Hybrid Baryons, a brief review

Abstract

This contribution is a brief review of the status of hybrid baryons, which are hypothetical baryons that incorporate a gluonic excitation. We first summarize the status of hybrid mesons, since this closely related topic has seen considerable recent activity with the identification of two exotic candidates. Next we review theoretical expectations for the masses and quantum numbers of hybrid baryons, which have come from studies of the bag model, QCD sum rules and the flux tube model. Finally hybrid baryon experiment is discussed, including suggestions for experimenters at COSY.

Full text

arXiv:nucl-th/0009011v1 5 Sep 2000
Hybrid Baryons, a brief review 1
T.Barnes
Physics Division, Oak Ridge National Laboratory
Department of Physics and Astronomy, University of Tennessee
Institut f¨ur Kernphysik, Forschungszentrum J¨ulich
Institut f¨ur Theoretische Kernphysik, Universit¨at Bonn
Abstract:
This contribution is a brief review of the status of hybrid baryons, which are hypothetical
baryons that incorporate a gluonic excitation. We first summarize the status of hybrid mesons,
since this closely related topic has seen considerable recent activity with the identification of
two exotic candidates. Next we review theoretical expectations for the masses and quantum
numbers of hybrid baryons, which have come from studies of the bag model, QCD sum rules
and the flux tube model. Finally hybrid baryon experiment is discussed, including suggestions
for experimenters at COSY.
1 Hybrid Mesons
Hybrids are hadrons in which the dominant component of the state consists of quarks
(antiquarks) and excited glue. This deliberately vague definition is necessary at present
because the subject has been studied mainly through various models, and each assumes
a particular description of excited glue. Fortunately the models often reach similar con-
clusions regarding the quantum numbers and approximate masses of these states, so from
the experimental viewpoint there are relatively clear predictions regarding how one might
find states with excited glue in the spectrum.
Hybrid mesons are usually modelled as q¯q+excited glue, and this system can have all
JP C quantum numbers. This implies that one can most usefully search for hybrids as
mesons with the so-called “exotic quantum numbers” JP C = 0−− ,0+−,1−+,2+−,3−+...
because these are strictly forbidden to the nonrelativistic quark model’s q¯qstates. Thus
if one discovers a JPC exotic meson, it is certain that something other than q¯qhas been
found. Whether this is a hybrid or not may be a more difficult question to answer, and
depends on a comparison with theoretical predictions for the masses, quantum numbers
1Invited contribution to the COSY Workshop on Baryon Excitations, J¨ulich, 2-3 May 2000.
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and decay couplings of hybrids.
Various models and methods have been used to predict the spectrum of hybrid mesons,
including the bag model, QCD sum rules, the flux tube model, and lattice gauge theory.
All these approaches agree that there should be a light exotic JPC = 1−+hybrid, with a
somewhat model dependent mass from ca. 1.5 GeV (bag model) to 1.9 GeV (flux tube
model) to 2.0 GeV (LGT). Only the flux tube model has been studied in detail for its
decay mode predictions, and it leads to an a priori rather surprising expectation that
hybrid mesons decay preferentially to meson pairs with one internal orbital excitation,
the so-called “S+P” modes, for example πf1and πb1rather than the more familiar “S+S”
modes such as ππ,πη and πρ.
Experimentally we now have two candidate JP C exotic mesons, with the same quantum
numbers, a rather broad I=1 1−+π1(1400) seen in ηπ [1], and a somewhat narrower
π1(1600) seen in ρπ,ηπ and b1π[2]. Although it is exciting to have possible confirmation
of the existence of exotic hybrid mesons, it is disturbing that the masses of these states
are rather lower than the ca. 2 GeV expected by LGT and the flux-tube model, and
their observation with large partial widths in the S+S modes πη and πρ disagrees with
expectations of the flux-tube decay model. Although there have been speculations that
the π1(1400) in particular might be a nonresonant final-state effect, there have been no
model calculations that show this possibility is viable. So, we are faced with a somewhat
ambiguous situation, in which hybrid mesons may have been discovered, but there are
important disagreements with theoretical expectations for masses and important decay
modes.
2 Theoretical Expectations for Hybrid Baryons
2.1 General expectations
Augmenting the quarks qand antiquarks ¯qby gluons gleads to additional states in the
spectrum relative to the expectations of the naive q¯qand qqq quark model. Physically
allowed (color singlet) states in the baryon spectrum may be constructed from |qqqgi
“hybrid” basis states, in addition to the familiar |qqqiquark model states:
|qqqi


color
=1⊗8⊗8⊗10 ,
|qqqgi


color
=1⊗8⊗8⊗10⊗8 = 12⊗85⊗... .
The lowest hybrid baryon basis state is color octet and spatially symmetric in the qqq
part of |qqqgi, making it a 70 of SU(6). Since this qqq subsystem is combined with the
angular momentum of the gluon, we find the interesting prediction that |qqqgimultiplets
do not span the same |flavor,Jtotistates as an SU(6) |qqqimultiplet. Thus we should find
evidence for “incomplete” or “overcomplete” SU(6) baryon multiplets due to the presence
of hybrids. More detailed predictions for the multiplet content typically require the use
of a specific model, although there has recently been work on the derivation of general
properties of hybrid baryon states and their decays in the large quark mass and large-Nc
limit [3].
2

2.2 Bag model
This model places relativistic quarks and gluons in a spherical cavity and allows them to
interact through QCD forces such as one gluon exchange (OGE), the color Compton effect
and so forth. Incorporation of these interactions to leading nontrivial order, O(αs), gives
predictions for the spectrum and Hilbert space decomposition of light hybrid baryons in
this model.
GeV
M
1/2+ N 1/2+ ∆ 3/2+ ∆5/2+ N3/2+ N
0.0
0.5
1.0
1.5
2.0
2.5
JP, flavor
Figure 1: The spectrum of light nonstrange hybrid baryons found by Barnes and Close [4] in
the bag model.
The first published calculation of light bag model hybrids was due to Barnes and
Close [4], who derived the spectrum of nonstrange nnng states. This reference found the
spectrum shown in Fig.1; in order of increasing mass the states are
(1/2+N)2; (3/2+N)2; (1/2+∆) ; (3/2+∆) ; (5/2+N) .
Note that the lightest hybrid baryon is predicted to be an “extra” 1/2+N∗P11 state
(“extra” meaning an overpopulation relative to the predictions of the qqq quark model)
at about 1.6 GeV, which might possibly be identified with the Roper resonance. A
subsequent calculation by Golowich, Haqq and Karl [5] basically confirmed these results,
but used a parameter set that gave a mass of about 1.5 GeV for this lightest hybrid, so
identification with the Roper was given more support. Carlson and Hansson [6] extended
these studies to strange hybrid baryons, and found that the bag model predicted two
relatively light uds-flavor hybrids, with the lightest expected at M(1/2+) = 1.63(4) GeV
with their parameters.
Decays are not usually considered in bag model calculations, which normally assume
that the states are stable Hamiltonian eigenstates. A model of decays of bag model hybrid
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baryons was developed by Duck and Umland [7], who studied the ∆πand Nπdecay modes
of the lightest N-flavor hybrid states. They concluded that the lightest hybrid has a much
larger coupling to ∆πthan Nπ.
2.3 QCD sum rules (and LGT)
This approach, which has been applied to hybrid baryons in several papers of the previous
decade, finds the masses and other parameters of the lowest-lying states in terms of
numerically known VEVs, called “condensates”. Since the sum rules relate known VEVs
to a sum of resonance contributions, there are systematic uncertainties in separating
the individual resonance and “continuum” parts. Identification of excited states such as
hybrids is rather difficult in this approach, since higher-mass contributions to the sum rules
are suppressed exponentially. This exercise can be carried out for hybrids, for example by
calculating matrix elements of several operators and diagonalizing the result. In practice
the calculations also use qqqg operators, which one would expect to have larger hybrid
couplings. To date only hybrids in the nucleon/Roper sector 1/2+N have been studied
using QCD sum rules.
The first published hybrid baryon QCD sum rule calculation was by Martynenko [8],
who estimated the lightest 1/2+N hybrid baryon mass to be near 2.1 GeV. A subsequent
study by Kisslinger and Li [9] reported algebra errors in the (very intricate) matrix el-
ements calculated in the Martynenko paper, and published a revised mass estimate of
about 1.5 GeV, again very suggestive of the Roper. A more recent review by Kisslinger
[10] concluded that the Roper is largely a hybrid (meaning dominantly |qqqgi), the nucleon
has little evidence for a hybrid component, and also considers how one might calculate
strong couplings. Some of this program of decay calculations was carried out by Kisslinger
and Li [11], who conclude that the lightest hybrid should have a rather small branching
fraction ratio N(ππ)S/ Nπ, consistent with observation for the Roper.
We note in passing that lattice gauge theory uses a very similar technique to QCD sum
rules for extracting masses, and can also be used to determine hybrid baryon masses, for
example as nonleading contributions to baryon operator correlation functions. Hybrids
are not specifically identified as such, but will appear in any determination of excited
baryon masses in LGT. In future, couplings to qqq versus qqqg operators may identify
states with large excited gluonic components. Preliminary results for the first 1/2+N∗
resonance in LGT have been reported by Sasaki et al. [12], and it appears that this excited
baryon may be identified through the use of a baryon operator that has little overlap with
the nucleon. This approach works well for heavier quarks, but has not yet been carried
out with high statistics for light quark masses.
2.4 Flux tube model
The flux tube model assumes that glue forms a dynamically excitable tube between quarks
and antiquarks, and that the lightest hybrids are states in which this flux tube is spatially
excited. The model is of special interest because of the reasonable agreement between
its predictions for the mass of the lightest JP C -exotic meson and the presumably more
reliable LGT prediction (ca. 1.9 GeV in the flux tube model, versus ca. 2.0 GeV from
LGT). The determination of excited states in the baryon sector (qqq + spatially excited
4

flux tube) is a rather complicated problem which has only recently been treated. Flux
tube model predictions for the lightest hybrid baryons were reported by Capstick and
Page in 1999 [13]. They find that the lightest hybrid baryons in the nnn flavor sector
are two each of 1/2+N and 3/2+N, all at a mass of 1.87(10) GeV. Their results for the N
flavor hybrids are shown in Fig.2, together with current experimental data.
N=0,1,2 bands
N=3 band
1200
1300
1400
1600
1700
1500
1800
1900
2000
2100
2200
--+++ +
Ν1/2 Ν3/2 Ν5/2 Ν7/2 Ν1/2 Ν3/2
* or **
--
Ν5/2 Ν7/2
1710
1440
1650 1675
1680
1700
1720
1990
2080
2100
2190 3* or 4*
1200
1300
1400
1600
1700
1500
1800
1900
2000
2100
2200
--+++ +
Ν1/2 Ν3/2 Ν5/2 Ν7/2 Ν1/2 Ν3/2 --
Ν5/2 Ν7/2
N experimental and model states below 2200 MeV
1535 1520
2090
2000
PDG mass range
2200
πN amplitudes
0 5 MeV1/2
>10
1900
light hybrids
Figure 2: The four light N flavor hybrid baryons found by Capstick and Page [13] in the flux-
tube model, compared to experiment. The estimated error is ±100 MeV (light blue background).
Thus the lowest flux-tube hybrid baryon level is predicted to include Roper quantum
numbers, as was found in the bag model, albeit twofold degenerate and at a higher mass. In
addition a degenerate 3/2+N pair is expected. There are other differences in the multiplet
content; the flux-tube hybrid baryon multiplet contains the states
(1/2+N)2; (3/2+N)2; (1/2+∆) ; (3/2+∆) ; (5/2+∆) ,
so the flux tube model finds a high-mass 5/2+∆; in the bag model the high-mass state
was a 5/2+N. The flux-tube ∆ hybrids are predicted to be degenerate, with a mass of
2.09(10) GeV.
The implications of this work for searches for hybrid baryons, including various ex-
perimental search strategies such as overpopulation, strong decays, EM couplings and
production amplitudes, were recently reviewed by Page [14]. In particular Page suggests
searches for hybrids in the final states Nη, Nρand Nω.
Although there are no strong decay amplitude calculations reported for flux-tube hy-
brid baryons as yet, one can see that the qualitative arguments that are applicable to
flux-tube hybrid mesons should apply here as well. Thus one would expect the flux-tube
decay model to predict that the largest couplings are to hadrons with internal orbital
5

excitation. Phase space would clearly prefer the orbital excitation to be in the baryon,
so hybrid baryons decays to πS11 (1535) for example may be favored. Since the S11 (1535)
has a large and characteristic Nηbranch, study of the decay chains
hybrid →πS11 (1535) ; S11 (1535) →Nη(1)
and
hybrid →ηS11 (1535) ; S11 (1535) →Nη(2)
may reveal hybrids in final states in which conventional baryons have somewhat suppressed
couplings. The chain hybrid →ηS11 (1535) →ηηN is especially attractive for detectors
with good photon detection; such a study is planned at ELSA using the Crystal Barrel
detector [15].
3 Identifying Hybrid Baryons
3.1 General Strategies
Hybrid mesons can be studied most easily by searching for JP C exotics; although we
cannot be certain that a JP C exotic is a hybrid, we can be certain that it is not a q¯qstate.
If such an exotic is found, one can then search for the exotic and non-exotic partners that
would confirm the presence of a hybrid multiplet.
In baryons there are unfortunately no JPexotics, so we must use other properties
of baryons to determine whether or not they are hybrids. In this approach we classify
the “background” of qqq states, learn to describe their couplings accurately, and then
identify non-qqq baryons through unusual couplings or as an overpopulation of states
relative to the qqq quark model predictions. One property of baryon resonances often
cited as a hybrid discriminator is their EM couplings, in other words their photoproduction
and electroproduction amplitudes. Other possible ways to identify hybrids are through
anomalous strong decay amplitudes and production systematics in novel channels such as
J/Ψ hadronic decays.
3.2 Photocouplings
Since photocouplings of baryon resonances are widely considered to be reasonably well
predicted by the qqq quark model, and new experimental facilities such as Jefferson Lab
will provide detailed results on baryon resonance photocouplings, the EM couplings pre-
dicted for hybrid baryons have received considerable attention.
Photocouplings of bag model hybrid baryons were derived by Barnes and Close [16];
those of the lightest “Roperlike” hybrid were of special interest due to problems with
predicting the EM couplings of the Roper in the qqq quark model. Barnes and Close
found a generalization of the Moorhouse selection rule [17], which in this case gave a
vanishing photocoupling of the Iz= +1/2 hybrid state from a proton,
γP6→ Pg.(3)
Experimentally this photocoupling is not small, which apparently invalidates the identi-
fication of the Roper with this bag model hybrid. Caution is appropriate here. First, the
6

photocouplings are due to the basis transitions γ|qqqi → |qqqiand γ|qqqgi → |qqqgi, so
γP→Pgactually tests the non-valence components |qqqiin the hybrid and |qqqgiin the
nucleon. These nonleading amplitudes may be strongly model dependent!
Subsequently it was noted by Li [18] that whereas Barnes and Close had assumed
that the basis state |2Sqqq +1flavorgluei=|4Ngiwas the zeroth-order “Roper” hybrid basis
state, as suggested by cavity QCD perturbation theory, one should actually use degenerate
perturbation theory in this mixing problem because at zeroth order the basis states |2Ngi
and |4Ngiare degenerate. The Moorhouse selection rule does not apply to this |2Ngi
component, so one might still identify the Roper with the bag model hybrid if this is
indeed an important configuration.
Carlson and Mukhopadhyay [19] noted that electroproduction amplitudes of baryon
resonances with dominant hybrid components might be very characteristic. They con-
cluded that the transverse-photon qqqg electroproduction form factor should fall faster
than the corresponding qqq form by an additional factor of 1/Q2. Thus a rapid fall of
electroproduction amplitudes with increasing Q2is a possible hybrid signature.
This suggestion was considered by Li, Burkert and Li [20], who compared theoretical
models for the Q2dependence of electroproduction amplitudes of radial-qqq and hybrid
states with experiment. In their study the theoretical radial-qqq electroproduction am-
plitude was quite large, and unlike the hybrid electroproduction amplitude did not fall
rapidly with Q2. They concluded that the rapid fall of the experimental Roper electro-
production amplitude with increasing Q2favored the identification of the Roper with a
hybrid (see Fig.3).
0 0.5 1.0 1.5 2.0
-100
-50
0
+50
p
1/2
-3 -1/2
A (10 GeV )
Q (GeV )
22
P (1440)
11
hybrid
qqq radial
+
+
Figure 3: An early comparison of hybrid and radial-qqq electroproduction amplitudes with
experimental Roper results (from [20]).
Unfortunately for this simple picture, subsequent calculations have shown that the
amplitude γ(qqq)1S→(qqq)2Sis sensitive to the details of the calculation, and small
radial-qqq electroproduction amplitudes can also be accommodated. Although electro-
production shows great promise as a way to identify anomalous baryon resonances, until
such time as electroproduction calculations are shown to be reliable for a wide range of
7

qqq states, including radial excitations, the classification of resonances through their EM
couplings will be problematic.
3.3 J/Ψhadronic decays.
Rather surprisingly, BES at BEPC is being used to study N∗spectroscopy using J/Ψ
hadronic decays. Zou et al. [21] note that one might expect hybrid baryons to have larger
production amplitudes from J/Ψ than conventional qqq baryons, because a ggg state
produced in J/Ψ annihilation should have a larger overlap with a final hybrid baryon
(see Fig.4). It is certainly interesting to establish which baryons are produced with large
amplitudes in J/Ψ annihilation, as any unusual states thus produced are possible hybrid
baryon candidates.
g
g
ghybrid baryon
qqq baryon
c
c
-
Figure 4: Production of qqqg states from J/Ψ radiative decays occurs at O(α5
s) (followed by
nonperturbative pair production), which leads J/Ψ→ggg →(qqq) + (¯q¯q¯q) by one power of αs.
To date BES has 7.8M J/Ψ events, from which they select p¯pπoand p¯pη. This approach
has the additional advantage that it is an I= 1/2 filter, so the many ∆ (and hybrid ∆)
states will not be present to complicate the analysis. The only clear peak in the present
data is the S11(1535), in the p¯pπochannel (see Fig.5). Since ca. 50M J/Ψ events are
expected in the near future, hybrid baryon candidates may yet be identified in this process.
Another interesting possibility, which may be undertaken at COSY, is the selection of
isospin states through the choice of unusual beams. This might be possible for example
using an αbeam, as discussed at this meeting by Morsch and collaborators [22]. This
technique has previously been shown to be effective in enhancing the Roper signal, and
could be useful in a search for the light N-flavor hybrids because the production of ∆
states may be much weaker than in the more familiar πN and γN reactions.
3.4 Overpopulation of the spectrum; strong decays
Since there are no JPexotic baryons, searches for baryon hybrids are in effect seaches
for evidence of overpopulation, in which one attempts to establish whether there is clear
experimental evidence for more states in the spectrum than predicted by the qqq quark
model alone.
This suggests that establishing the conventional qqq baryon spectrum and studying
the properties of these “ordinary hadrons” is a very important part of the search for ex-
otica; what is unusual may only be evident once the background of conventional states is
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1 1.2 1.4 1.6 1.8 2
0
50
100
150
N events
M (GeV)
pπo
Figure 5: BES data for the pπoinvariant mass distribution in J/Ψ→ppπo[21], showing
evidence for the 1/2−N11(1535).
very well understood. This includes not only the quantum numbers, masses and widths
of the baryons, but also their EM couplings and strong decay amplitudes, since these
may be useful as probes of the internal structure of unusual resonances. This program of
establishing all nonstrange baryon resonances should be pursued at least to ca. 2.2 GeV,
since this is somewhat above the highest mass estimate for the lightest nonstrange hybrid
baryon. This conservative strategy of identifying all states is especially appropriate be-
cause we have little evidence regarding which model of hybrids is most accurate, and this
must be decided by comparing with a reasonably complete experimental spectrum. In the
worst case there could be large mixing angles between conventional and hybrid baryons,
so that the distinction between these states is rather artificial; simple state counting
is then the most direct approach for establishing the presence of additional degrees of
freedom. Another complication is that there are probably additional types of baryons,
such as (qqq)(q¯q) “molecular” states, which would presumably also be found in a detailed
experimental study of the baryon spectrum.
Strong decay amplitudes may also prove useful in identifying hybrid baryons, so the
careful determination of strong branching fractions and decay amplitudes of experimental
baryon resonances is especially important. In the meson case there are striking predictions
that hybrids should decay preferentially to states with internal orbital excitation, and if
this rule is confirmed we have a very useful signature that may also be applicable to
hybrid baryons. (This is being investigated by Black and Page [23].) One should note
however that the strong decays of conventional qqq baryons may not be well understood;
the usual models simply assume q¯qpair production with 0++ quantum numbers, which
appears to work well in certain test cases but has not been compared to high-statistics
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experimental resonance data for a wide range of states, simply because such data has not
been available. Since very detailed predictions for baryon resonance decay amplitudes
have now been published by Capstick and Roberts in this model [24] and data from
CEBAF is becoming available, we should soon be able to establish whether we can predict
conventional qqq baryon strong decays accurately. If so, hybrid baryons and other exotica
might be identifiable through their anomalous strong decays.
4 Summary and Conclusions
An overpopulation of baryon resonances is expected relative to the predicitons of the qqq
quark model, due to excitation of the glue degree of freedom. Excited glue will lead to
novel baryon resonances, which are known as “hybrid baryons”. Analogous JP C exotic
meson hybrids may already have been identified (the π1(1400) and π1(1600)). Theorists
have derived the spectrum of light hybrid baryons and some of their properties using
various models, and expect that the lightest hybrid will have 1/2+N “Roper” quantum
numbers and a (rather model dependent) mass of ca. 1.5-1.9 GeV. (It is amusing that this
range of masses is also predicted for the lightest exotic hybrid meson.) Strange baryon
hybrids are also anticipated, and a relatively light 1/2+Λ hybrid is predicted. Hybrids
may be identifiable through distinctive decay modes such as π+ P-wave baryon (similar to
the S+P modes of meson hybrids) and unusual photo- and electroproduction amplitudes.
A systematic search for these light hybrids can be carried out by completing the study
of N∗spectroscopy to ca. 2.2 GeV, and by accurately determining the decay amplitudes
and flavor partners of all observed states. COSY can contribute to the search for hybrids
by helping to establish the baryon resonance spectrum and strong decay amplitudes up
to this mass scale, ideally in both nonstrange and strange sectors.
5 Acknowledgements
It was a great pleasure to contribute to the COSY Workshop on Baryon Spectroscopy by
presenting this material on hybrid baryons. I am indebted to N.Black, S.Capstick and
P.R.Page for several discussions of their recent work on hybrid baryons, and to S.Capstick
for providing Fig.2. This research was supported in part by the DOE Division of Nuclear
Physics, at ORNL, managed by UT-Battelle, LLC, for the US Department of Energy
under Contract No. DE-AC05-00OR22725, and by the Deutsche Forschungsgemeinschaft
DFG at the University of Bonn and the Forschungszentrum J¨ulich under contract Bo
56/153-1.
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