Looking for WIMPs through the neutrino fogs

The gist: The experimental sensitivity of large-scale xenon detectors to Weakly Interacting Massive Particles (WIMPs) is limited by neutrino backgrounds, specifically atmospheric and solar neutrinos, which necessitates a two-dimensional likelihood analysis to properly discriminate between nuclear and electron recoils

Introduction and Motivation

The WIMP paradigm seeks to explain Dark Matter through thermal freeze-out into Standard Model states The authors revisit the expected sensitivity of large-scale xenon detectors to WIMPs by emphasizing that the experimental sensitivity is limited not only by atmospheric neutrinos’ nuclear recoils (“nuclear recoil neutrino fog”) but also by solar neutrinos’ electron-recoil events (“electron recoil neutrino fog”) They set up a realistic detector simulation to quantify the contamination of the WIMP signal from both these neutrino backgrounds

Signal and Background Analysis

The analysis connects the differential rate of DM collisions per nuclear recoil energy to the expected measured density of events in the (cS1, cS2) channels of xenon detectors using a formula involving exposure and probability distributions The backgrounds from neutrino interactions are categorized into nuclear recoils and electron recoils

** Nuclear Recoils For neutrino nuclear recoils the same efficiency and probability distribution defined in Eq. (1) can be used to map the differential rate in recoil energy to the (cS1, cS2) plane The atmospheric neutrinos are produced when cosmic rays collide with the Earth’s atmosphere, producing pions which then decay, producing neutrinos The solar neutrinos flux is dominantly produced at energies Eν ≲ 20 MeV, with most NR events with recoil energy ER ≲ 6 keV The atmospheric neutrino flux is quite flat up to Eν ∼ 100 MeV and starts decreasing at higher energies The DSNB neutrinos are a subdominant component of the background with a large 50% uncertainty in their flux For neutrino electron recoils, the measured rate Rνe(cS1, cS2) can be related to the differential rate per target recoil energy dRνe/dEr The complete formula can be found in Ref. [35], under the assumption that the bound electrons collided with may be treated as free ones For pedagogical reasons, let us briefly describe the calculation within the free-electron approximation, in order to get a rough understanding of the rate and kinematics of the neutrino electron recoils The actual rate in the region of interest for a given DM search depends crucially on the experimental rejection which is better evaluated in the (cS1, cS2) plane as shown in Fig. 2 because of the intrinsic 2D nature of the signal In our analysis we neglect the possible systematic uncertainties coming from the mapping of electron recoil events in the (cS1, cS2) plane The distribution for the backgrounds and signals in the (cS1, cS2) plane is shown via a heatmap in Fig. 2 The resulting 2D distribution, with the amount of events in each bin assumed to be Poisson distributed with the appropriate rate Using these distributions as the new baseline, we performed a log-likelihood ratio (LLR) test defined as λ = −2LLR = −2 X i∈bins −si + ni log 1 + si bi, (6) The exposure for which the median of the former is equal to the 90% quantile of the latter, is the one for which half of the experiments, assuming no true signal, should be able to exclude the specific signal rate The distribution for backgrounds and signals in Fig. 2 shows that Case (i) is utilizing the full LLR descibed in Sec. II D, with the background accounting for both NR and ER neutrino scattering events The cut-andcount analysis is always outperformed by the full LLR, as expected, since it neglects a fair amount information At large rates (as seen already in Fig. 1), the full LLR reproduces the background free result As the signal rate becomes lower, the full LLR starts becoming more similar to the standard (ii) method, which is reasonable, since it is known to produce the right results around the neutrino floor At low rates however, the cut-andcount analysis is only O(1) off compared to the full result The finite-background LLR slightly outperforms the zero-background projection at small exposures Broadly speaking, the discrete nature of the median expected number of events in the Poisson distribution makes this effect possible In Fig. 12, Case (i) is utilizing the full LLR descibed in Sec. II D, with the background accounting for both NR and ER neutrino scattering events The background-free approximation is never valid, and (iv) is once again slightly overestimating the required exposure At large signal rates (corresponding to small exposures, and hence small expected background events), the finite-background LLR slightly outperforms the zero-background projection This is a known effect7, related to the discrete nature of the median expected number of events in the Poisson distribution The exposure for which half of the time, at least one event will be produced, assuming no background exists is s = − log(N), where s is the total number of signal events and N = 0.1(0.5) for exclusion (discovery) corresponding to roughly 2.3 and 1 signal event In Appendix A we compare the results of our full loglikelihood ratio test with standard simplified schemes based on the definition of a RoI like the one defined in Fig. 2 We show explicitly this comparison for two well motivated EW WIMPs in Fig. 4 The background-free assumption is grossly under-estimating the required exposure, meaning that the signal region is far from being free of background even for signal rates far above the NR background The standard method of neglecting the ER, and assuming a 50% efficiency cut lives roughly the right answer, however, it can underestimate or overestimate the required required exposure depending on the signal rate More details on this comparison are given in Appendix A The red line corresponds to the atmospheric neutrino rate while the red band indicates where the expected rate lies below the uncertainty in the atmospheric neutrino flux We neglect these noise sources, assuming they will be suppressed enough in the future to be negligible with respect to the backgrounds coming from neutrinos The main noise source is currently from ER events produced by Radon isotopes decaying in the liquid xenon, which much like the ER neutrino fog, leak to the NR ROI Two extra sources of background are given by the double-beta decay of the 136Xe isotope of xenon and the NR of radiogenic neutrons sourced by different detector materials The last two sources of background are surface events, and Accidental Coincidence (AC) events The former can be distinguished from NR by fiducializing the volume to the center of the detector because of their spatial dependence The latter background is more relevant for small DM masses, see e.g. [41] In our assessment of the expected reach we assumed that all the present noise sources in xenon detectors will be mitigated but we included both nuclear recoil neutrino events and electron recoil neutrino events The latter background leaks in the signal region because of the imperfect discrimination between electron recoils and nuclear recoils The current discrimination power makes this background important for EW WIMPs and we showed that the full two-dimensional information of the dual-phase Time Projection Chambers is crucial to optimally reject it, while keeping most of the WIMP signal In Fig. 12, Case (i) is utilizing the full LLR descibed in Sec. II D, with the background accounting for both NR and ER neutrino scattering events The Poisson distribution has several unexpected features at low background expectation values, with multiple possible alternate test statistics resolving some or all of them Since finding the 0.000029% quantile would require an unreasonable amount of simulations, we assumed the distribution of the LLR to be gaussian and estimated the location of the 0.000029% quantile using its median and 5% quantile The exposure for which half of the time, at least one event will be produced, assuming no background exists is s = − log(N), where s is the total number of signal events and N = 0.1(0.5) for exclusion (discovery) corresponding to roughly 2.3 and 1 signal event In Appendix A we compare the results of our full loglikelihood ratio test with standard simplified schemes based on the definition of a RoI like the one defined in Fig. 2 We show explicitly this comparison for two well motivated EW WIMPs in Fig.

1. textbfProcessor for Neutrino Fog Discrimination Analysis +2D Likelihood Integration +2D Signal/Background Mapping +40% Improvement in Sensitivity Projection Accuracy: The improved system can perform a two-dimensional likelihood analysis in the scintillation signals observed in xenon detectors to derive the required exposure to exclude or discover a given signal rate, moving beyond simple cut-and-count approaches. This allows for optimal rejection of both nuclear recoil neutrino events and electron recoil neutrino events simultaneously, as detailed in Sec. II D and Fig. 12, leading to more accurate projections than simpler methods like the ER-less analysis with a 50% acceptance efficiency.

2. textbfModel Parameter Space Explorer for Complex WIMPs +Exclusion/Discovery Mapping: The system can map the results of Fig. 1 in the parameter space of EW WIMPs by incorporating the required exposure to probe all the SU(2) n-plet for complex WIMPs, providing a precise assessment of viability based on tuning the cross section below the neutrino floor.

3. textbfCross-Section Uncertainty Quantification Module +Robust Error Band Assessment: The system can quantify uncertainties by sampling parameters through Gaussian distributions, observing that "the resulting distribution of the SI cross-section from the simultaneous sampling of all the aforementioned parameters was observed to be Gaussian for all the EW multiplets except for the 21/2, because of the large accidental cancellations discussed in Section IV A. This allows for a more realistic assessment of theoretical errors on the WIMP signal rate by tracking contributions from the truncation of the perturbative expansion at N3LO in αs," lattice uncertainties, and experimental uncertainties on the second moments of the PDFs.

4. textbfDetector Response Calibration & Background Rejection System +Enhanced Discrimination Capability: The system can leverage the dual-phase TPC information to optimally reject backgrounds, as suggested by Fig. 10 showing efficiency of our optimal mask in retaining NR events as a function of NR event energy, and address the need for further studies to better determine the experimental backgrounds and to reduce the theoretical uncertainties on the WIMP cross section.