¯qq,qg,¯qgand gg partonic channels. The
complete set of Feynman diagrams and related interferences is taken into account, including
single-resonant Z/γ∗→e−¯νeW+(→µ+νµ)sub-topologies. Pentagons represent the most
involved one-loop topologies.
In addition to NLO corrections also squared quark-loop contributions to the partonic
channels gg →4`,gg →4`+ g,gq→4`+q,g ¯q→4`+ ¯q, and q¯q→4`+ g are computed.
Corresponding Feynman diagrams are shown in Fig. 2. The most involved diagrams are
again pentagons. As discussed in Section 2.3, the inclusion of the quark-induced channels
is mandatory for a correct description of the full spectrum of jet emission based on the
merging of 4`and 4`+jsimulations. Contributions where the leptons are coupled to
quark triangles via Z/γ∗exchange, like in the first two diagrams of Fig. 2, vanish due to
electroweak Ward identities [10]. In contrast, related topologies with an extra gluon in
the final state, like the last two diagrams in Fig. 2, yield non-vanishing contributions. The
various NLO and squared quark-loop amplitudes generated for the present study comprise
all relevant Higgs-boson contributions, including the interference of the Higgs signal with the
four-lepton continuum. However, for the background predictions presented in Sections 4–5
all Higgs-boson contributions have been decoupled by setting MH→ ∞.
A series of checks has been performed to validate all ingredients of the QCD correc-
tions. To check the correctness of the q¯q→4`+ 0,1g OpenLoops matrix elements we
used an independent computer-algebra generator, originally developed for the calculations
of Refs. [43,45]. The squared quark-loop gg →4`+ 0,1g amplitudes have been checked
– 11 –

g
ge−
¯νe
νµ
µ+
Z/γ W−
W+
g
ge−
νµ
µ+
¯νe
Z/γ W+
g
ge−
¯νe
νµ
µ+
W−
W+
g
ge−
¯νe
νµ
µ+
HW−
W+
g
g g
e−
¯νe
νµ
µ+
W−
W+
g
g g
e−
¯νe
νµ
µ+
W−
W+
g
q q
e−
¯νe
νµ
µ+
W−
W+
g
g g
e−
¯νe
νµ
µ+
Z/γ W−
W+
g
g g
e−
νµ
µ+
¯νe
Z/γ W+
Figure 2. Sample Feynman diagrams involved in the squared quark-loop NNLO contributions to
pp →µ+νµe−¯νeand pp →µ+νµe−¯νe+ 1j.
against MCFM [60] and Ref. [29]. The NLO and squared quark-loop integrated cross sec-
tions for pp →4`+ 0,1jand gg →4`+ 0,1g have been found to agree with various
results in the literature [13,27,29]. Finally, the NLO cross sections for hadronic 4`+ 0,1j
production have been reproduced with sub-permil statistical precision using an indepen-
dent Monte-Carlo generator, which was developed by S. Kallweit in the framework of the
pp →W+W−b¯
bcalculation of Ref. [45].
The calculation of tree-level matrix elements is performed either by the Amegic++ [61]
or the Comix [62] matrix-element generator, where Comix is used only for pp →4`+ 2j
subprocesses. Integrated and real subtraction terms are computed with the method of
Catani and Seymour [53], using the automated implementation in Amegic++ [63].
3.3 Matching to the parton shower, multi-jet NLO merging,
and scale variations
The perturbative content of the various fixed-order, matched and merged simulations that
are presented in Sections 4and 5is illustrated in Table 1. Parton-level NLO predictions
for pp →4`+ 0,1jare denoted as Nlo 4`and Nlo 4`+ 1j. Their NLO predictive power is
restricted to the 0- and 1-jet bins, respectively.4In bins with one extra jet with respect to
4In this discussion of the perturbative accuracy we refer to jet bins in the inclusive sense. The 0-, 1-
and 2-jet bins should namely be understood as final states with ≥0,≥1and ≥2jets, or equivalently as
observables that explicitly or implicitly involve a corresponding number of jets.
– 12 –

Nlo simulations 0-jet 1-jet 2-jet
Nlo 4`NLO LO -
Nlo 4`+ 1j- NLO LO
Mc@Nlo 4`NLO+PS LO+PS PS
Mc@Nlo 4`+ 1j- NLO+PS LO+PS
Meps@Nlo 4`+ 0,1jNLO+PS NLO+PS LO+PS
Loop2simulations 0-jet 1-jet 2-jet
Loop24`LO - -
Loop24`+ 1j- LO -
Loop2+PS 4`LO+PS PS PS
Loop2+PS 4`+ 1j- LO+PS PS
Meps@Loop24`+ 0,1jLO+PS LO+PS PS
Table 1. Perturbative accuracy of various fixed-order, matched and merged simulations for final
states with 0, 1 and 2 jets.
the simulated process, the precision decreases to LO, and higher-multiplicity bins are not
populated at all.
This is overcome by matching Nlo 4`or Nlo 4`+ 1jmatrix elements to the parton
shower. Corresponding predictions are denoted as Mc@Nlo 4`and Mc@Nlo 4`+ 1j. The
shower radiates an arbitrary number of extra jets, which effectively resums large Sudakov
logarithms that arise when QCD radiation is constrained by tight cuts, such as in presence
of jet vetoes. Similarly as the underlying NLO matrix elements, Mc@Nlo predictions
provide NLO precision only for one particular jet multiplicity. In the following sections
we will consider only Mc@Nlo 4`predictions. This corresponds to the usual inclusive
NLO+PS samples used in experimental studies, where observables involving one jet are
only LO accurate, and the emission of additional jets is entirely based on the parton-shower
approximation.
Our best NLO predictions are denoted as Meps@Nlo 4`+0,1jand result from merging
Mc@Nlo 4`and Mc@Nlo 4`+1jsamples. This provides shower-improved NLO precision
in the first two jet bins. To ensure that the formal NLO accuracy is preserved in the 0-
and 1-jet bins, the merging scale Qcut should not exceed the pT-threshold used for jet
binning. On the other hand, in the limit of small Qcut the fact that higher-logarithmic
terms in the fixed-order Nlo 4`+ 1jcalculation are not resummed in the Sudakov form
factor gives rise to a logarithmic sensitivity to the merging scale. Such logarithms are
beyond the shower accuracy but can be numerically non-negligible [64,65]. Thus the
merging scale should not be set too far below the jet-pTthreshold. Following this reasoning
the value Qcut = 20 GeV has been used as merging scale, and the stability of the results
with respect to this technical parameter has been tested using variations in the range
– 13 –

15 GeV ≤Qcut ≤35 GeV. The corresponding uncertainties are discussed in Section 5for
the case of the H→WW∗analysis, where they turn out to be at the percent level. The
Meps@Nlo 4`+ 0,1jsample is further improved by including LO matrix elements with
two jets in the merging procedure. As explained in Section 2.2, this guarantees a better
(CKKW-type) scale choice for the αsfactor associated with the second jet emission.
In order to gain insights into the importance of parton-shower and merging effects,
we will present systematic comparisons of NLO, Mc@Nlo and Meps@Nlo predictions.
While Sudakov resummation effects due to the parton shower show up in the difference
between Nlo 4`and Mc@Nlo 4`, comparing Mc@Nlo 4`to Meps@Nlo 4`+0,1jallows
one to assess NLO corrections to the first emission.
As already mentioned, squared quark-loop terms included in our simulation represent
NNLO contributions to pp →4`+ (0)1j. On the other hand, since NNLO is the first order
at which the gg →4`+ 0(1)g channels start contributing to 4`+ (0)1jproduction, these
corrections can also be regarded as LO contributions. As indicated in Table 1, squared
quark-loop terms behave as LO predictions also for what concerns the number of external
QCD partons. In fact, fixed-order squared quark-loop predictions, which we denote as
Loop24`and Loop24`+ 1j, populate only a single jet bin. In particular, Loop24`
predictions completely miss exclusive jet emission and suppression effects resulting from
jet vetoes. A first realistic estimate of jet-veto effects is obtained by showering squared
quark-loop contributions. The corresponding predictions are labelled as Loop2+PS 4`and
Loop2+PS 4`+ 1j, depending on the jet multiplicity of the underlying matrix elements.
Merging the Loop2+PS simulations with 0 and 1 jets results in a single Meps@Loop24`+
0,1jsample, which provides a reliable description of the full spectrum of jet emission, from
soft to hard regions. This merged squared quark-loop simulation comprises also partonic
channels with initial-state quarks. To assess their relative importance, in Section 4, full
Meps@Loop24`+ 0,1jpredictions are compared to corresponding predictions involving
only initial-state gluons.
As a default renormalisation (µR), factorisation (µF) and resummation (µQ) scale we
adopt the average W-boson transverse energy
µ0=1
2ET,W++ET,W−,(3.5)
where E2
T,W=M2
W+(~pT,` +~pT,ν )2. As discussed in Section 4, motivated by the comparison
of hard-jet emission from parton shower and matrix elements, in the case of squared quark-
loop contributions we decided to reduce the resummation scale by a factor two, i.e. we set
µQ=µ0/2.
Renormalisation- and factorisation-scale uncertainties are assessed by applying inde-
pendent variations µR=ξRµ0and µF=ξFµ0, with factor-two rescalings (ξR, ξF)=(2,2),
(2,1),(1,2),(1,1),(1,0.5),(0.5,1),(0.5,0.5). The renormalisation scale is varied in all αs
terms that arise in matrix elements or from the shower. In Nlo and Mc@Nlo predictions
all αsterms arising from matrix elements are evaluated at µR=ξRµ0, while in Meps@Nlo
the scale µ0is used only in tree and loop contributions to the pp →4`core process, which
results from 4`+jets configurations via clustering of all hard jets. For the αsfactors asso-
– 14 –

ciated with jet emissions a CKKW scale choice is applied, as discussed in Section 2.2. As
a consequence, Meps@Nlo predictions are less sensitive to the choice of the central scale
µ0. Also in Meps@Loop2merging the scale of αsfactors associated to QCD emissions is
dictated by the CKKW prescription. In this case the core process involves a term α2
s(µR),
which renders squared quark-loop corrections more sensitive to the choice of the central
scale µ0.
In addition to usual QCD-scale studies, the Sherpa framework allows also for auto-
mated variations of the resummation scale µQ, which corresponds to the starting scale of
the parton shower. This scale is varied by factors µQ/µ0= 1/√2,1,√2, while keeping µR
and µFfixed. As discussed in Section 2.2, this reflects uncertainties related to subleading
logarithms beyond the shower approximation and yields more realistic error estimates for
exclusive observables such as jet-vetoed cross sections. In order to quantify the total scale
uncertainty we will regard (µR, µF)and µQvariations as uncorrelated and add them in
quadrature.5Uncertainties related to the PDFs, αs(MZ), hadronisation, and underlying
event are not considered in this study.
The presented results were obtained with a Sherpa 2.0 pre-release version6. First
partial results of this simulation have been presented in Ref. [31]. In addition to the squared
quark-loop contributions, which were not included in Ref. [31], in this paper we investigate
various new observables. Due to the difference between (3.5) and the scale choice µ0=M`ν`ν
in Ref. [31], results presented here should not be directly compared to those of Ref. [31].
4 Analysis of inclusive `ν`ν + 0,1jets production
As a first application of our simulation we study µ+νµe−¯νeand µ+νµe−¯νe+ 1 jet production
without any Higgs-analysis specific cuts. To this end we adopt the cuts of the MC_WWJETS
truth analysis provided with the Rivet Monte-Carlo validation framework [66]. Specifically,
we require charged leptons with pT,` >25 GeV and |η`|<3.5. Missing transverse energy
is identified with the vector sum of the neutrino transverse momenta and required to fulfil
E/T>25 GeV. Jets are defined using the anti-kTalgorithm [67] with a distance parameter
of R= 0.4. No jet-rapidity cuts are applied.
To illustrate the importance of the various corrections and the respective scale un-
certainties, we present cross sections and distributions at the different levels of simulation
introduced in Section 3.3. In Section 4.1 we compare fixed-order predictions to matched
and merged NLO simulations. Squared quark-loop corrections are discussed in Section 4.2.
5Another natural way of combining these two sources of uncertainty is to consider simultaneous varia-
tions of (µR, µF, µQ), excluding rescalings in opposite directions as usual. The variations resulting from this
alternative approach are likely to be even smaller than those obtained by adding QCD- and resummation-
scale uncertainties in quadrature.
6This pre-release version corresponds to SVN revision 21825 and the main difference with respect to
the final Sherpa 2.0 release version is the tuning of parton shower, hadronisation and multiple parton
interactions to experimental data.
– 15 –

Analysis Lo 4`(+1j)Nlo 4`(+1j)Mc@Nlo 4`Meps@Nlo 4`+ 0,1j
≥0jets 217.99(2) +1.9%
−2.8% 328.08 +3.1%
−2.4% 326.70(29) +4.5%
−2.8%
+0.0%
−0.2% 356.01(58) +1.3%
−0.8%
+1.8%
−0.0%
≥1jets 73.61(1) +14.5%
−11.6% 101.70 +5.2%
−4.9% 83.23(15) +9.9%
−9.0%
+2.4%
−4.6% 103.45(28) +2.8%
−3.7%
+3.3%
−0.5%
Table 2. Cross-section predictions in femtobarns for the µ+νµe−¯νeanalyses requiring ≥0and
≥1jets. Fixed-order LO and NLO results for the ≥0-jet and ≥1-jet analyses correspond to 4`
and 4`+ 1jproduction, respectively. They are compared to an inclusive Mc@Nlo 4`simulation
and to Meps@Nlo 4`+ 0,1jpredictions. Uncertainties associated to variations of the QCD scales
(µR, µF) and the resummation scale (µQ) are shown separately as σ±δQCD ±δres. Statistical errors
are given in parenthesis.
4.1 Fixed-order, matched and merged NLO simulations
Rates for the inclusive analysis and when requiring (at least) one jet with pT>30 GeV
are shown in Table 2. Fixed-order LO and NLO predictions for pp →4`or 4`+ 1j,
depending on the jet bin, are compared to the inclusive Mc@Nlo 4`simulation and to the
NLO merged simulation of 4`+ 0,1j. For 0- and 1-jet production we observe positive NLO
corrections of 50% and 38%, respectively, consistent with the typical size of K-factors in the
literature. At NLO, scale uncertainties range from 3 to 5 percent, which is twice as large as
compared to our previous Higgs-background predictions in exclusive jet bins [31]. This can
be attributed to the new scale choice (3.5) and to the fact that results in Table 2correspond
to inclusive jet bins. In fact, as shown in Ref. [17], the choice of the central scale and a
jet veto can have a strong impact on scale uncertainties in 4`+ 1jproduction [17]. In this
respect, we note that the central scale used in Ref. [31], i.e. the total four-lepton invariant
mass, is more than a factor two higher than the transverse-energy scale (3.5) adopted for
the present study.
Comparing the Mc@Nlo and Nlo simulations we observe one-percent level agreement
and rather similar uncertainties in the inclusive analysis. This agreement, as well as the tiny
resummation-scale uncertainties of Mc@Nlo, reflect the unitarity of the parton shower for
inclusive observables. In contrast, in the 1-jet bin Mc@Nlo predictions exhibit a deficit
of about 20% and much larger uncertainties as compared to Nlo. This is due to the fact
that the inclusive matched calculation is only LO accurate in the 1-jet bin.
The inclusive Meps@Nlo cross section is found to be roughly 30 fb larger as com-
pared to the Nlo calculation, which can be interpreted as a result of NLO corrections to
the first emission in the merged sample. In fact, the shift of 30 fb is comparable to the
difference between the Nlo and Mc@Nlo cross sections with ≥1jets, which corresponds
to NLO effects in the 1-jet bin. Finally, variations of the QCD and resummation scales in
Meps@Nlo amount to only 1–3% in both jet bins. As already mentioned, the fact that
fixed-order NLO cross sections feature significantly larger scale variations is related to the
choice of the central scale µ0. This scale plays only a marginal role in Meps@Nlo, since
the pp →4`core process does not depend on the strong coupling, and αsterms resulting
from jet emissions are controlled by the CKKW prescription.
Distributions in the hardest-jet transverse momentum and in the total transverse en-
– 16 –

ergy HT—defined as the scalar sum of the transverse momenta of leptons, missing ET,
and all reconstructed jets—are displayed in Fig. 3. The bands are obtained by adding
QCD- and resummation-scale variations in quadrature. The Mc@Nlo and Meps@Nlo
pT-distributions agree fairly well in the soft region, but Mc@Nlo develops an increasingly
large deficit at higher pT, which reaches 30% in the tail. Similarly as Mc@Nlo, also Nlo
predictions for inclusive four-lepton production are only LO accurate in the first-jet emis-
sion and tend to underestimate the tail. The shapes of the Mc@Nlo and Nlo tails are
however somewhat different. This is due to the fact that, in the MC@NLO method, the
weights of the first shower emission and of its MC-subtraction counterpart differ by an
O(αs)relative factor, which involves the αs(pT)/αs(µR)ratio as well as unresolved NLO
corrections. This difference disappears above the resummation scale, i.e. where the parton
shower stops emitting. This is however not visible in the plot, since due to the dynamical
nature of the resummation-scale choice (3.5), this transition takes place only far above the
scale MW. In the pT→0limit, the Nlo 4`calculation involves an infrared singularity of
the form dσ/dpT∼αsln(pT)/pT, which manifests itself as a linear rise if the distribution
is plotted against ln(pT)as in Fig. 3.a. This feature is qualitatively clearly visible but
quantitatively very mild, and the corresponding enhancement does not exceed 20% down
to pT= 5 GeV. This signifies that the effect of resumming Sudakov logarithms is impor-
tant but not dramatic in the considered pT-range. Higher Sudakov logarithms are partially
included in the Nlo calculation of 4`+ 1jproduction, which remains infrared divergent
at pT→0, but turns out to be in better agreement with Mc@Nlo and Meps@Nlo pre-
dictions for pT>5GeV. The Nlo 4`+ 1jdistribution has a higher tail with respect to
inclusive Nlo and Mc@Nlo predictions, as expected, but for pT&MWit starts to be
above the Meps@Nlo curve as well. This can be explained by the fact that, in contrast to
the Meps@Nlo approach, in fixed-order predictions the scale of αscouplings associated
with jet emission is not adapted to the jet-pT(cf. discussion in Section 2.3).
The total transverse energy, plotted in Fig. 3.b, is dominated by hard multi-jet emis-
sions that cannot be properly described neither by the inclusive Nlo calculation nor by
the Mc@Nlo approach and its parton-shower emissions. This starts to be visible at
HT∼200GeV and the deficit with respect to Meps@Nlo approaches 50% at 1TeV.
Matching and merging effects in presence of a jet veto and jet binning are illustrated
in Fig. 4, where the integrated cross sections in the exclusive 0-jet bin (pT< pmax
T) and
in the inclusive 1-jet bin (pT> pmin
T) are plotted as a function of the corresponding upper
and lower transverse-momentum bounds. In the 0-jet bin, Mc@Nlo and Meps@Nlo pre-
dictions agree well at small jet-veto scales and differ by less than 10% at large pmax
T. The
respective uncertainties are as small as a few percent and nearly independent of pmax
T. For
sufficiently inclusive jet-veto values, the Nlo pp →4`calculation is in excellent agreement
with Mc@Nlo. In the pmax
T→0limit, Nlo predictions develop a double-logarithmic
singularity of the form −αsln2(pmax
T/Q), while Mc@Nlo and Meps@Nlo vetoed cross
sections consistently tend to zero as a result of the exponentiation of Sudakov logarithms.
In this infrared regime, the exponentiation of double logarithms should manifest itself as a
positive correction beyond NLO, while for pmax
T&10 GeV we observe that matched/merged
predictions are still below the Nlo jet-vetoed cross section. This is due to the fact that
– 17 –

Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
MC@NLO 4ℓ
NLO 4ℓ
NLO 4ℓ+1j
10−4
10−3
10−2
Transverse momentum of leading jet
dσ/dpT[pb/GeV]
10 110 2
0.6
0.8
1
1.2
1.4
pT[GeV]
Ratio
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
MC@NLO 4ℓ
NLO 4ℓ
10−8
10−7
10−6
10−5
10−4
10−3
Total transverse energy
dσ/dHT[pb/GeV]
10 210 3
0.6
0.8
1
1.2
1.4
HT[GeV]
Ratio
Figure 3. Leading-jet transverse momentum (left) and total transverse energy (right): Nlo 4`
(green dashed) and Nlo 4`+ 1j(green dotted) results are compared to an inclusive Mc@Nlo 4`
simulation (blue) and to Meps@Nlo 4`+ 0,1jpredictions (red). Uncertainty bands describe com-
bined QCD- and resummation-scale uncertainties (added in quadrature).
Sudakov logarithms are relatively mild in this region (cf. Fig. 3.a), and parton-shower ef-
fects are dominated by subleading logarithms associated with the running of αsin the
αs(pT) ln(pT)/pTterms. Double logarithms become dominant at much smaller transverse
momenta, and we checked that they drive the Nlo cross sections into the negative range
only at pmax
T∼2GeV. For pmax
T'25–30 GeV, which corresponds to the jet-veto values in
the H→WW∗analyses at the LHC, fixed-order and matched/merged results deviate by less
than 5%. This represents the net effect of Sudakov logarithms beyond NLO, and its small-
ness is due to the moderate size of the logarithmic terms but also to cancellations between
leading and subleading logarithms. The uncertainty due to subleading Sudakov logarithms
that are not included in the Mc@Nlo and Meps@Nlo approximations are quantified via
resummation-scale variations, which are reflected in the respective scale-variation bands,
and turn out to be at the percent level.
As shown in Fig. 4.b, in the inclusive 1-jet bin the discrepancies between the various
approximations become more sizable. The inclusive Mc@Nlo simulation underestimates
the 1-jet cross section by 20–30% for 30 GeV < pmin
T<100 GeV. For transverse-momentum
thresholds up to 50 GeV, the fixed-order 4`+ 1jcross section is in quite good agreement
with the Meps@Nlo prediction as expected. However, as already observed in Fig. 3.a,
the Nlo cross section develops a significant excess in the tail. The uncertainties of the
Meps@Nlo and Mc@Nlo cross sections in the 1-jet bin are rather independent of the
pT-threshold and amount to about 5% and 10%, respectively.
4.2 Squared quark-loop contributions
Detailed results for the squared quark-loop cross sections in the inclusive analysis and
requiring one or more jets with pT>30 GeV are presented in Table 3. Fixed-order cal-
– 18 –

Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
MC@NLO 4ℓ
NLO 4ℓ
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Integrated cross section in the exclusive 0-jet bin
σ(pTjet <pmax
T)[pb]
10 20 30 40 50 60 70 80 90 100
0.85
0.9
0.95
1.0
1.05
1.1
1.15
pmax
T[GeV]
Ratio
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
MC@NLO 4ℓ
NLO 4ℓ+1j
0
0.05
0.1
0.15
0.2
0.25
Integrated cross section in the inclusive 1-jet bin
σ(pTjet >pmin
T)[pb]
10 20 30 40 50 60 70 80 90 100
0.7
0.8
0.9
1.0
1.1
1.2
1.3
pmin
T[GeV]
Ratio
Figure 4. Integrated cross sections in the exclusive 0-jet bin (left) and in the inclusive 1-jet bin
(right) as a function of the respective transverse-momentum bounds, pmax
Tand pmin
T.Nlo results
with appropriate jet multiplicity (green) are compared to Mc@Nlo 4`(blue) and Meps@Nlo 4`+
0,1j(red) simulations. Uncertainty bands correspond to QCD-scale variations combined with the
resummation-scale variations in quadrature.
Analysis Loop24`(+1j)Loop2+PS 4`Meps@Loop2
pp →4`+ 0,1j
Meps@Loop2
gg →4`+ 0,1g
≥0jets 8.71(3) +28%
−20% 8.76(3) +28%
−21%
+0.2%
−0.1% 9.24(4) +31%
−20%
+20%
−14% 9.10(3) +28%
−21%
+15%
−12%
≥1jets 3.98(7) +48%
−30% 1.75(1) +32%
−25%
+55%
−51% 2.75(3) +40%
−24%
+5%
−6% 2.01(2) +35%
−25%
+1.4%
−3.2%
Table 3. Squared quark-loop predictions in femtobarns for the µ+νµe−¯νeanalyses requiring ≥0
jets and ≥1jets. Fixed-order results (Loop2) with a number of jets corresponding to the actual
analysis are compared to an inclusive parton-shower simulation (Loop2+PS 4`) and to predictions
from the merged Meps@Loop24`+ 0,1jsimulation with and without the inclusion of quarks in
the initial state. Scale variations and statistical errors are presented as in Table 2.
culations for 4`or 4`+ 1jproduction, depending on the jet bin, are compared to an in-
clusive simulation obtained by showering four-lepton matrix elements (Loop2+PS 4`) and
to merged predictions (Meps@Loop24`+ 0,1j). Additionally, to assess the importance
of quark-induced channels, we show merged squared quark-loop results that involve only
gluon–gluon partonic channels and, for consistency, only g→gg splittings in the parton
shower.
As compared to the Meps@Nlo cross sections in Table 2, squared quark loops repre-
sent a correction of about 3%, both in the inclusive analysis and in the 1-jet bin. In the
inclusive case, fixed-order and shower-improved predictions are in excellent agreement, as
expected from the unitarity of the shower. In contrast, the Loop2+PS simulation—which
corresponds to the approach typically adopted in present experimental studies, where jet
emission is entirely based on the shower approximation—underestimates the squared quark-
– 19 –

loop cross section in the inclusive 1-jet bin by around 50%. Due to their LO α2
sand α3
s
dependence, squared quark-loop corrections feature a QCD-scale dependence of 30–40%.
The resummation-scale uncertainty of the Loop2+PS simulation is close to zero in the
inclusive case (due to unitarity), while in the 1-jet bin it is as large as 50%, due to the fact
that the 1-jet bin is entirely filled by shower emissions.
Comparing Loop2+PS predictions to the merged sample we observe that the matrix-
element description of jet emission significantly increases the cross section, especially in
the 1-jet bin. The QCD-scale uncertainty remains at 30–40% level, but resummation-scale
variations change substantially: the 1-jet bin cross section becomes almost independent of
the resummation scale, since, as a result of merging, 1-jet events are described in terms of
matrix elements, and shower emissions induce only minor bin migrations. In contrast, in
the inclusive analysis the merged simulation features a significantly higher resummation-
scale dependence of approximately 15%, which can be attributed to unitarity violations
induced by the merging procedure: the resummation-scale dependence that arises from the
region below the merging cut, where 0-jet matrix elements are combined with the Sudakov
suppression factor, is not compensated by an opposite dependence from above Qcut, since
the parton shower is superseded by 1-jet matrix elements in that region. We note that this
kind of resummation-scale sensitivity is due to the LO nature of squared quark-loop merging
and is strongly reduced in the case of NLO merging (cf. last column in Table 2). The fact
that the Meps@Loop2cross section in the 1-jet bin is 30% below the fixed-order result can
be attributed to the CKKW scale choice in the merging approach and is consistent with the
size of renormalisation-scale variations. Finally, comparing the last two columns in Table 3,
we observe that quark-induced channels account for roughly 1.5% and 30% of the squared
quark-loop corrections in the 0- and 1-jet bins, respectively. This corresponds to about 0.5
permil and 1 percent of the total cross section in the respective jet bins. We note that the
individual impact of quark channels at matrix-element or parton-shower level is significantly
larger, i.e. a naive merging approach based on pure-gluon matrix elements plus a standard
parton shower would lead to bigger deviations with respect to the Meps@Loop2results in
Table 3.
Squared quark-loop corrections to differential observables are compared to NLO merged
predictions in Fig. 5. As already found in Tables 2and 3, their impact typically amounts to
a few percent. Both for the leading-jet transverse momentum and for the dilepton invariant
mass they feature a rather different kinematic dependence as compared to Meps@Nlo
results. In the considered range their relative importance varies from one to seven percent,
and the maximum lies in the region of small dilepton mass, which corresponds to the signal
region of the H→WW∗analysis.
Merging effects are illustrated in the left plot of Fig. 6, where predictions from the inclu-
sive squared quark-loop gg →4`matrix element supplemented with a regular parton shower
(Loop2+PS) are compared to the merged pp →4`+0,1jsimulation (Meps@Loop2). The
latter is decomposed into contributions from 4`+ 0jand 4`+ 1jmatrix elements. In the
region well below the merging cut, Qcut = 20 GeV, merged predictions are dominated by 0-
jet matrix elements and agree almost perfectly with the Loop2+PS curve. The agreement
remains better than 10% up to pT∼Qcut, where the Meps@Loop2sample is characterised
– 20 –

Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
MEPS@LOOP24ℓ+0, 1j
10−6
10−5
10−4
10−3
10−2
Transverse momentum of leading jet
dσ/dpT[pb/GeV]
10 110 2
0.02
0.04
0.06
0.08
pT[GeV]
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
MEPS@LOOP24ℓ+0, 1j
10−6
10−5
10−4
10−3
10−2
Invariant mass of oppositely charged leptons
dσ/dmℓℓ [pb/GeV]
0 50 100 150 200 250 300
0.02
0.04
0.06
0.08
mℓℓ [GeV]
dσ/dσMEPS@NLO
Figure 5. Comparison of merged squared quark-loop (blue) and NLO (red) predictions for 4`+0,1j
production: transverse momentum of the leading jet (left) and invariant mass of the two charged
leptons (right).
Sherpa+OpenLoops
MEPS@LOOP24ℓ+0, 1j
4ℓ+0j
4ℓ+1j
LOOP2+PS 4ℓ
10−9
10−8
10−7
10−6
10−5
10−4
Transverse momentum of leading jet
dσ/dpT[pb/GeV]
10 110 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
pT[GeV]
Ratio
Sherpa+OpenLoops
MEPS@LOOP2pp →4ℓ+0, 1 j
MEPS@LOOP2gg →4ℓ+0, 1g
10−6
10−5
10−4
10−3
Transverse momentum of leading jet
dσ/dpT[pb/GeV]
10 110 2
0
0.5
1
1.5
2
pT[GeV]
Ratio
Figure 6. Squared quark-loop corrections to the leading-jet pT-distribution: (a) a simulation based
on 4`matrix elements plus parton shower (blue) is compared to complete merged predictions (red
solid). The latter are split into the contributions from 4`+ 0j(red dashed) and 4`+ 1j(red dotted)
matrix elements; (b) full merged predictions (red) are compared to a corresponding simulation
involving only gluon contributions (blue). Uncertainty bands correspond to the combination (in
quadrature) of QCD- and resummation-scale variations.
by the transition from the 0-jet to the 1-jet matrix-element regime. This supports the use of
the 0-jet plus shower approximation up to the merging scale. Starting from pT&40 GeV,
where 1-jet matrix elements dominate and render Meps@Loop2predictions more reliable,
the parton-shower results feature a sizable deficit and are also strongly sensitive to the
resummation scale.
– 21 –

Setting the resummation scale equal to the default scale (3.5), we found that the slight
excess of the parton shower at pT∼Qcut propagates to higher transverse momenta reaching
up to 40% at pT&100 GeV. In order to avoid such an unnatural parton-shower excess at
high pT, and a corresponding excess in the Sudakov suppression at low pT, as anticipated
in Section 4.1 we decided to evaluate squared quark-loop contributions using a smaller
resummation scale, µQ=µ0/2. Of course the small value of µQamplifies the natural
deficit of the shower at large pTand yields a quite small Loop2+PS cross section in the
1-jet bin (cf. Table 3). However this side-effect is compensated by 1-jet matrix elements in
the Meps@Loop2simulation. The bands describe the total scale uncertainty, obtained by
adding QCD- and resummation-scale variations in quadrature. Apart from the suppressed
high-pTtail of the Loop2+PS distribution, we find a rather constant uncertainty of about
30%.
The right plot in Fig. 6illustrates the impact of quark-channel contributions on the
leading-jet pT-distribution. Plotted are full Meps@Loop2results and corresponding pre-
dictions involving only gg-induced matrix elements and g→gg shower splittings. As is
clearly visible from the ratio plot, the quark channels enhance hard-jet emissions and induce
a related Sudakov suppression at low pT. The resulting distortion in the jet-pTdistribution
amounts to ±50%. When looking at Table 3, such opposite behaviour in the hard and soft
regions explains why the quark-channel contribution reaches 30% in the 1-jet bin but goes
down to 1.5% in the inclusive case.
Jet-veto and jet-binning effects on squared quark-loop contributions are shown in Fig. 7,
where the integrated cross sections in the exclusive 0-jet bin (pT< pmax
T) and in the in-
clusive 1-jet bin (pT> pmin
T) are plotted as a function of pmax
Tand pmin
T. In the 0-jet bin,
apart from the minor excess around 30 GeV, Loop2+PS predictions agree quite well with
Meps@Loop2ones for any jet-veto scale up to 100 GeV. The corresponding scale uncer-
tainties are in the 20–40% range. As in Table 3,Meps@Loop2uncertainties tend to be
larger in the inclusive limit. Fixed-order gg →4`contributions are inherently inclusive and
independent of pmax
T. Comparing them to the Meps@Loop2and Loop2+PS curves we
observe that jet-veto scales of 25–30 GeV, as those used in the experimental H→WW∗
analyses, correspond to a moderate cross-section suppression of approximately 30%. In this
regime the parton shower should provide a sufficiently reliable resummation of Sudakov
logarithms.
The right plot of Fig. 7compares fixed-order, shower-improved and merged predictions
in the inclusive 1-jet bin. For a jet threshold of 30 GeV, the various approximations agree
only marginally within the respective errors, while higher and smaller values of pmin
Tlead to
very large discrepancies. As compared to Meps@Loop2predictions, at large pTwe observe
a dramatic deficit of the shower approximation, while the fixed-order squared quark-loop
calculation yields a rather constant 40% excess as in Table 3. The resummation of Sudakov
logarithms becomes relevant only for transverse-momentum thresholds below 30 GeV, where
the excess of the fixed-order prediction grows up to 150% at 10 GeV.
– 22 –

Sherpa+OpenLoops
MEPS@LOOP24ℓ+0, 1j
LOOP2+PS 4ℓ
LOOP24ℓ+0j
0
0.002
0.004
0.006
0.008
0.01
0.012
Integrated cross section in the exclusive 0-jet bin
σ(pTjet <pmax
T)[pb]
10 20 30 40 50 60 70 80 90 100
0.6
0.8
1
1.2
1.4
pmax
T[GeV]
Ratio
Sherpa+OpenLoops
MEPS@LOOP24ℓ+0, 1j
LOOP2+PS 4ℓ
LOOP24ℓ+1j
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
Integrated cross section in the inclusive 1-jet bin
σ(pTjet >pmin
T)[pb]
10 20 30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
pmin
T[GeV]
Ratio
Figure 7. Integrated squared quark-loop cross sections in the exclusive 0-jet bin (left) and in
the inclusive 1-jet bin (right) as a function of the respective transverse-momentum bounds, pmax
T
and pmin
T. Fixed-order Loop24`(+1j)results (green) are compared to Loop2+PS 4`(blue) and
Meps@Loop24`+ 0,1j(red) simulations. Uncertainty bands correspond to QCD-scale variations
combined with resummation-scale variations in quadrature.
5Atlas and Cms H→WW∗analyses in the 0- and 1-jet bins
In this section we study the irreducible four-lepton background to the Atlas [3] and
Cms [4]H→WW∗→µ+νµe−¯νeanalyses at 8 TeV. We restrict ourselves to the ex-
clusive 0- and 1-jet bins, which contain the bulk of the four-lepton background associated
with diboson production, and focus on opposite-flavour µ+νµe−¯νe+jets final states, which
provide the highest sensitivity to the Higgs-boson signal. Technically, within the automated
Sherpa+OpenLoops framework, the simulation of `ν`ν+jets production with same lep-
ton flavour is almost equivalent to the opposite-flavour case. Also for what concerns QCD
corrections and uncertainties we do not expect any important difference between opposite-
and same-flavour channels.
In the following we apply the cuts listed in Appendix B, which correspond to the
Atlas [3] and Cms [4] analyses at 8 TeV. Let us remind that the two experiments employ
different definitions of the WW transverse mass, reported in eq. (B.1), and different anti-
kTjet radii. Note also that Atlas employs a lower transverse-momentum threshold for
central jets. After a pre-selection, which basically requires two hard leptons and large
missing energy, two complementary selections based on pT,``0,∆φ``0,m``0and mT, are used
to define a signal and a control region. The latter is exploited to normalise WW-background
simulations to data. Separate analyses are performed in the 0-, 1-, and 2-jet bins in order
to improve the sensitivity to the Higgs-boson signal and the data-driven normalisation of
the various background components.
In Section 5.1 we investigate kinematic distributions that are relevant for the experi-
mental selection after pre-selection cuts. In Section 5.2 we consider the control and signal
regions and discuss the observables that are exploited in the final stage of the Higgs analyses,
– 23 –

namely the WW transverse mass and the dilepton invariant mass. Finally, in Section 5.3
we present predictions for the 0- and 1-jet bin cross sections in the signal and control re-
gions, as well as uncertainties associated with variations of renormalisation, factorisation,
resummation, and merging scales.
For each observable we present results for the Atlas and Cms analyses in the exclusive
0- and 1-jet bins and, to provide insights into the convergence of the perturbative expansion
and the size of Sudakov logarithms in jet bins, we compare Nlo,Mc@Nlo,Meps@Nlo
and squared quark-loop predictions. As discussed in Section 3, in Nlo predictions for the 0-
and 1-jet bins we always include the corresponding number of jets at matrix-element level.
In contrast, Mc@Nlo results refer as usual to a single simulation of inclusive µ+νµe−¯νe
production, which is NLO accurate in the 0-jet bin and only LO accurate in the 1-jet bin.
Only Meps@Nlo predictions are consistently matched to the parton shower and NLO
accurate in both jet bins.
5.1 Kinematic distributions after pre-selection cuts
In Figures 8–10 we present jet and lepton observables after pre-selection cuts. The curves for
Meps@Nlo,Mc@Nlo,Nlo, and Meps@Loop2correspond to the central scale choice
(3.5). The middle and lower panels show relative Mc@Nlo and Nlo deviations from
Meps@Nlo, and squared quark-loop contributions normalised to the central Meps@Nlo
result. Scale-variation bands are shown only for Meps@Loop2and Meps@Nlo. In the lat-
ter case, renormalisation- and factorisation-scale variations ∆QCD (red band), resummation-
scale variations ∆res (blue band), and their combination in quadrature ∆tot = (∆2
QCD +
∆2
res)1/2(yellow band), are displayed as colour-additive regions. The various band regions
assume different colours corresponding to the various possible overlaps. The band bound-
ary, corresponding to variations δin the range ∆QCD,∆res < δ < ∆tot, is yellow. Orange
areas appear in kinematic regions dominated by QCD-scale variations (∆res < δ < ∆QCD),
while green areas reflect dominant resummation-scale variations (∆QCD < δ < ∆res), and
the central band area (δ < ∆res,∆QCD ), where all three colours overlap, is brown. Note
that scale-variation bands are somewhat distorted by statistical fluctuations, which tend to
increase in the tails of some distributions.
Before splitting the event sample into exclusive jet bins, in Fig. 8we show the transverse
momenta of the hardest (upper plots) and second-hardest (lower plots) jet. Here all Nlo
curves correspond to 4`+1 jet production. In the case of the first jet, Mc@Nlo predictions
are only LO accurate and significantly underestimate the tail of the pTdistribution. On
the other hand, Nlo predictions feature a 20% excess at high pT. As already observed
in Fig. 3.a, this behaviour can be explained by the fact that the scale (3.5) used in the
fixed-order calculation does not adapt to the transverse momentum of the jet.
In the case of the second-jet pT,Nlo and Meps@Nlo results are both only LO accu-
rate, and the shape differences at large pTare more pronounced but qualitatively similar as
for the first jet. The excess of the Nlo distribution below 10 GeV reveals the presence of
the infrared singularity at pT→0. The Mc@Nlo prediction for the second jet is entirely
based on the shower approximation. It remains low over the entire spectrum, and above
30 GeV the deficit starts to be considerable.
– 24 –

The increase of Meps@Nlo scale variations from a few percent for the first jet to 10%
for the second one, is due to the transition from NLO to LO accuracy. The abundance
of orange and brown areas in the Meps@Nlo bands indicates that the uncertainty tends
to be dominated by QCD-scale variations. Green band areas, which correspond to larger
resummation-scale uncertainties, show up less frequently and only in the leading-jet pT
distribution. Even in the small-pTregion, where Sudakov logarithms have the highest
possible impact, QCD- and resummation-scale variations do not exceed 10%. This suggests
that subleading-logarithmic corrections beyond the Meps@Nlo accuracy should be rather
modest.
Squared quark-loop corrections range from 1 to 6 percent and feature a more pro-
nounced dependence on the jet pTas compared to the inclusive analysis (cf. Fig. 5).
The largest effects arise around pT'20 GeV, which corresponds to the 0-jet bin of the
H→WW∗analysis.
Let us now switch to leptonic observables in the exclusive 0- and 1-jet bins of the
H→WW∗analyses. Distributions in the azimuthal dilepton separation ∆φ``0and in
the dilepton invariant mass m``0are displayed in Figures 9and 10. These observables
play an important role for the description of the background acceptance and for the opti-
misation of the Higgs-boson sensitivity in the experimental analyses. The corresponding
Meps@Nlo distributions are NLO accurate in both jet bins. This is very well reflected by
the Meps@Nlo uncertainty bands, which do not exceed the few-percent level. Also here,
resummation-scale variations tend to be slightly subdominant with respect to QCD-scale
variations. Comparing Nlo,Mc@Nlo and Meps@Nlo distributions in the 0-jet bin,
where none of these approximations loses NLO accuracy, we find overall agreement at the
few-percent level. In the 1-jet bin, the agreement between Nlo and Meps@Nlo remains,
as expected, quite good. Due to the lack of NLO accuracy, inclusive Mc@Nlo predictions
feature the characteristic 10–15% deficit in the 1-jet bin, which is accompanied by minor
shape distortions. Given the good agreement with Nlo within the small uncertainty band,
the shape of Meps@Nlo distributions seems to be very well under control.
In the 0-jet bin, Meps@Loop2corrections are very sensitive both to the azimuthal
separation and to the invariant mass of the dilepton system. At small ∆φ``0and m``0,
which corresponds to the Higgs-signal region, they reach up to 8% and 6%, respectively. A
similar but weaker sensitivity is visible also in the 1-jet bin.
Inspecting the transverse-momentum distributions of the harder and softer charged
lepton (not shown here) we found that the various NLO corrections behave very similarly
as for ∆φ``0and m``0, while squared quark-loop corrections are less sensitive to the lepton-pT
and vary between 2% and 4% only.
5.2 Kinematic distributions in control and signal regions
We now turn to the control (C) and signal (S) regions of the experimental analyses (see
Table 7) and discuss the distributions in the WW transverse mass, mT, and in the dilepton
invariant mass, m``0. These observables are sensitive to the Higgs-boson signal, and their
shape permits to increase the signal-to-background discrimination in the final fit. Separate
– 25 –

Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
5
10
15
20
Leading jet pT(ATLAS)
dσ/dpT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
2
4
6
8
10
12
14
16
Leading jet pT(CMS)
dσ/dpT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
10 110 2
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
pT[GeV]
dσ/dσMEPS@NLO
10 110 2
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
pT[GeV]
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
5
10
15
20
25
30
35
40
45
Subleading jet pT(ATLAS)
dσ/dpT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
5
10
15
20
25
30
35
Subleading jet pT(CMS)
dσ/dpT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
10 110 2
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
pT[GeV]
dσ/dσMEPS@NLO
10 110 2
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
pT[GeV]
dσ/dσMEPS@NLO
Figure 8.Atlas (left) and Cms (right) analysis at 8TeV after pre-selection cuts: transverse-
momentum distributions of the first (top) and second (bottom) jet. Meps@Nlo (black solid),
inclusive Mc@Nlo (red dashed), and Nlo (blue dashed) predictions at the central scale. The ratio
plots in the middle panels show relative uncertainties as well as Mc@Nlo and Nlo deviations
with respect to Meps@Nlo. The lower panels display relative Meps@Loop2corrections and
uncertainties normalised to Meps@Nlo at the central scale. The factor-two variations of µRand
µF(red band), and factor-√2variations of µQ(blue band), are combined in quadrature (yellow
band). Scale-variation bands are colour additive, i.e. yellow+blue=green, yellow+red=orange, and
yellow+red+blue=brown.
– 26 –

Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ
0
10
20
30
40
50
60
70
80
90
Azimuthal lepton distance (ATLAS, Njet =0)
dσ/d∆φℓℓ [fb]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ
0
10
20
30
40
50
60
70
80
90
Azimuthal lepton distance (CMS, Njet =0)
dσ/d∆φℓℓ [fb]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
0 0.5 1 1.5 2 2.5 3
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
∆φℓℓ
dσ/dσMEPS@NLO
0 0.5 1 1.5 2 2.5 3
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
∆φℓℓ
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
5
10
15
20
25
Azimuthal lepton distance (ATLAS, Njet =1)
dσ/d∆φℓℓ [fb]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
5
10
15
20
25
Azimuthal lepton distance (CMS, Njet =1)
dσ/d∆φℓℓ [fb]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
0 0.5 1 1.5 2 2.5 3
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
∆φℓℓ
dσ/dσMEPS@NLO
0 0.5 1 1.5 2 2.5 3
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
∆φℓℓ
dσ/dσMEPS@NLO
Figure 9.Atlas (left) and Cms (right) analysis at 8TeV after pre-selection cuts: azimuthal
separation of the charged leptons in the 0-jet (top) and 1-jet (bottom) bins. Similar predictions
and uncertainty bands as in Fig. 8.
distributions for the exclusive 0- and 1-jet bins and for the two experiments are shown in
Figures 11–13.
In the signal and control regions, as well as in both jet bins, the size of the vari-
ous corrections and the Meps@Nlo uncertainties behave fairly similar to what observed
at pre-selection level. The Nlo,Mc@Nlo and Meps@Nlo distributions agree at few-
percent level in the 0-jet bin, while in the 1-jet bin discrepancies between Mc@Nlo and
– 27 –

Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Lepton pair mass (ATLAS, Njet =0)
dσ/dmℓℓ [fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Lepton pair mass (CMS, Njet =0)
dσ/dmℓℓ [fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
50 100 150 200 250 300
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
mℓℓ [GeV]
dσ/dσMEPS@NLO
50 100 150 200 250 300
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
mℓℓ [GeV]
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
0.1
0.2
0.3
0.4
0.5
Lepton pair mass (ATLAS, Njet =1)
dσ/dmℓℓ [fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
0.1
0.2
0.3
0.4
0.5
Lepton pair mass (CMS, Njet =1)
dσ/dmℓℓ [fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
50 100 150 200 250 300
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
mℓℓ [GeV]
dσ/dσMEPS@NLO
50 100 150 200 250 300
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
mℓℓ [GeV]
dσ/dσMEPS@NLO
Figure 10.Atlas (left) and Cms (right) analysis at 8TeV after pre-selection cuts: dilepton
invariant mass distribution in the 0-jet (top) and 1-jet (bottom) bins. Similar predictions and
uncertainty bands as in Fig. 8.
Meps@Nlo on the 10–15% level and little Mc@Nlo shape distortions appear. The size
of the corrections and the scale uncertainties for the two experimental analyses are qualita-
tively and quantitatively similar. Obviously, due to the different cuts, absolute background
predictions for Atlas and Cms behave differently. The shapes of Meps@Nlo distribu-
tions are again in excellent agreement with Nlo, suggesting moderate Sudakov logarithms
beyond NLO. This is consistent with the small scale uncertainty of the merged simulation.
– 28 –

0-jet bin Nlo 4`(+1j)Mc@Nlo 4`Meps@Nlo 4`+ 0,1jMeps@Loop24`+ 0,1j
σS[fb] 34.28(9) +2.1%
−1.6% 32.52(8) +2.1%
−0.8%
+1.2%
−0.7% 33.81(12) +1.4%
−2.2%
+2.0%
−0.4%
+1.6%
−1.7% 1.98(2) +23%
−16.5%
+27%
−20%
σC[fb] 55.76(9) +2.0%
−1.7% 52.28(9) +1.4%
−0.7%
+1.4%
−1.1% 54.18(15) +1.4%
−1.9%
+2.5%
−0.4%
+1.7%
−2.0% 2.41(2) +22%
−17%
+27%
−18%
1-jet bin Nlo 4`(+1j)Mc@Nlo 4`Meps@Nlo 4`+ 0,1jMeps@Loop24`+ 0,1j
σS[fb] 8.99(4) +4.9%
−9.5% 8.02(4) +8.5%
−6.4%
+0%
−3.1% 9.37(9) +2.6%
−2.7%
+2.5%
−0.0%
−0.1%
−4.1% 0.46(1) +40%
−18%
+2.2%
−6.3%
σC[fb] 26.50(8) +6.4%
−12.5% 24.58(8) +6.1%
−6.5%
+1.2%
−3.0% 28.32(13) +3.1%
−4.7%
+4.1%
−0.0%
+0.6%
−2.7% 0.79(1) +33%
−20%
+15%
−7%
Table 4. Exclusive 0- and 1-jet bin µ+νµe−¯νe+jets cross sections in the signal (S) and control
(C) regions of the Atlas analysis at 8TeV. Fixed-order Nlo results (with appropriate jet multi-
plicity) are compared to Mc@Nlo and Meps@Nlo predictions. Squared quark-loop contributions
(Meps@Loop2) are presented separately. Scale uncertainties are shown as σ±δQCD ±δres ±δQcut,
where δQCD,δres and δQcut correspond respectively to variations of the QCD (µR, µF), resummation
(µQ) and merging (Qcut) scales. Statistical errors are given in parenthesis.
0-jet bin Nlo 4`(+1j)Mc@Nlo 4`Meps@Nlo 4`+ 0,1jMeps@Loop24`+ 0,1j
σS[fb] 156.65(18) +1.7%
−1.6% 147.8(2) +1.3%
−0.6%
+1.2%
−1.0% 153.6(3) +2.1%
−1.9%
+2.8%
−0.0%
+1.6%
−2.2% 6.65(4) +22%
−17%
+26%
−18%
σC[fb] 59.26(15) +1.3%
−1.3% 55.92(11) +0.8%
−0.2%
+0.5%
−0.9% 58.06(21) +2.1%
−2.0%
+2.2%
−0.2%
+1.5%
−2.1% 1.47(2) +26%
−17%
+28%
−16%
1-jet bin Nlo 4`(+1j)Mc@Nlo 4`Meps@Nlo 4`+ 0,1jMeps@Loop24`+ 0,1j
σS[fb] 43.01(9) +3.3%
−7.4% 37.87(9) +7.6%
−6.8%
+0.9%
−3.6% 44.99(18) +2.5%
−4.2%
+2.9%
−0.0%
+0.5%
−2.5% 1.83(2) +34%
−20%
+6%
−7%
σC[fb] 20.48(6) +4.8%
−10.3% 18.90(7) +7.4%
−7.3%
+1.8%
−3.3% 21.70(11) +3.2%
−4.1%
+3.4%
−0.0%
+0.5%
−1.6% 0.62(1) +39%
−16%
+16%
−6%
Table 5. Exclusive 0- and 1-jet bin µ+νµe−¯νe+jets cross sections in the signal (S) and control (C)
regions of the Cms analysis at 8TeV. Similar predictions and conventions as in Table 4.
Squared quark-loop corrections feature a nontrivial sensitivity to mTand m``0, which
varies depending on the experimental analysis, the selection region, and the jet bin. The
largest squared quark-loop corrections arise in the 0-jet bin, at small m``0and at large mT.
The corrections to the transverse-mass distribution start growing at mT= 100–150 GeV
and for the Atlas (Cms) analysis they reach 10-20%(5-10%) in the tail. The largest effects
arise in the signal region and in the Atlas analysis, which implements tighter m``0and
∆φ``0cuts. For what concerns the m``0distribution, Fig. 13 shows that in the 0-jet bin of
the Cms signal region squared quark-loop corrections behave similarly as in the inclusive
case (cf. Fig. 5). The fact that the characteristic enhancement at small m``0is not visible
in the Atlas signal region, is simply due to the cut on m``0at 50 GeV. For what concerns
the 1-jet bin, Meps@Loop2corrections are generally slightly smaller and less dependent
on mTand m``0.
5.3 Exclusive 0- and 1-jet bin cross sections in control and signal regions
A precise quantitative assessment of the various correction effects and residual uncertainties
is provided in Tables 4and 5, where we present exclusive 0- and 1-jet bin cross sections in
the signal and control regions of the two experimental analyses. The Nlo and Meps@Nlo
– 29 –

Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
mTin ATLAS control region (Njet =0)
dσ/dmT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
mTin CMS control region (Njet =0)
dσ/dmT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
100 150 200 250 300
0.05
0.1
0.15
MEPS@LOOP24ℓ+0, 1j
mT[GeV]
dσ/dσMEPS@NLO
50 100 150 200 250 300
0.05
0.1
0.15 MEPS@LOOP24ℓ+0, 1j
mT[GeV]
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
0.05
0.1
0.15
0.2
mTin ATLAS control region (Njet =1)
dσ/dmT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
0.05
0.1
0.15
0.2
mTin CMS control region (Njet =1)
dσ/dmT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
100 150 200 250 300
0.05
0.1
0.15 MEPS@LOOP24ℓ+0, 1j
mT[GeV]
dσ/dσMEPS@NLO
50 100 150 200 250 300
0.05
0.1
0.15 MEPS@LOOP24ℓ+0, 1j
mT[GeV]
dσ/dσMEPS@NLO
Figure 11. Control region of the Atlas (left) and Cms (right) analysis at 8TeV: transverse-mass
distribution in the 0-jet (top) and 1-jet (bottom) bins. Similar predictions and uncertainty bands
as in Fig. 8.
predictions at the central scale differ by only 1.5–3% and 4–6% in the 0-jet and 1-jet bins,
respectively. This confirms that the discrepancy of order 5% observed in the inclusive 0-jet
bin (cf. Table 2) is due the NLO corrections to the first jet emission in Meps@Nlo. The
differences between Mc@Nlo and Meps@Nlo in the exclusive 0- and 1-jet bins reach 2–4%
and 13–16%, respectively, and the discrepancy in the 1-jet bin is consistent with the deficit
of Mc@Nlo observed in differential distributions. Deviations between the Nlo,Mc@Nlo
– 30 –

Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ
0
0.1
0.2
0.3
0.4
0.5
mTin ATLAS signal region (Njet =0)
dσ/dmT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ
0
0.5
1
1.5
2
mTin CMS signal region (Njet =0)
dσ/dmT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
60 80 100 120 140 160 180 2 00 220 240
0.05
0.1
0.15
0.2
0.25
MEPS@LOOP24ℓ+0, 1j
mT[GeV]
dσ/dσMEPS@NLO
100 150 200 250
0.05
0.1
0.15
0.2
0.25 MEPS@LOOP24ℓ+0, 1j
mT[GeV]
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
0.02
0.04
0.06
0.08
0.1
0.12
mTin ATLAS signal region (Njet =1)
dσ/dmT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
0.1
0.2
0.3
0.4
0.5
mTin CMS signal region (Njet =1)
dσ/dmT[fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
60 80 100 120 140 160 180 2 00 220 240
0.05
0.1
0.15
0.2
0.25 MEPS@LOOP24ℓ+0, 1j
mT[GeV]
dσ/dσMEPS@NLO
100 150 200 250
0.05
0.1
0.15
0.2
0.25 MEPS@LOOP24ℓ+0, 1j
mT[GeV]
dσ/dσMEPS@NLO
Figure 12. Signal region of the Atlas (left) and Cms (right) analysis at 8TeV: transverse-mass
distribution in the 0-jet (top) and 1-jet (bottom) bins. Similar predictions and uncertainty bands
as in Fig. 8.
and Meps@Nlo approximations are fairly similar in the various analyses and kinematic
regions. As compared to corresponding results in Ref. [31], the various cross sections in
Tables 4and 5differ by 1-5% and 1-10% in the 0- and 1-jet bins, respectively. These
shifts are consistent with scale-variation uncertainties and can be attributed, as observed
in Section 4.1, to the new scale choice (3.5) used in the present study.
Adding (µR, µF),µQand Qcut variations in quadrature, the combined scale uncer-
– 31 –

Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ
0
0.2
0.4
0.6
0.8
1
1.2
mℓℓ in ATLAS signal region (Njet =0)
dσ/dmℓℓ [fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
mℓℓ in CMS signal region (Njet =0)
dσ/dmℓℓ [fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
10 15 20 25 30 35 40 45 50
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
mℓℓ [GeV]
dσ/dσMEPS@NLO
20 40 60 80 100 120 140 160 180 200
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
mℓℓ [GeV]
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
mℓℓ in ATLAS signal region (Njet =1)
dσ/dmℓℓ [fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
Sherpa+OpenLoops
MEPS@NLO 4ℓ+0, 1j
µF,R/2 ···2µF,R
µQ/√2···√2µQ
Unc. quad. sum
MC@NLO 4ℓ
NLO 4ℓ+1j
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
mℓℓ in CMS signal region (Njet =1)
dσ/dmℓℓ [fb/GeV]
0.8
0.9
1.0
1.1
1.2
dσ/dσMEPS@NLO
10 15 20 25 30 35 40 45 50
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
mℓℓ [GeV]
dσ/dσMEPS@NLO
20 40 60 80 100 120 140 160 180 200
0.02
0.04
0.06
0.08 MEPS@LOOP24ℓ+0, 1j
mℓℓ [GeV]
dσ/dσMEPS@NLO
Figure 13. Signal region of the Atlas (left) and Cms (right) analysis at 8TeV: dilepton invariant-
mass distribution in the 0-jet (top) and 1-jet (bottom) bins. Similar predictions and uncertainty
bands as in Fig. 8.
tainties of Meps@Nlo cross-section predictions do not exceed 4(6)% in the 0(1)-jet bin.
Renormalisation-, factorisation-, resummation- and merging-scale variations yield compara-
ble contributions to the total scale uncertainty. In the 1-jet bin, Meps@Nlo results feature
smaller QCD-scale variations as compared to the Nlo calculation. This can be attributed
to the variation of extra αsterms originating from the shower and to the CKKW scale
choice in Meps@Nlo.
– 32 –

Atlas Nlo 4`(+1j)Mc@Nlo 4`Meps@Nlo 4`+ 0,1jMeps@Nlo+Loop2δS/C
σS/σC0-jet 0.615 −0.1%
−0.1% 0.622 −0.7%
+0.1%
+0.2%
−0.4% 0.624 +0%
−0.3%
+0.5%
−0%
+0.1%
−0.3% 0.632 −0.3%
+0.5%
+0.2%
+0.3% 1.3%
σS/σC1-jet 0.339 +1.4%
−3.4% 0.326 −2.3%
−0.1%
+1.2%
+0.1% 0.331 +0.5%
−2.1%
+1.5%
−0%
+0.7%
+1.4% 0.338 −0.4%
−1.8%
+1.8%
+0.1% 2.1%
Cms Nlo 4`(+1j)Mc@Nlo 4`Meps@Nlo 4`+ 0,1jMeps@Nlo+Loop2δS/C
σS/σC0-jet 2.64 −0.4%
+0.3% 2.64 −0.5%
+0.4%
−0.7%
+0.1% 2.65 +0%
−0.1%
−0.6%
−0.2%
−0.1%
+0.1% 2.69 −0.2%
+0.2%
−0.9%
+0.2% 1.5%
σS/σC1-jet 2.10 +1.4%
−3.2% 2.00 −0.2%
−0.5%
+0.9%
+0.3% 2.07 +0.7%
+0.1%
+0.5%
−0%
+0%
+0.9% 2.10 +0.4%
+0.4%
+0.7%
+0.1% 1.4%
Table 6. Ratios of signal- to control-region cross sections in the 0- and 1-jet bins of the two
experimental analyses. Fixed-order Nlo results (with appropriate jet multiplicity) are compared to
Mc@Nlo and Meps@Nlo predictions. The combination of Nlo and squared quark-loop merged
results, denoted as Meps@Nlo+Loop2, represents the best prediction. Upper and lower variations
are obtained from corresponding QCD-, resummation- and merging-scale uncertainties in Tables 4
and 5assuming correlated σSand σCvariations. The last column shows the relative difference
between Meps@Nlo and full Meps@Nlo+Loop2predictions, which corresponds to the shift
induced by squared quark-loop corrections.
Comparing Nlo and Mc@Nlo cross sections in the 0-jet bin we observe a rather
constant difference of about 5% that can be interpreted as the contribution from resummed
Sudakov logarithms beyond NLO. On the one hand, this indicates that matching to the
parton shower is essential in order to reach few-percent precision. On the other hand, the
rather mild impact of Sudakov resummation suggests that subleading Sudakov logarithms
beyond the shower approximation should not have a large impact on the H→WW∗
analysis. This is confirmed by the fact that resummation-scale variations of Mc@Nlo and
Meps@Nlo cross sections do not exceed 2-3% in the various jet bins.
The relative impact of squared quark-loop corrections as compared to merged Nlo
predictions varies between 2.5 and 6 percent, depending on the experiment, the kinematic
selection region, and the jet bin. In both experiments and jet bins, squared quark-loop
effects increase when moving from control to signal regions. In the case of Cms they grow
from 2-3.5% to 4%, while in the Atlas analysis, due to the tighter ∆φ``0and m``0cuts,
the effects are more pronounced and increase from 3-4.5% to 5-6%. Squared quark-loop
uncertainties amount to 30–40%, similarly as for the inclusive analysis of Section 4.
Detailed results for the ratios of signal- to control-region cross sections, σS/σC, are
presented in Table 6. These ratios and the related uncertainties play an important role for
the extrapolation from control to signal regions in data-driven WW-background determi-
nations. In addition to Nlo,Mc@Nlo and Meps@Nlo ratios, we also present results
obtained from the combination of Nlo and squared quark-loop merging. These latter are
denoted as Meps@Nlo+Loop2and represent our best predictions. Upper and lower vari-
ations are obtained from corresponding QCD-, resummation- and merging-scale variations
in Tables 4and 5. More precisely, the ratios are evaluated at different scales,
R(ξR, ξF, ξQ, Qcut) = σS(ξRµR, ξFµF, ξQµQ, Qcut)
σC(ξRµR, ξFµF, ξQµQ, Qcut),(5.1)
applying correlated variations in signal and control regions. As shown in Table 6, due to
– 33 –

almost complete cancellations between σSand σCvariations this naive approach results
in typical σS/σCshifts at the sub-percent level, which cannot be regarded as realistic
estimates of uncertainties due to unknown higher-order corrections. On the other hand,
applying uncorrelated scale variations to σSand σCwould tend to overestimate σS/σC
uncertainties. This becomes clear if one considers the ideal limit of identical signal and
control regions, where σS/σC= 1 and the uncertainty must vanish. The reason why scale
variations are not adequate to quantify theory uncertainties associated to the extrapolation
between different kinematic regions, is that they tend to shift the normalisation of scattering
amplitudes without altering their kinematic dependence. In this respect, squared quark-
loop corrections provide much more useful insights into kinematic effects associated to
higher-order corrections. As shown in the last column of Table 6, their impact on the
σS/σCratios amounts to δS/C'1.5%, which largely exceeds the typical scale variations
of Meps@Nlo and Meps@Nlo+Loop2predictions. This is due to the fact that squared
quark-loop effects induce genuine NNLO kinematic distortions. Moreover, squared quark
loops constitute only a subset of the full NNLO corrections, and their impact on σS/σCcan
be assumed to be quantitatively similar to the still unknown NNLO contributions. With
other words, the δS/Cshifts in Table 6can be considered as a realistic estimate of the
Meps@Nlo+Loop2uncertainty of the σS/σCratios.
6 Conclusions
In this publication we have presented the first results for the simulation of hadronic four-
lepton plus jets production using the novel Meps@Nlo multi-jet merging technology at
NLO, and including also NNLO contributions from squared quark loops. This was also the
first phenomenological application of the fully automated approach provided by the combi-
nation of the Sherpa Monte Carlo with the OpenLoops generator of one-loop amplitudes.
The OpenLoops algorithm is based on a new numerical approach for the recursive con-
struction of cut-opened loop diagrams, which allows for a very fast evaluation of NLO
matrix elements within the Standard Model. For the calculation of tensor integrals it relies
on the Collier library, which implements the numerically stable reduction algorithms by
Denner–Dittmaier.
Four-lepton plus jets final states are of large topical interest due to their implications
on ongoing Higgs-boson studies, and in this paper we discussed detailed predictions for the
Atlas and Cms H→WW∗analyses at 8TeV in the 0- and 1-jet bins. For a thorough
description of four-lepton production—including off-shell vector-boson effects, non-resonant
topologies, and related interferences—the complex-mass scheme was applied. The use of
exclusive jet bins, which is mandatory in order to suppress the background provided by
top-quark production and decay, introduces potentially large theory uncertainties and ul-
timately requires a very robust modelling of jet-production properties and related errors.
This requires an NLO accurate description of jet radiation, with a careful assessment of the
uncertainties stemming from the usual perturbative scale variations, but also a resummation
of Sudakov logarithms arising from jet vetoes, and an analysis of the related uncertainties.
The Meps@Nlo approach as implemented in Sherpa allows to carry out this program in
– 34 –

a fully automated way. In particular, the resummation of Sudakov logarithms is effectively
implemented by matching NLO matrix elements to the Sherpa parton shower, and uncer-
tainties related to subleading Sudakov logarithms beyond the shower approximation can be
assessed through resummation-scale variations.
In order to allow precise statements on the impact of jet vetoes and jet binning on
the H→WW∗analyses, we merged matrix elements for four leptons plus up to one jet at
NLO accuracy, thus arriving at a simulation of the WW background with unprecedented
accuracy. As a result of this calculation the residual scale uncertainty is reduced to about 5%
on observables related to the hardest jet up to transverse momenta of the order of 200 GeV.
We note large differences of up to 40% with respect to NLO or Mc@Nlo simulations of
the pp →4`process. These differences typically manifest themselves in regions of large
jet momentum, where inclusive NLO or Mc@Nlo predictions are bound to undershoot
the QCD activity. This of course is even more pronounced for observables related to the
subleading jet. As compared to NLO predictions for pp →4`+ 1j, apart from a generally
good agreement, multi-jet merging yields quite significant corrections in the tail of the
first-jet pTdistribution. This effect can be attributed to the fact that the CKKW-merging
approach implemented in Meps@Nlo consistently adapts the renormalisation scale to the
transverse momenta of the emitted jets.
The multi-jet merging thus improves the quality and stability of the perturbative series,
especially for jet observables. This holds for hard phase-space regions as well as for low
jet momentum, where fixed-order calculations start to suffer from the missing resummation
of potentially large logarithms. Studying the case of a jet veto, we found that for veto
scales around 30(10) GeV resummation effects beyond NLO amount to about 5(20)% of
the vetoed four-lepton cross section. Their relatively small magnitude can be attributed
to the limited size of Sudakov logarithms but also to cancellations between leading- and
subleading-logarithmic contributions.
In the case of the inclusive four-lepton cross section, as a result of NLO corrections to the
first QCD emission, Meps@Nlo results turn out to be 9% higher as compared to inclusive
NLO and Mc@Nlo calculations. Moreover, the CKKW scale choice in Meps@Nlo leads
to a milder renormalisation-scale dependence as compared to fixed-order and Mc@Nlo
predictions evaluated at a scale of the order of the W-boson transverse mass. For lep-
tonic observables in the exclusive jet bins of the H→WW∗analyses, typically NLO and
Mc@Nlo provide a good description in the 0-jet bin, but Mc@Nlo exhibits a deficit of
about 10–15% in the 1-jet bin. It is notable that, for these observables, we find scale uncer-
tainties of only a few percent in our best NLO prediction, i.e. Meps@Nlo. Our analysis
indicates that also the uncertainties related to the choice of resummation scale, and thus
due to the parton shower and its resummation properties, are at the percent level. This is
consistent with the observation that Sudakov logarithms beyond NLO have a rather mod-
erate impact on the jet bins of the H→WW∗analysis, and it suggests that subleading
logarithmic corrections beyond the Meps@Nlo accuracy should not be important.
In addition to matched and merged NLO simulations, we also studied NNLO contribu-
tions to four-lepton plus jets production that emerge through squared one-loop amplitudes
involving closed quark loops. These contributions are dominated by the gluon–gluon chan-
– 35 –

nel, which is enhanced by the high partonic flux. Moreover, squared quark-loop corrections
are quite sensitive to lepton–lepton correlations that play a key role in the H→WW∗
analysis. Their relative impact as compared to the full NLO contributions amounts to only
3% in the inclusive case, but grows to 6% if Higgs-analysis cuts are applied. This corre-
sponds to about 50% of the Higgs-boson signal in the relevant analysis regions, which calls
for a detailed theoretical investigation of squared quark-loop terms and of their nontriv-
ial kinematic features. To this end we considered all relevant squared quark-loop matrix
elements for the production of four leptons plus up to one jet. In particular, in addition
to the well-known gluon–gluon fusion contributions, for the first time we also studied the
gq→4`+q,g¯q→4`+ ¯q, and q¯q→4`+ g channels. In order to merge squared quark-loop
corrections with different jet multiplicity, we extended the tree-level multi-jet merging in
Sherpa to include also purely loop-induced processes. In this context, the inclusion of the
quark channels is indispensable for a consistent merging. The net effect of this merging is
a visibly harder tail in the jet transverse momentum distribution with respect to the one
obtained from only taking the leading gg →4`contribution supplemented with the parton
shower. To the best of our knowledge this has not been studied before.
In the H→WW∗analyses, the size of squared quark-loop corrections turns out to vary
from 2% to 6%, depending on the jet bin, on the kinematic region and on the experiment.
The merging approach is especially important in order to guarantee decent predictions in
the 1-jet bin. Due to their nontrivial kinematic dependence, squared quark-loop corrections
have a quite significant impact on the extrapolation of the WW-background from control
to signal regions. The resulting shift in the relevant cross-section ratios is of order 1.5%,
and we argued that these corrections can be regarded as a realistic estimate of unknown
higher-order effects in the data-driven determination of the WW-background at the LHC.
At this point it should be stressed that all the studies reported here are at the parton
level only, with one choice of PDFs to facilitate a clear and direct comparison between the
different approaches. It is, however, a straightforward exercise to allow for different PDFs
or to go from the parton to the hadron level in a simulation like the one presented here:
switching on hadronisation and the underlying event modelling allows to assess these effects
automatically. As a further extension, it is possible to extend the current study to cases
including all possible other four-lepton final states or to study in more detail the two-jet bin
of the simulation, which is crucial for the vector-boson fusion signatures. For the latter case,
the simulation could be extended to the production of four leptons in association with two
jets at next-to leading order accuracy. It can be anticipated that a simulation on the level
presented here would certainly lead to a similarly relevant reduction of QCD uncertainties
for this important channel of Higgs physics.
A Treatment of bottom- and top-quark contributions
Consistently with the five-flavour evolution of PDFs and αs, for bottom quarks we adopt
the massless approximation. Top quarks are thus the only QCD partons that we treat
as massive. They can contribute to pp →W+W−+jets through closed quark loops, but
also via resonant top propagators in sub-processes with external b quarks, such as gb →
– 36 –

W+W−band gg →W+W−b¯
b. Partonic channels of this type are dominated by Wt and
t¯
tproduction, and are more conveniently handled as separate processes. Therefore, as
operational definition of W+W−+jets production, we consider only partonic channels that
do not involve b quarks in the initial or final state. As pointed out in Ref. [17], when
excluding external b quarks, care must be taken to avoid NLO infrared singularities in
pp →W+W−j. This issue is related to the renormalisation of the external-gluon wave
function, which receives a b-quark contribution
δZ(b)
A=αs
6πµ2ε∆IR −µ2ε∆UV= 0,(A.1)
where µis the scale of dimensional regularisation, and infrared (IR) and ultraviolet (UV)
singularities in D= 4 −2εdimensions yield
∆IR,UV =(4π)ε
Γ(1 −ε)
1
ε, µ2ε∆IR,UV = ∆IR,UV + ln µ2+O(ε).(A.2)
The renormalisation constant (A.1) vanishes due to an exact IR–UV compensation. How-
ever, while its UV pole µ2ε∆UV cancels in renormalised q¯q→W+W−gamplitudes,7the
compensation of the IR pole µ2ε∆IR requires a q¯q→W+W−b¯
breal-emission counterpart
involving collinear g→b¯
bsplittings. The inclusion of W+W−b¯
bfinal states—at least in
the collinear region—is thus indispensable for an infrared-safe NLO definition of W+W−j
production in the five-flavour scheme.
In Ref. [17], the IR cancellation was achieved by including the contribution of g→b¯
b
splittings to the Catani–Seymour I-operator [53],
I(b) =−αs
6π∆IR +1
2ln µ2
2pqpg
+ ln µ2
2p¯qpg+8
3,(A.3)
where pq, p¯qand pgare the quark, anti-quark and gluon momenta, respectively. Combining
δZ(b)
A+I(b) yields an IR-finite and ln µ-independent result. The I-operator contribution
(A.3) results from dipole-subtraction terms, which approximate g→b¯
bsplittings in the
collinear limit, upon integration over the entire b¯
bphase space. In principle, it should
be combined with a subtracted real-emission counterpart, which is free from singularities
but depends on the cuts applied to the b¯
bpair. In Ref. [17], this finite real-emission part
was omitted, arguing that its contribution should be small if b¯
bpairs are confined in a
jet cone. This kinematic restriction of the b¯
bphase space would also suppress t¯
tand tW
contributions. However, confining b¯
bpairs in narrow jets would introduce potentially large
logarithms of the jet radius. Moreover, the consistent inclusion of the real-emission part
would exactly cancel the 8/3term in (A.3), which results from the unphysical dipoles, and
replace it by an unknown cut-dependent contribution. The inclusion of I-operator terms
(A.3) without corresponding real-emission parts should thus be regarded as a regularisa-
tion prescription, which guarantees the correct cancellation of poles and large logarithms
corresponding to inclusive b¯
bemission, but involves ad-hoc constant parts. This ambiguity
can be removed only upon inclusion of the dipole-subtracted W+W−b¯
bremnant.
7Here we discuss only partonic processes with gluons in the final state. Similar arguments apply also to
the crossing-related qg→W+W−qand ¯qg→W+W−¯qchannels.
– 37 –

Based on these considerations, we adopt a splitting approach similar to Ref. [17], but
we prefer to subtract only the singular and logarithmically-enhanced terms arising from
inclusive g→b¯
bemissions. More precisely, instead of the subtraction term (A.3) we use8
I(b)
mod =−αs
6π∆IR + ln µ2
µ2
R.(A.4)
Since the renormalisation scale µRis typically of the same order of the kinematic invariants
in (A.3), the main difference between (A.3) and (A.4) amounts to
I(b) − I(b)
mod =−αs
6π1
2ln µ2
R
2pqpg
+ ln µ2
R
2p¯qpg+8
3' −4αs
9π' −1.7%,(A.5)
and can be regarded as the typical ambiguity inherent in the separation of the W+W−j
and W+W−b¯
bcross sections. Note that, in order to reflect this kind of uncertainty in
standard scale-variation studies, we intentionally introduce a fake ln µRdependence in the
IR-subtraction term (A.4).
This small ambiguity is due to the absence of the dipole-subtracted W+W−b¯
bemis-
sion, which is supposed to be included in a separate calculation of W+W−b¯
bproduction,
i.e. of t¯
tand Wt off-shell production. It can be removed by combining the W+W−+jets
and W+W−b¯
bcalculations in a single simulation. For a consistent matching of the two
processes, the I-operator term (A.3) in the pp →W+W−b¯
bcalculation should be replaced
by the finite shift9(A.5).
In summary, due to collinear g→b¯
bsingularities, the splitting of pp →W+W−jand
pp →W+W−b¯
bis not unique, and the subtraction term (A.4) corresponds to a natural
matching prescription, which is free from large logarithms and ad-hoc constants.
B Cuts of the Atlas and Cms H→WW∗analyses in 0- and 1-jet bins
The cuts of the Atlas [3] and Cms [4]H→WW∗→µ+νµe−¯νeanalyses at 8 TeV in the
exclusive 0- and 1-jet bins are listed in Table 7. To be close to the experimental definitions
of both Atlas and Cms, lepton isolation is implemented at the particle level. The scalar
sum of the transverse momenta of all visible particles within a R= 0.3cone around the
lepton candidate is not allowed to exceed 15% of the lepton pT. Partons are recombined
into jets using the anti-kTalgorithm [67]. The different WW transverse-mass definition
employed in Atlas and Cms is consistently taken into account,
m2
T=


qp2
T,``0+m2
``0+E/T2−

pT,``0+E/T


2for ATLAS
2|pT,``0||E/T|(1 −cos ∆φ``0, E/T) for CMS
,(B.1)
where pT,``0and m``0are the transverse momentum and the mass of the di-lepton system,
respectively, E/Tis the missing transverse momentum, and ∆φ``0,E/Tis the difference in
8Technically, we circumvent the explicit implementation of the subtraction term (A.4) by assigning the
values ∆IR →0and µ→µRto the dimensional-regularisation parameters.
9Here we assume that pp →W+W−b¯
bis computed using dipole subtraction, but the matching procedure
can be obviously adapted to any other subtraction method.
– 38 –

anti-kTjets Atlas Cms
R=0.4 0.5
pT,j(|ηj|)>25 GeV (|ηj|<2.4)30 GeV (|ηj|<4.7)
30 GeV (2.4<|ηj|<4.5)
Pselection Atlas Cms
pT,{`1, `2}>25,15 GeV 20,10 GeV
|η{e, µ}|<2.47, 2.5 2.5, 2.4
|ηe|/∈[1.37,1.57]
pT,``0>see S,C 30 GeV
m``0>10 GeV 12 GeV
E/(proj )
T>25 GeV 20 GeV
Sregion Atlas Cms
∆φ``0, E/T> π/2(0 jets only)
pT,``0>30 GeV (0 jets only)
∆φ``0<1.8 rad
m``0<50 GeV 200 GeV
mT∈[60 GeV,280 GeV]
Cregion Atlas Cms
∆φ``0, E/T> π/2(0 jets only)
pT,``0>30 GeV (0 jets only)
m``0∈[50,100] GeV (0 jets only) >100 GeV
>80 GeV (1 jet only)
Table 7. Jet definitions and selection cuts in the Atlas and Cms analyses of H→WW∗→
µ+νµe−¯νeat 8TeV. The cuts refer to various levels and regions, namely event pre-selection (P
cuts), the signal region (Pand Scuts) and the control region (Pand Ccuts). The projected missing
transverse energy E/(proj)
Tis defined as E/(proj )
T=E/T·sin (min{∆φnear , π/2}), where ∆φnear denotes
the angle between the missing transverse momentum E/Tand the nearest lepton in the transverse
plane.
azimuth between E/Tand pT,``0. After a pre-selection (P), additional cuts are applied that
define a signal (S) and a control (C) region. The latter is exploited to normalise background
simulations to data in the experimental analyses in each jet bin. In the Atlas analysis,
different cuts are applied in the 0- and 1-jet bins. All cuts have been implemented in form
of a Rivet [66] analysis.
Acknowledgments
We are grateful to A. Denner, S. Dittmaier and L. Hofer for providing us with the one-loop
tensor-integral library Collier. We thank T. Gehrmann for discussions and S. Kallweit for
cross-checking four-lepton plus 0- and 1-jet NLO cross sections. The research of F. Cascioli,
– 39 –

P. Maierhöfer and S. Pozzorini is supported by the SNSF. Stefan Höche was supported by
the U.S. Department of Energy under Contract No. DE–AC02–76SF00515. Frank Siegert’s
work was supported by the German Research Foundation (DFG) via grant DI 784/2-1.
We gratefully thank the bwGRiD project for computational resources. This research used
resources of the National Energy Research Scientific Computing Center, which is supported
by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-
05CH11231.
References
[1] ATLAS Collaboration Collaboration, G. Aad et al., Observation of a new particle in the
search for the Standard Model Higgs boson with the ATLAS detector at the LHC,Phys.Lett.
B716 (2012) 1–29, [arXiv:1207.7214].
[2] CMS Collaboration Collaboration, S. Chatrchyan et al., Observation of a new boson at a
mass of 125 GeV with the CMS experiment at the LHC,Phys.Lett. B716 (2012) 30–61,
[arXiv:1207.7235].
[3] ATLAS Collaboration, Measurements of the properties of the Higgs-like boson in the
W W ∗→``νν decay channel with the ATLAS detector using 25 fb−1of proton-proton
collision data. ATLAS-CONF-2013-030.
[4] CMS Collaboration, Evidence for a particle decaying to W+W−in the fully leptonic final
state in a standard model Higgs boson search in pp collisions at the LHC.
CMS-PAS-HIG-13-003.
[5] J. Ohnemus, An Order αscalculation of hadronic W−W+production,Phys.Rev. D44 (1991)
1403–1414.
[6] S. Frixione, A Next-to-leading order calculation of the cross-section for the production of W+
W- pairs in hadronic collisions,Nucl.Phys. B410 (1993) 280–324.
[7] J. Ohnemus, Hadronic ZZ,W−W+, and W±Zproduction with QCD corrections and
leptonic decays,Phys.Rev. D50 (1994) 1931–1945, [hep-ph/9403331].
[8] L. J. Dixon, Z. Kunszt, and A. Signer, Vector boson pair production in hadronic collisions at
order αs: Lepton correlations and anomalous couplings,Phys.Rev. D60 (1999) 114037,
[hep-ph/9907305].
[9] J. M. Campbell and R. K. Ellis, An Update on vector boson pair production at hadron
colliders,Phys.Rev. D60 (1999) 113006, [hep-ph/9905386].
[10] J. M. Campbell, R. K. Ellis, and C. Williams, Vector boson pair production at the LHC,
JHEP 1107 (2011) 018, [arXiv:1105.0020].
[11] S. Frixione and B. R. Webber, Matching NLO QCD computations and parton shower
simulations,JHEP 0206 (2002) 029, [hep-ph/0204244].
[12] S. Frixione, P. Nason, and C. Oleari, Matching NLO QCD computations with Parton Shower
simulations: the POWHEG method,JHEP 0711 (2007) 070, [arXiv:0709.2092].
[13] T. Melia, P. Nason, R. Rontsch, and G. Zanderighi, W+W-, WZ and ZZ production in the
POWHEG BOX,JHEP 1111 (2011) 078, [arXiv:1107.5051].
– 40 –

[14] R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, R. Pittau, et al., Four-lepton production at
hadron colliders: aMC@NLO predictions with theoretical uncertainties,JHEP 1202 (2012)
099, [arXiv:1110.4738].
[15] J. M. Campbell, R. K. Ellis, and G. Zanderighi, Next-to-leading order predictions for
W W + 1 jet distributions at the LHC,JHEP 0712 (2007) 056, [arXiv:0710.1832].
[16] S. Dittmaier, S. Kallweit, and P. Uwer, NLO QCD corrections to WW+jet production at
hadron colliders,Phys.Rev.Lett. 100 (2008) 062003, [arXiv:0710.1577].
[17] S. Dittmaier, S. Kallweit, and P. Uwer, NLO QCD corrections to pp/p¯p→W W +jet +X
including leptonic W-boson decays,Nucl.Phys. B826 (2010) 18–70, [arXiv:0908.4124].
[18] B. Jaeger, C. Oleari, and D. Zeppenfeld, Next-to-leading order QCD corrections to W+W-
production via vector-boson fusion,JHEP 0607 (2006) 015, [hep-ph/0603177].
[19] B. Jaeger and G. Zanderighi, Electroweak W+W-jj prodution at NLO in QCD matched with
parton shower in the POWHEG-BOX,JHEP 1304 (2013) 024, [arXiv:1301.1695].
[20] T. Melia, K. Melnikov, R. Rontsch, and G. Zanderighi, NLO QCD corrections for W+W−
pair production in association with two jets at hadron colliders,Phys.Rev. D83 (2011)
114043, [arXiv:1104.2327].
[21] N. Greiner, G. Heinrich, P. Mastrolia, G. Ossola, T. Reiter, et al., NLO QCD corrections to
the production of W+ W- plus two jets at the LHC,Phys.Lett. B713 (2012) 277–283,
[arXiv:1202.6004].
[22] T. Melia, K. Melnikov, R. Rontsch, and G. Zanderighi, Next-to-leading order QCD
predictions for W+W+jj production at the LHC,JHEP 1012 (2010) 053,
[arXiv:1007.5313].
[23] A. Denner, L. Hosekova, and S. Kallweit, NLO QCD corrections to W+ W+ jj production in
vector-boson fusion at the LHC,Phys.Rev. D86 (2012) 114014, [arXiv:1209.2389].
[24] B. Jaeger and G. Zanderighi, NLO corrections to electroweak and QCD production of
W+W+ plus two jets in the POWHEGBOX,JHEP 1111 (2011) 055, [arXiv:1108.0864].
[25] F. Campanario, M. Kerner, L. D. Ninh, and D. Zeppenfeld, WZ production in association
with two jets at NLO in QCD,Phys.Rev.Lett. 111 (2013) 052003, [arXiv:1305.1623].
[26] T. Binoth, M. Ciccolini, N. Kauer, and M. Kramer, Gluon-induced WW background to Higgs
boson searches at the LHC,JHEP 0503 (2005) 065, [hep-ph/0503094].
[27] T. Binoth, M. Ciccolini, N. Kauer, and M. Kramer, Gluon-induced W-boson pair production
at the LHC,JHEP 0612 (2006) 046, [hep-ph/0611170].
[28] J. M. Campbell, R. K. Ellis, and C. Williams, Gluon-Gluon Contributions to W+ W-
Production and Higgs Interference Effects,JHEP 1110 (2011) 005, [arXiv:1107.5569].
[29] T. Melia, K. Melnikov, R. Rontsch, M. Schulze, and G. Zanderighi, Gluon fusion
contribution to W+W- + jet production,JHEP 1208 (2012) 115, [arXiv:1205.6987].
[30] N. Kauer and G. Passarino, Inadequacy of zero-width approximation for a light Higgs boson
signal,JHEP 1208 (2012) 116, [arXiv:1206.4803].
[31] The LHC Higgs Cross Section Working Group Collaboration, S. Heinemeyer et al.,
Handbook of LHC Higgs Cross Sections: 3. Higgs Properties,arXiv:1307.1347.
[32] T. Gleisberg, S. Hoeche, F. Krauss, M. Schonherr, S. Schumann, et al., Event generation with
SHERPA 1.1,JHEP 0902 (2009) 007, [arXiv:0811.4622].
– 41 –

[33] F. Cascioli, P. Maierhoefer, and S. Pozzorini, Scattering Amplitudes with Open Loops,
Phys.Rev.Lett. 108 (2012) 111601, [arXiv:1111.5206].
[34] A. Denner, S. Dittmaier, and L. Hofer. In preparation.
[35] A. Denner and S. Dittmaier, Reduction of one loop tensor five point integrals,Nucl.Phys.
B658 (2003) 175–202, [hep-ph/0212259].
[36] A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals,Nucl.Phys.
B734 (2006) 62–115, [hep-ph/0509141].
[37] A. Denner and S. Dittmaier, Scalar one-loop 4-point integrals,Nucl.Phys. B844 (2011)
199–242, [arXiv:1005.2076].
[38] S. Hoeche, F. Krauss, M. Schonherr, and F. Siegert, A critical appraisal of NLO+PS
matching methods,JHEP 1209 (2012) 049, [arXiv:1111.1220].
[39] S. Hoeche, F. Krauss, M. Schonherr, and F. Siegert, W+n-jet predictions at the Large
Hadron Collider at next-to-leading order matched with a parton shower,Phys.Rev.Lett. 110
(2013) 052001, [arXiv:1201.5882].
[40] T. Gehrmann, S. Hoeche, F. Krauss, M. Schonherr, and F. Siegert, NLO QCD matrix
elements + parton showers in e+e−→hadrons,JHEP 1301 (2013) 144, [arXiv:1207.5031].
[41] S. Hoeche, F. Krauss, M. Schonherr, and F. Siegert, QCD matrix elements + parton showers:
The NLO case,JHEP 1304 (2013) 027, [arXiv:1207.5030].
[42] A. Denner, S. Dittmaier, M. Roth, and L. Wieders, Electroweak corrections to
charged-current e+e−→4 fermion processes: Technical details and further results,
Nucl.Phys. B724 (2005) 247–294, [hep-ph/0505042].
[43] A. Bredenstein, A. Denner, S. Dittmaier, and S. Pozzorini, NLO QCD corrections to
pp →t¯
tb¯
b+Xat the LHC,Phys.Rev.Lett. 103 (2009) 012002, [arXiv:0905.0110].
[44] A. Bredenstein, A. Denner, S. Dittmaier, and S. Pozzorini, NLO QCD Corrections to Top
Anti-Top Bottom Anti-Bottom Production at the LHC: 2. full hadronic results,JHEP 1003
(2010) 021, [arXiv:1001.4006].
[45] A. Denner, S. Dittmaier, S. Kallweit, and S. Pozzorini, NLO QCD corrections to WWbb
production at hadron colliders,Phys.Rev.Lett. 106 (2011) 052001, [arXiv:1012.3975].
[46] A. Denner, S. Dittmaier, S. Kallweit, and S. Pozzorini, NLO QCD corrections to off-shell
top-antitop production with leptonic decays at hadron colliders,JHEP 1210 (2012) 110,
[arXiv:1207.5018].
[47] A. van Hameren, Multi-gluon one-loop amplitudes using tensor integrals,JHEP 0907 (2009)
088, [arXiv:0905.1005].
[48] P. Draggiotis, M. Garzelli, C. Papadopoulos, and R. Pittau, Feynman Rules for the Rational
Part of the QCD 1-loop amplitudes,JHEP 0904 (2009) 072, [arXiv:0903.0356].
[49] G. Ossola, C. G. Papadopoulos, and R. Pittau, Reducing full one-loop amplitudes to scalar
integrals at the integrand level,Nucl.Phys. B763 (2007) 147–169, [hep-ph/0609007].
[50] S. Catani, Y. L. Dokshitzer, M. Olsson, G. Turnock, and B. R. Webber, New clustering
algorithm for multijet cross sections in e+e−annihilation,Phys. Lett. B269 (1991) 432–438.
[51] S. Catani, B. R. Webber, and G. Marchesini, QCD coherent branching and semiinclusive
processes at large x,Nucl. Phys. B349 (1991) 635–654.
– 42 –

[52] I. W. Stewart and F. J. Tackmann, Theory Uncertainties for Higgs and Other Searches Using
Jet Bins,Phys.Rev. D85 (2012) 034011, [arXiv:1107.2117].
[53] S. Catani and M. Seymour, A General algorithm for calculating jet cross-sections in NLO
QCD,Nucl.Phys. B485 (1997) 291–419, [hep-ph/9605323].
[54] S. Schumann and F. Krauss, A Parton shower algorithm based on Catani-Seymour dipole
factorisation,JHEP 0803 (2008) 038, [arXiv:0709.1027].
[55] S. Hoeche, S. Schumann, and F. Siegert, Hard photon production and matrix-element
parton-shower merging,Phys.Rev. D81 (2010) 034026, [arXiv:0912.3501].
[56] S. Hoeche, F. Krauss, S. Schumann, and F. Siegert, QCD matrix elements and truncated
showers,JHEP 0905 (2009) 053, [arXiv:0903.1219].
[57] S. Catani, F. Krauss, R. Kuhn, and B. Webber, QCD matrix elements + parton showers,
JHEP 0111 (2001) 063, [hep-ph/0109231].
[58] P. Agrawal and A. Shivaji, Di-Vector Boson + Jet Production via Gluon Fusion at Hadron
Colliders,Phys.Rev. D86 (2012) 073013, [arXiv:1207.2927].
[59] H.-L. Lai, M. Guzzi, J. Huston, Z. Li, P. M. Nadolsky, et al., New parton distributions for
collider physics,Phys.Rev. D82 (2010) 074024, [arXiv:1007.2241].
[60] J. M. Campbell and R. Ellis, MCFM for the Tevatron and the LHC,Nucl.Phys.Proc.Suppl.
205-206 (2010) 10–15, [arXiv:1007.3492].
[61] F. Krauss, R. Kuhn, and G. Soff, AMEGIC++ 1.0: A Matrix element generator in C++,
JHEP 0202 (2002) 044, [hep-ph/0109036].
[62] T. Gleisberg and S. Hoeche, Comix, a new matrix element generator,JHEP 0812 (2008)
039, [arXiv:0808.3674].
[63] T. Gleisberg and F. Krauss, Automating dipole subtraction for QCD NLO calculations,
Eur.Phys.J. C53 (2008) 501–523, [arXiv:0709.2881].
[64] L. Lonnblad and S. Prestel, Unitarising Matrix Element + Parton Shower merging,JHEP
1302 (2013) 094, [arXiv:1211.4827].
[65] L. Lonnblad and S. Prestel, Merging Multi-leg NLO Matrix Elements with Parton Showers,
JHEP 1303 (2013) 166, [arXiv:1211.7278].
[66] A. Buckley, J. Butterworth, L. Lonnblad, H. Hoeth, J. Monk, et al., Rivet user manual,
arXiv:1003.0694.
[67] M. Cacciari, G. P. Salam, and G. Soyez, The Anti-k(t) jet clustering algorithm,JHEP 0804
(2008) 063, [arXiv:0802.1189].
– 43 –