Search for Coherent Elastic Scattering of Solar 8B Neutrinos in the XENON1T Dark Matter Experiment

We report on a search for nuclear recoil signals from solar 8 B neutrinos elastically scattering off xenon nuclei in XENON1T data, lowering the energy threshold from 2.6 to 1 . 6 keV. We develop a variety of novel techniques to limit the resulting increase in backgrounds near the threshold. No significant 8 B neutrinolike excess is found in an exposure of 0 . 6 t × y. For the first time, we use the nondetection of solar neutrinos to constrain the light yield from 1 – 2 keV nuclear recoils in liquid xenon, as well as nonstandard neutrino-quark interactions. Finally, we improve upon world-leading constraints on dark matter-nucleus interactions for dark matter masses between 3 and 11 GeV c − 2 by as much as an order of magnitude.

Introduction -Neutrinos from the Sun, atmospheric cosmic-ray-showers, and supernovae can produce observable nuclear recoils (NRs) via coherent elastic scattering off nuclei in liquid xenon (LXe) detectors searching for dark matter (DM) [1].The coherent elastic neutrinonucleus scattering (CEνNS) process [2,3] produces the same signature as the one expected from DM-nucleus interactions, and thus the two can only be distinguished by their recoil spectra.Solar 8 B neutrinos are expected to contribute the greatest number of CEνNS events in LXe DM search experiments.These events fall near the energy thresholds of such detectors, with a spectrum indistinguishable from 6 GeV c −2 DM.
The XENON1T dark matter search experiment, operated at the INFN Laboratori Nazionali del Gran Sasso (LNGS) until Dec. 2018, used a sensitive target of 2.0 t of LXe in a two-phase time projection chamber (TPC).Two arrays of photomultiplier tubes (PMTs) at the top and bottom of the TPC allowed simultaneous detection of scintillation light (S1) and, via electroluminescence, ionization electrons (S2) [4,5].With the largest exposure of any LXe TPC, data from XENON1T has been used to search for a variety of DM candidates, resulting in world-leading upper limits for DM-nucleus interactions [6][7][8][9].Though no excess of CEνNS from 8 B neutrinos ( 8 B CEνNS) was observed due to the energy threshold in these analyses, they will soon become an important background given the large exposures of next-generation multi-ton LXe detectors [10][11][12].In this Letter, we present a search for 8 B CEνNS events in XENON1T data between Feb. 2, 2017 and Feb. 8, 2018 ("SR1" in Ref. [6]).In this new analysis, we achieve unprecedented sensitivity by reducing the energy threshold.
Analysis Strategy -The 8 B CEνNS expectation in XENON1T depends on: the 8 B neutrino flux Φ, measured [13,14] as (5.3 ± 0.2) × 10 6 cm −2 s −1 ; the CEνNS cross section, from the Standard Model; the nuclear recoil scintillation light yield in xenon L y ; and the ionization yield Q y .We first present a search for 8 B CEνNS events in XENON1T, expecting 2.7 CEνNS events given nominal estimates of the above variables.We then combine XENON1T data with external measurements, as appropriate, to constrain these variables.We constrain L y by considering external measurements of Q y and Φ. Next, by including external measurements of Q y and L y , we use XENON1T data to determine Φ independently.We also constrain non-standard neutrino interactions by relaxing the standard model assumption on the CEνNS cross section.Finally, by considering 8 B CEνNS as a background and applying external constraints on all variables, we use the data to set limits on DM-nucleus interactions.
CEνNS Signal -The expected recoil spectrum of 8 B CEνNS in LXe is shown in Fig. 1 (top, dotted red).The scintillation and ionization responses are relatively uncertain at 8 B CEνNS energies (< 2 keV), and NR calibration measurements in XENON1T scarcely overlap this region, instead producing S1s and S2s similar to DM of mass ≥ 30 GeV c −2 .Therefore, we modify the NR model in [6,15] by decoupling the light and charge yields to allow for additional freedom.
The NR charge yield Q y has been measured down to 0.3 keV [16], providing strong constraints at 8 B CEνNS energies which are included in v2.1.0 of the NEST package [17].We use the best-fit and uncertainty from NEST to define the shape of Q y , fitting a single free "interpolation parameter" q to the measurements which specifies Q y within this uncertainty, resulting in the model shown in Fig. 1 (middle).The central black line (edges of the shaded interval) in the figure corresponds to q equalling 0 (±1).Measurements of the LXe NR light yield L y [18] have a large (≈ 20 %) uncertainty near 1 keV.Since the NEST L y uncertainty is largely set by measurements at energies far above our region of interest (ROI), we fit these measurements using a free parameter that scales the NEST best-fit L y .These measurement and the resulting model are shown in Fig. 1 (bottom).The L y and Q y parameter fits use external measurements between 0.9 and 1.9 keV, a central interval containing 68 % of expected 8 B CEνNS events after all acceptance losses.We conservatively assume zero L y below 0.5 keV, the lowest energy measurement available [19].This treatment has a percent-level effect on the expected CEνNS rate, since the detection efficiency below this "cutoff energy" is < 10 −3 .
The XENON1T S1 detection threshold was previously limited by the requirement that three or more PMTs detect pulses above threshold (denoted as "hits") within 50 ns [21], leading to a 1% acceptance of CEνNS recoils above the 0.5 keV cutoff.We reduce this "tightcoincidence" requirement to two hits within 50 ns, increasing the total acceptance above the 0.5 keV cutoff to 5 %.Another efficiency loss comes from 8 B CEνNS S2s failing the software trigger (defined in Ref. [22]) or the S2 analysis threshold.The sensitivity is therefore impaired by the presence of electronegative impurities in the LXe, which reduce S2s along the drift path.The 120 PE S2 analysis threshold, reduced from 200 PE, cuts 8 % of CEνNS events that pass the software trigger.Ac- The ROI for the CEνNS search is defined by S2s between 120 and 500 photoelectrons (PE), and S1s between 1 and 6 PE consisting of two or three hits.In this ROI, the 8 B CEνNS signal expectation increases twentyfold with respect to previous NR searches [6,8,9] because of the relaxed tight-coincidence requirement and lower S2 threshold, derived from integrating the expected event rate in Fig. 1 (top).Due to the minimal overlap with previously studied data, we consider this a blind analysis.
Backgrounds -This analysis considers all backgrounds described in [6,15].Radon daughters decaying on the inner surface of the TPC wall produce events with reduced S2s, contributing to the background in the ROI.In order to reduce this background to a negligible level, we use a fiducial volume of 1.04 t, similar to the one chosen for [20] but smaller than the one used in [6].
The accidental coincidence (AC) of S1 and S2 peaks incorrectly paired by the XENON1T reconstruction software mimics real interactions.AC background events are modeled by sampling (with replacement) from isolated S1s and S2s and assigning a random time separation between them.Most S1s contributing to AC events originate from the pileup of lone hits from individual PMTs.Other sources include low-energy events occurring below the cathode or on the inner detector surface, and light leaking inside the active volume.AC forms the dominant background for this search, since the overall rate of isolated S1s increases by two orders of magnitude when we require only two hits.The rate and distribution of isolated S1s are determined using S1 peaks found in the extended event window of 1 ms before the S1 of highenergy events, as in [6,15].For this analysis, the data is reprocessed with an updated algorithm [23] to better retain the isolated S1s preceding these high-energy events, eliminating the dominant systematic uncertainty in the AC rate [6].
High-energy events from gamma-ray backgrounds can also contaminate subsequent events with lone hits, a dominant source of S1s in this analysis.For each event, the preceding event with the highest potential to produce lone hits is identified by dividing its largest S2 area by its time difference from the current event, denoted as S2 prev /∆t prev .The selection on S2 prev /∆t prev reduces the rate of isolated S1s by 65 %, accepting 82 % of 8 B CEνNS signals.Furthermore, we require the PMT signal sum within the first 1 ms of an event to be < 40 PE and that this interval contains at most a single S1, accepting 96 % of remaining events.After these selections, the total isolated-S1 rate is 11.2 Hz, ten times higher than for a threefold tight-coincidence requirement [6].The total exposure after these selection criteria is 0.6 t × y.
The same high-energy events can also produce small S2s appearing in subsequent events [24], potentially leading to unaccounted-for correlations between the isolated-S1 and isolated-S2 samples.In order to reduce these correlations, we further require that no S2 signal is found within the first millisecond of the event, and apply a cut on the horizontal spatial distance between the current and previous S2.AC background for S2s down to 80 PE and reduce the isolated-S2 event rate therein to 0.7 mHz.For comparison, the isolated-S2 event rate in [6] was 2.6 mHz for S2s above 100 PE [6].
Selections that require both S1 and S2, such as the fiducial volume and S2 signal width [21] cuts (which depend on the interaction depth Z), are next applied to the combined synthetic AC events.Interactions on the TPC electrodes and in the xenon gas above the liquid surface contribute significantly to the isolated-S2 event rate, motivating a selection in a high-dimensional feature space as in [7].In this analysis, a gradient boosted decision tree (GBDT) [25] ensemble is trained using the scikit-learn package [26] to optimize the signal and AC background discrimination based on the S2 area, the S2 rise time, the fraction of S2 area on the top array of PMTs, and Z.The GBDT selection reduces the AC background by 70 % while accepting ≥ 85 % of 8 B CEνNS events.
A background control region with S2 < 120 PE contains > 50 % of the AC background, and is excluded from the search for 8 B CEνNS due to its low detection probability.After closer inspection of the candidate waveforms in the control region, four events whose S1s contain more than one hit in the same channel, possibly due to afterpulsing of the PMTs [5], were removed.Twenty-three events remain, consistent with the AC background pre-diction of 27.7 ± 1.4 events in the control region.Though the methods above yield a ≤ 5 % uncertainty on the AC background, we conservatively use an uncertainty of 20 % in the analysis to reflect the statistical uncertainty from the control region, but find that the CEνNS search is not strongly dependent on the uncertainty value within this range.Fig. 2 shows the AC model, events failing the GBDT cut, and science data projected onto Z and quantiles of S2 prev /∆t prev .
Neutrons originating from radio-impurities inside detector materials produce NRs in the TPC, but the tight ROI reduces these to 0.039 +0.002 −0.004 events.To limit the electronic recoil (ER) background dominated by β-decays of 214 Pb (a daughter of 222 Rn), we additionally require cS2 b , the S2 area in the bottom array after a positiondependent correction [6], to be < 250 PE.This reduces the ER background to 0.21 ± 0.08 events in the ROI, leading to a 4.2 % absolute acceptance loss for CEνNS.The same simulation procedure described in [15] is used to assess the neutron and ER backgrounds, as well as the associated uncertainties.The selection on cS2 b has negligible effect on the AC background.
In the interpretation of the data, we utilize several features that differ between true S1-S2 events and AC.Lone hits are spread uniformly across the top and bottom PMT arrays, whereas scintillation light from the LXe volume mostly falls on the bottom array.Furthermore, an S1 with more than 2 PE on one PMT is very unlikely to be part of an AC, since most lone hits in XENON1T consist of a single photoelectron.We split the data into six "hit categories" according to the number and arrangement of S1 hits, and the largest hit-area (LHA), listed in Tab.I.
Inference -We analyze the data with a statistical model adapted from [15], with three continuous analysis dimensions; S2, Z, and the quantiles of equal signal acceptance in S2 prev /∆t prev .The likelihood for XENON1T is the product of the likelihoods for each hit category, indexed with i: (1) Here, θ are the nuisance parameters.The extended unbinned likelihood terms L i (Φ, Q y , L y , θ) are of the same form as Eq. ( 20) in [15], and include models in S2, Z and S2 prev /∆t prev for the 8 B CEνNS signal and AC, ER, and neutron backgrounds.The background component rates θ m are constrained by the external measurement terms L m (θ m ).
For the 8 B CEνNS search, the nuisance parameters are the expectation values of the backgrounds, each with a constraint term, as well as the NR response parameters Q y and L y .The total likelihood used in the CEνNS search is the product of L Xe1T , defined in Eq. 1, and external constraints on Q y and L y , as detailed above.The CEνNS discovery significance as well as DM upper limits are computed using the log-likelihood-ratio test statistic compared to toy Monte-Carlo (toy-MC) simulations of the test statistic distribution [15,27].
To construct confidence intervals in Φ, Q y , and L y , we define a test statistic from the sum of profiled loglikelihoods of XENON1T and external constraints.By including external measurements of Q y , we can constrain L y .Since the CEνNS signal spans a narrow energy range, we use a constant L y value to construct the intervals.This allows us to make use of the degeneracy between Φ and the NR response parameters Q y and L y , all three of which primarily affect the CEνNS expectation value.Details on the construction of these confidence intervals may be found in the supplemental material.By including external constraints on Φ, Q y , and L y , this analysis can be used to consider physics processes beyond the Standard Model.We consider a benchmark model in which non-standard neutrino interactions modify the CEνNS cross section [3,28,29].Our confidence interval on Φ assuming the Standard Model cross section can be reinterpreted as a confidence interval on the modified CEνNS cross section if we use the externallymeasured value of Φ.We also consider DM-nucleus interactions, including CEνNS as a background contribution, and Q y and L y as nuisance parameters.We use the same profile construction approach to compute upper limits as [15], including a power-constraint [30].
Results -We estimated the probability of observing a 3σ (2σ) CEνNS excess in this data to be 20 % (50 %) for the nominal (NEST) values of Q y , L y .Inverting the GBDT cut gave an AC-rich validation region that was unblinded first (Tab.I).Background-only goodness-offit (GOF) tests using a binned Poisson likelihood were performed on the validation region, both for the six S1 hit categories and in the continuous analysis space, with p-values of 0.95 and 0.33, respectively, which exceeded the 0.05 validation criterion.The science dataset was unblinded following the successful validation region unblinding.Six events were found, as listed in Tab.I.The events are compatible with the background-only hypothesis, with a CEνNS discovery significance of p > 0.50.The same GOF tests used to assess the validation region unblinding show good agreement, with p = 0.64 and p = 0.72, respectively.The XENON1T confidence interval in Φ, Q y , and L y does not strongly constrain any of the parameters due to the significant correlation in particular between Φ and L y , as shown by the green shaded region in Fig. 3 (top).On the other hand, Φ can be constrained if the external constraints on Q y and L y are included, as shown in the pink region, with a 90 % upper limit on Φ of 1.71 × 10 7 cm −2 s −1 .The blue region in Fig. 3 shows the confidence interval from a combination of the XENON1T likelihood, constraints on Φ [31], and on Q y .The 90 % upper limit on L y (assumed constant over the 0.9 − 1.9 keV energy range) is 8.5 ph/keV.
In the benchmark model of non-standard neutrino interactions considered, the electron neutrino has vector couplings to the up (u) and down (d) quarks of ε dV ee and ε uV ee , respectively [3,28,29].The 90 % confidence interval for ε dV ee and ε uV ee from XENON1T data is shown in light blue in Fig. 4 (top).
The result for a spin-independent DM-nucleus interaction is shown in Fig. 4 (bottom).This constraint improves on previous world-leading limits [6,7] in the mass range between 3 GeV c −2 and 11 GeV c −2 by as much as an order of magnitude.The limit lies at roughly the 15th percentile, reflecting the downwards fluctuation with respect to the background model (including CEνNS), but is not extreme enough to be power-constrained.
Outlook -The XENONnT experiment, currently being commissioned at LNGS, aims to acquire a 20 t × y exposure [12].As the isolated-S1 rate scales up with the larger number of PMTs and the isolated-S2 rate with Qy scaling parameter FIG. 3. Projections of the 90 % confidence volumes in Ly and Φ (top), and in Ly and the Qy interpolation parameter q (bottom).The green area shows constraints using only the XENON1T data.Combining the XENON1T data and external constraints on Qy [16] and Ly [19,32] (shown in black dash-dotted lines) gives the confidence interval shown in pink, and an upper limit on Φ.Conversely, combining the XENON1T data and constraints on Φ [14] and Qy yields the dark blue interval and upper limits on Ly.The dashed white line displays the 68 % confidence interval.Ly is assumed constant in the 8 B CEνNS ROI for these constraints.
the detector surface area, the AC background will be the biggest challenge for the discovery of 8 B CEνNS.
The AC background modeling and discrimination techniques used in this analysis will improve the sensitivity of XENONnT to 8 B CEνNS and low-mass DM.The novel cryogenic liquid circulation system developed to ensure efficient purification in XENONnT will mitigate the reduction of S2s due to impurities, improving the acceptance of low-energy NRs from 8 B neutrinos and DM.Additionally, the data will be analyzed in a triggerless mode to minimize efficiency loss and better understand the AC background.Together with the significantly larger exposure, these techniques give XENONnT strong potential to discover 8 B CEνNS.
The large uncertainty in both Q y and L y will be the dominant systematic in constraining new physics from DM and non-standard neutrino interactions.Improving these uncertainties by calibrating NRs in LXe using insitu low energy neutron sources [40] and dedicated de- Top: Constraints on non-standard vector couplings between the electron neutrino and quarks, where the XENON1T 90 % confidence interval (light blue region) is compared with the results from COHERENT [3,28] (pink and dark red regions) and CHARM [33] (green).Bottom: The 90 % upper limit (blue line) on the spin-independent DM-nucleon cross section σSI as function of DM mass.Dark and light blue areas show the 1σ and 2σ sensitivity bands, and the dashed line the median sensitivity.Green lines show other XENON1T limits on σSI using the threefold tight-coincidence requirement [6] and an analysis using only the ionization signal [7], and other constraints [34][35][36][37][38] are shown in red.The dash-dotted line shows where the probability of a 3σ DM discovery is 90 % for an idealised, extremely low-threshold (3 eV) xenon detector with a 1000 t × y exposure [39].The black dot denotes DM that has a recoil spectrum and rate identical to the 8 B neutrinos.
tectors [16] can crucially improve the sensitivity of nextgeneration experiments to both 8 B CEνNS and light DM.
The S1 and S2 detection efficiencies in the CEνNS ROI cannot easily be measured with a calibration source.Therefore, we use a waveform simulation, which produces PMT waveforms in the CEνNS ROI, to calculate those efficiencies.
Some of the S1s detected by two or more PMTs do not meet the requirement that hits on those PMTs occur within 50 ns.The fraction of the S1s passing this tight-coincidence requirement thus correlates with the S1 width.We use an exponential function to describe the distribution of photons detected by PMTs in the simulation to facilitate tuning of the S1 width.The S1 time distribution is independent of the number of hits in XENON1T data.This allows us to calibrate the exponential function by matching simulated S1s to those in data.
Four more detector effects are included in the simulation: the probability that the PMT photocathode emits two photoelectrons when absorbing one photon, the electronic noise level, the single photoelectron spectrum of the PMTs, and PMT after-pulses.The full simulation process establishes the relation between the number of detected photons and the size of the S1 and S2 [15].
The mean and spread of the S1 width distribution vary with the size of the S1.Simulated waveforms and XENON1T data are processed with the same software.The S1 width parameter in the simulation is tuned to minimize the chi-square between simulated and observed mean width as shown in Fig. 5.
The software trigger efficiency of the S2 varies with its size and the position of the event.Events from the deeper part of the detector produce wider S2s, and have a lower trigger efficiency.Specifically, in waveform simulation, we use effective models to reproduce the diffusion, size, and temporal distribution of ionization signals.Together with the four detector effects mentioned above, the simulation output is compared to background S2s originating on the detector wall in both width and triggered fraction, since wall events have a smaller S2 size due to charge loss.The excellent matching, shown in Fig. 5 and Fig. 6, validates the response of the detector to small S2s.

Signal expectations
From the standard solar model, the energy of solar 8 B neutrinos is below ∼ 20 MeV, giving a maximum momentum transfer q max ∼ 40 MeV, much smaller than the Z boson mass [1].Under this condition, the Standard Model predicts that the tree-level differential CEνNS cross section is given by: where E r is the NR energy, G F is the Fermi constant, M is the target nuclear mass of the recoiling atom, E ν is the incoming neutrino energy, F (E r ) is the nuclear form factor, and Q w is the nuclear weak charge [2].Here, we have neglected the contribution from the hadronic axial-vector current, because the spin-dependent structure factors are negligible compared with spin-independent structure factors for xenon [8].Since M E ν E r , terms of higher order in E r /E ν are dropped as well.
We also consider a non-standard interaction following [28,29], where the weak charge in electron neutrino scattering is replaced by Q w → Q w = N (1 + 2ε uV ee + 4ε dV ee ) + Z(4 sin 2 θ w − 1 + 4ε uV ee + 2ε dV ee ), with two non-standard couplings ε uV ee and ε dV ee .Neutrino oscillation must be included, since our model assumes that only electron neu-trinos have non-zero non-standard interactions.In the energy range of solar 8 B neutrinos, their oscillation to other flavors through interactions with matter in the Sun (the MSW effect) is important.We use the mean value of the MSW-LMA solution in [41] to compute the survival probability P f (E ν ) for the three neutrino flavors f = e, µ, τ .Using Φ = (5.3± 0.2) × 10 6 cm −2 s −1 , the expected CEνNS rate from the solar neutrinos with flavor f = e, µ, τ is in which η(E r ) is the NR acceptance.By varying ε uV ee and ε dV ee , the CEνNS rate for electron neutrino is scaled up or down.Thus the upper limit on Φ can be converted into ε uV ee -ε dV ee space by solving: where • denotes the isotopic average (assuming natural abundances in xenon), and Φ limit = 1.71 × 10 7 cm −2 s −1 is the upper limit on Φ (see Results section).

Details on inference
Since the NR response uncertainty is large, the test statistic distribution for confidence intervals will depend on the true values of Φ, Q y , and L y .To compute unified confidence intervals in the manner of [15], we would have to estimate the distribution of the test statistic using toy-MC computations in these three dimensions.However, the strong degeneracy between these parameters allows us to avoid this extensive computation.Studies of the CEνNS model showed that for the relevant range for this search, the CEνNS distribution could be considered constant with Q y , L y , so that Φ, Q y , and L y all appear in the likelihood only in the expression for the expectation value of detected CEνNS events, µ CEνNS (Φ, Q y , L y ).Therefore, we can compute the profile likelihood ratio and toy-MC estimates of the test statistic distribution in the space of µ CEνNS alone.External constraints on Φ, L y , and Q y are implemented as terms λ F , λ Ly , and λ Qy , corresponding to the profiled log-likelihood-ratios for Gaussian measurements of each parameter.We combine the XENON1T profiled loglikelihood ratio λ Xe1T (µ CEνNS (Φ, Q y , L y )) and different combinations of external constraints into test statistics Λ: Λ A (Φ, Q y , L y ) =λ Xe1T (µ CEνNS (Φ, Q y , L y )) Λ B (Φ, Q y , L y ) =λ Xe1T (µ CEνNS (Φ, Q y , L y ))+ λ Qy (Q y ) + λ CEνNS (Φ) Λ C (Φ, Q y , L y ) =λ Xe1T (µ CEνNS (Φ, Q y , L y ))+ λ Qy (Q y ) + λ Ly (L y ). ( For each Λ, the toy-MC results of λ Xe1T (µ CEνNS ) is combined with random realizations of the other profiled likelihoods in a grid of Φ, Q y , and L y to provide the 90th percentile of Λ for each point in parameter space, which is compared with Λ(Φ, Q y , L y ) to construct confidence intervals.The test statistic Λ A , shown in green in Fig. 3, represents the confidence interval using the XENON1T data only.The strong anti-correlation between Φ and L y is apparent in Fig. 3 (top).To compute a confidence interval on L y , we include constraints on Q y [16] and Φ [31] in Λ B , shown in dark blue in Fig. 3. Last, combining XENON1T, and constraints on Q y [16] and L y [19,32] into Λ C yields an upper limit on the CEνNS interaction rate Φ.

FIG. 4 .
FIG.4.Constraints on new physics using XENON1T data.Top: Constraints on non-standard vector couplings between the electron neutrino and quarks, where the XENON1T 90 % confidence interval (light blue region) is compared with the results from COHERENT[3,28] (pink and dark red regions) and CHARM[33] (green).Bottom: The 90 % upper limit (blue line) on the spin-independent DM-nucleon cross section σSI as function of DM mass.Dark and light blue areas show the 1σ and 2σ sensitivity bands, and the dashed line the median sensitivity.Green lines show other XENON1T limits on σSI using the threefold tight-coincidence requirement[6] and an analysis using only the ionization signal[7], and other constraints[34][35][36][37][38] are shown in red.The dash-dotted line shows where the probability of a 3σ DM discovery is 90 % for an idealised, extremely low-threshold (3 eV) xenon detector with a 1000 t × y exposure[39].The black dot denotes DM that has a recoil spectrum and rate identical to the 8 B neutrinos.

FIG. 5 .FIG. 6 .
FIG. 5. Matching of the S1 and S2 properties of the waveform simulation and detector data.The plots show (a) the interquartile range (IQR), the range of time covering the central 50 % area, as a function of S1 size, (b) IQR of S2 < 200 PE as a function of depth (Z), and (c) the fraction of signal detected by the top PMT array in each S2 (−10 cm < Z < 90 cm).The dots denote quantiles of the detector data, corresponding to ± 2 σ (blue), ± 1 σ (green), and median (black).Colored bands show the same quantiles with the simulation data.Both detector and simulation data are events close to the wall, with the same position, S1 size, and S2 size distributions.
These selections, together with the selection on S2 prev /∆t prev , allow us to model the FIG.2.Events in the science dataset (pink circles) and the AC-enriched validation region (blue crosses) projected onto Z and the quantile of the S2prev/∆tprev value for NR signals.The AC model is shown in gray.Smaller panels show the projection of the model and data onto each axis, as well as the 8 B CEνNS model (green dashed), normalised to its upper limit.The AC-enriched region data in blue has a slightly different Z-distribution due the inverted GBDT cut, but is included for illustration, scaled by 0.36, the ratio of expected AC events in each dataset.

TABLE I .
Signal and background expectation values and observed event counts in six S1 hit classes based on number of S1 PMT hits in total, the number in the top array (TA), and the largest hit-area (LHA).Expectation values are computed for the nominal (NEST best-fit) Qy, Ly, and CEνNS flux for the 0.6 t × y exposure.The neutron background is not shown separately in the table as it is significantly smaller than AC and ER, but is included in the background total.The last two columns show the result from the AC validation region, where the expectation value is dominated (97 %) by AC events, with the remainder from the expected 8 B CEνNS leakage.The relative uncertainties on the background and signal expectations are described in the text.