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The black, red, blue, purple and green curves are the probability of a hierarchy determination with 1 σ , 2 σ , 3 σ , 4 σ and 5 σ of sensitivity as a function of ∆ χ 2 .
Source publication
In the next decade, a number of experiments will attempt to determine the
neutrino mass hierarchy. Feasibility studies for such experiments generally
determine the expected value of Delta chi^2. As the hierarchy is a discrete
choice, Delta chi^2 does not obey a one degree of freedom chi^2 distribution
and so the number of sigmas of confidence of th...
Context in source publication
Citations
... Several studies have reported that this approximation may not be valid for neutrino oscillation studies [73,74]. Therefore, a Feldman-Cousins procedure should ultimately be applied when interpreting the experimental results in the future. ...
A bstract
This article presents the potential of a combined analysis of the JUNO and KM3NeT/ORCA experiments to determine the neutrino mass ordering. This combination is particularly interesting as it significantly boosts the potential of either detector, beyond simply adding their neutrino mass ordering sensitivities, by removing a degeneracy in the determination of ∆ $$ {m}_{31}^2 $$ m 31 2 between the two experiments when assuming the wrong ordering. The study is based on the latest projected performances for JUNO, and on simulation tools using a full Monte Carlo approach to the KM3NeT/ORCA response with a careful assessment of its energy systematics. From this analysis, a 5 σ determination of the neutrino mass ordering is expected after 6 years of joint data taking for any value of the oscillation parameters. This sensitivity would be achieved after only 2 years of joint data taking assuming the current global best-fit values for those parameters for normal ordering.
... where erfc(x) is the complementary error function. This definition implies that we identify 1σ, 2σ and 3σ with a C.L. (1 − α) of 68.27%, 95.45% and 99.73%, respectively [7,72,73]. Apart from evaluating α, it is important to look for more statistical tools that help us to have a better idea of how feasible it is to observe Earth matter effects at a certain level of confidence; one of these tools is the sensitivity to discriminate between the signal and the background fluctuations which can be defined as the separation between the means of the signal and the background fluctuation distributions, compared against the standard deviation of the signal and background fluctuation distribution. Mathematically it can approximately be written as where µ s and µ b are the means of the signal and background fluctuation distributions and σ s and σ b their standard deviations, respectively. ...
The observation of Earth matter effects in the spectrum of neutrinos coming from a next galactic core-collapse supernova (CCSN) could, in principle, reveal if neutrino mass ordering is normal or inverted. One of the possible ways to identify the mass ordering is through the observation of the modulations that appear in the spectrum when neutrinos travel through the Earth before they arrive at the detector. These features in the neutrino spectrum depend on two factors, the average neutrino energies, and the difference between the primary neutrino fluxes of electron and other flavors produced inside the supernova. However, recent studies indicate that the Earth matter effect for CCSN neutrinos is expected to be rather small and difficult to be observed by currently operating or planned neutrino detectors mainly because of the similarity of average energies and fluxes between electron and other flavors of neutrinos, unless the distance to CCSN is significantly smaller than the typically expected one, ∼ 10 kpc. Here, we are looking towards the possibility if the non-standard neutrino properties such as decay of neutrinos can enhance the Earth matter effect. In this work we show that invisible neutrino decay can potentially enhance significantly the Earth matter effect for both ν e and ν̅ e channels at the same time for both mass orderings, even if the neutrino spectra between electron and other flavors of neutrinos are very similar, which is a different feature not expected for CCSN neutrinos with standard oscillation without the decay effect.
... 8 Note that more sophisticated methods can be used to estimate the real sensitivity of Monte Carlo analyses of neutrino mass ordering measurements, see Refs. [43,61,62]. In this paper, for simplicity we assume normal distributions and interpret the significance as #σ ¼ ffiffiffiffiffiffiffiffi ...
The flagship measurement of the JUNO experiment is the determination of the neutrino mass ordering. Here we revisit its prospects to make this determination by 2030, using the current global knowledge of the relevant neutrino parameters as well as current information on the reactor configuration and the critical parameters of the JUNO detector. We pay particular attention to the nonlinear detector energy response. Using the measurement of θ13 from Daya Bay, but without information from other experiments, we estimate the probability of JUNO determining the neutrino mass ordering at ≥3σ to be 31% by 2030. As this probability is particularly sensitive to the true values of the oscillation parameters, especially Δm212, JUNO’s improved measurements of sin2θ12, Δm212 and |Δmee2|, obtained after a couple of years of operation, will allow an updated estimate of the probability that JUNO alone can determine the neutrino mass ordering by the end of the decade. Combining JUNO’s measurement of |Δmee2| with other experiments in a global fit will most likely lead to an earlier determination of the mass ordering.
... where erfc(x) is the complementary error function. This definition implies that we identify 1σ, 2σ and 3σ with a C.L. (1 − α) of 68.27%, 95.45% and 99.73%, respectively [7,72,73]. Apart from evaluating α, it is important to look for more statistical tools that help us to have a better idea of how feasible it is to observe Earth matter effects at a certain level of confidence; one of these tools is the sensitivity to discriminate between the signal and the background fluctuations which can be defined as the separation between the means of the signal and the background fluctuation distributions, compared against the standard deviation of the signal and background fluctuation distribution. Mathematically it can approximately be written as ...
The observation of Earth matter effects in the spectrum of neutrinos coming from a next galactic core-collapse supernova (CCSN) could, in principle, reveal if neutrino mass ordering is normal or inverted. One of the possible ways to identify the mass ordering is through the observation of the modulations that appear in the spectrum when neutrinos travel through the Earth before they arrive at the detector. These features in the neutrino spectrum depend on two factors, the average neutrino energies, and the difference between the primary neutrino fluxes of electron and other flavors produced inside the supernova. However, recent studies indicate that the Earth matter effect for CCSN neutrinos is expected to be rather small and difficult to be observed by currently operating or planned neutrino detectors mainly because of the similarity of average energies and fluxes between electron and other flavors of neutrinos, unless the distance to CCSN is significantly smaller than the typically expected one, $\sim 10$ kpc. Here, we are looking towards the possibility if the non-standard neutrino properties such as decay of neutrinos can enhance the Earth matter effect. In this work we show that invisible neutrino decay can potentially enhance significantly the Earth matter effect for both $\nu_e$ and $\bar{\nu}_e$ channels at the same time for both mass orderings, even if the neutrino spectra between electron and other flavors of neutrinos are very similar, which is a different feature not expected for CCSN neutrinos with standard oscillation without the decay effect.
... The characteristic shape results from near degeneracy between matter and CPV effects that occurs near δ CP = π/2( −δ CP = π/2) for true normal (inverted) ordering. Studies have indicated that special attention must be paid to the statistical interpretation of neutrino mass ordering sensitivities [99][100][101] because the ∆χ 2 metric does not follow the expected chi-square function for one degree of freedom, so the interpretation of the ∆χ 2 as the sensitivity is complicated. However, it is clear from Fig. 17 (bottom), which correspond to their 3σ NuFIT range of values, as well as the NuFIT central value. ...
... However, it is clear from Fig. 17 (bottom), which correspond to their 3σ NuFIT range of values, as well as the NuFIT central value. and maximal mixing IO, and using the corrections from, for example, Ref. [99], DUNE would still achieve 5σ significance for the central 68% of all throws shown in Fig. 17. We note that for both seven and ten years (it was not checked for lower exposures), there were no parameter throws used in generating the plots (∼300,000 each) for which the incorrect mass ordering was preferred. ...
The sensitivity of the Deep Underground Neutrino Experiment (DUNE) to neutrino oscillation is determined, based on a full simulation, reconstruction, and event selection of the far detector and a full simulation and parameterized analysis of the near detector. Detailed uncertainties due to the flux prediction, neutrino interaction model, and detector effects are included. DUNE will resolve the neutrino mass ordering to a precision of 5σ, for all δCP values, after 2 years of running with the nominal detector design and beam configuration. It has the potential to observe charge-parity violation in the neutrino sector to a precision of 3σ (5σ) after an exposure of 5 (10) years, for 50% of all δCP values. It will also make precise measurements of other parameters governing long-baseline neutrino oscillation, and after an exposure of 15 years will achieve a similar sensitivity to sin22θ13 to current reactor experiments.
... The characteristic shape results from near degeneracy between matter and CPV effects that occurs near δ CP = π/2 (−δ CP = π/2) for true normal (inverted) ordering. Studies have indicated that special attention must be paid to the statistical interpretation of neutrino mass ordering sensitivities [99][100][101] because the Δχ 2 metric does not follow the expected chi-square function for one degree of freedom, so the interpretation of the Δχ 2 as the sensitivity is complicated. However, it is clear from Fig. 17 (bottom), which correspond to their 3σ NuFIT range of values, as well as the NuFIT central value. ...
... However, it is clear from Fig. 17 (bottom), which correspond to their 3σ NuFIT range of values, as well as the NuFIT central value. and maximal mixing IO, and using the corrections from, for example, Ref. [99], DUNE would still achieve 5σ significance for the central 68% of all throws shown in Fig. 17. We note that for both seven and ten years (it was not checked for lower exposures), there were no parameter throws used in generating the plots (∼300,000 each) for which the incorrect mass ordering was preferred. ...
The sensitivity of the Deep Underground Neutrino Experiment (DUNE) to neutrino oscillation is determined, based on a full simulation, reconstruction, and event selection of the far detector and a full simulation and parameterized analysis of the near detector. Detailed uncertainties due to the flux prediction, neutrino interaction model, and detector effects are included. DUNE will resolve the neutrino mass ordering to a precision of 5σ, for all δ_(CP) values, after 2 years of running with the nominal detector design and beam configuration. It has the potential to observe charge-parity violation in the neutrino sector to a precision of 3σ (5σ) after an exposure of 5 (10) years, for 50% of all δ_(CP) values. It will also make precise measurements of other parameters governing long-baseline neutrino oscillation, and after an exposure of 15 years will achieve a similar sensitivity to sin²θ₁₃ to current reactor experiments.
... This approach should however be taken with care as it typically overestimates the discrimination power of the experiment. Alternative approaches discussed in [140,[161][162][163], and providing a more rigorous statistical treatment, are followed in section 4.6. An example of asymmetry plots (following the definition of equation (19)) for n m and n e obtained with ORCA software tools and a smearing on energy and angle is shown in figure 53. ...
The main objectives of the KM3NeT Collaboration are (i) the discovery and subsequent observation of high-energy neutrino sources in the Universe and (ii) the determination of the mass hierarchy of neutrinos. These objectives are strongly motivated by two recent important discoveries, namely: (1) the high-energy astrophysical neutrino signal reported by IceCube and (2) the sizable contribution of electron neutrinos to the third neutrino mass eigenstate as reported by Daya Bay, Reno and others. To meet these objectives, the KM3NeT Collaboration plans to build a new Research Infrastructure consisting of a network of deep-sea neutrino telescopes in the Mediterranean Sea. A phased and distributed implementation is pursued which maximises the access to regional funds, the availability of human resources and the synergistic opportunities for the Earth and sea sciences community. Three suitable deep-sea sites are selected, namely off-shore Toulon (France), Capo Passero (Sicily, Italy) and Pylos (Peloponnese, Greece). The infrastructure will consist of three so-called building blocks. A building block comprises 115 strings, each string comprises 18 optical modules and each optical module comprises 31 photo-multiplier tubes. Each building block thus constitutes a three-dimensional array of photo sensors that can be used to detect the Cherenkov light produced by relativistic particles emerging from neutrino interactions. Two building blocks will be sparsely configured to fully explore the IceCube signal with similar instrumented volume, different methodology, improved resolution and
... In [150][151][152][153], the νMH sensitivity at nσ has been proven to be determined by the reveal that, if we want to achieve the best possible νMH sensitivity, the baselines to both Taishan and Yangjiang reactors must be about 50 km. Moreover, to ensure a sensitivity better than 3σ (equivalently, ∆χ 2 MH > 9), the difference between any 2 cores must be less than 500 m. ...
The JUNO experiment is a multi-purpose liquid scintillator neutrino experiment with the main objective of determining the neutrino mass hierarchy (nuMH) with a significance better than 3sigma. To achieve this goal, it is crucial that JUNO has an unprecedented energy resolution of 3% at 1 MeV. Therefore, the JUNO Central Detector (CD) will be built with 20000 ton high transparency liquid scintillator and high photomultiplier tube (PMT) photocathode coverage of 78%, which is provided by 18000 20"-PMTs (LPMTs) and 25000 3"-PMTs (SPMTs). At the same time, the background induced by atmospheric muons should be vetoed by using reconstructed muon tracks. The Top Tracker (TT) is a muon tracker installed on top of the CD for precise muon tracking.This thesis details firstly the optimisation of the LPMT and the SPMT systems, which are directly related to the antineutrino calorimetry. New designs of light concentrator tailored for the JUNO LPMT are studied in order to verify their performance on increasing the JUNO photoelectron yield. By comparing different configurations, the relation between the SPMT system performance and the non-uniform distribution of the SPMT emplacements is studied, and the scheme used for cabling between SPMTs and their Under Water Boxes (UWBs) is studied to ensure a minimal performance degradation in case of UWB failure.Afterwards, this thesis reports on the design and optimisation of the TT trigger algorithms. Due to the background induced by natural radioactivity in the JUNO cavern, the TT cannot work correctly without a trigger system. The results show that a 2-level trigger with the optimised trigger algorithm is effective for the background suppression and thus a muon detection efficiency of 93% can be achieved.A discussion about the TT contribution to the suppression and the measurement of the atmospheric muon-induced background, is also included.
... and hence does not follow a chi-square distribution. It was proven that if there are no pull parameters ("simple vs simple" scenario), the ∆χ 2 defined in 1.1 follows a Gaussian distribution, with µ = ∆χ 2 and σ = 2 |∆χ 2 | [5]; this is also true when pull parameters are taken into account, if some conditions are satisfied [6,7,8].In particular, it seems that these conditions are satisfied in RNE (at least in some simplified models), but not in LBNE, as can be seen from Fig. 1; more details on the models used can be found in [9]. We will discuss now how to quantify the sensitivity in the mass hierarchy determination, using a frequentist or a Bayesian approach. ...
... Since the CL depends only on the choice of T c,NH and T c,IH , not on the actual result of the experiment (which tells us only if such a CL is achieved or not), it can be convenient to use the hypothesis test to quantify the sensitivity to the MH of future experiments. There are a couple of possible definition of sensitivity often used in literature [7,8]; in the Gaussian, symmetric case (i.e. when µ NH = ∆χ 2 = −µ IH ; µ NH an µ IH are the average value of ∆χ 2 for the NH and IH) we have • Median sensitivity: T c,NH(IH) = −(+)∆χ 2 ; CL (expressed as number of σ 's) is ∆χ 2 , but β = 0.5 ...
... The test should be able to select the two-component interpretation when the energy recoil spectrum has a significant kink feature, as shown in figure 2, since this feature cannot be explained with only one DM particle. The statistical techniques used in this study have been previously applied and thoroughly detailed in the context of neutrino mass ordering analyses [42][43][44]. We then show in subsequent subsections that the best model discriminator is the mass splitting between the two DM components. ...
... standard deviation given by 2 T 2DM 0 . In this appendix we show why this is true, following the method of ref. [44]. We start by writing the data x i as a Gaussian distributed variable ...
We study the case of multi-component dark matter, in particular how direct detection signals are modified in the presence of several stable weakly-interacting-massive particles. Assuming a positive signal in a future direct detection experiment, stemming from two dark matter components, we study the region in parameter space where it is possible to distinguish a one from a two-component dark matter spectrum. First, we leave as free parameters the two dark matter masses and show that the two hypotheses can be significantly discriminated for a range of dark matter masses with their splitting being the critical factor. We then investigate how including the effects of different interaction strengths, local densities or velocity dispersions for the two components modifies these conclusions. We also consider the case of isospin-violating couplings. In all scenarios, we show results for various types of nuclei both for elastic spin-independent and spin-dependent interactions. Finally, assuming that the two-component hypothesis is confirmed, we quantify the accuracy with which the parameters can be extracted and discuss the different degeneracies that occur. This includes studying the case in which only a single experiment observes a signal, and also the scenario of having two signals from two different experiments, in which case the ratios of the couplings to neutrons and protons may also be extracted.
