A Review of Basic Energy Reconstruction Techniques in Liquid Xenon and Argon Detectors for Dark Matter and Neutrino Physics Using NEST
M. Szydagis, G.A. Block, C. Farquhar, A.J. Flesher, E.S. Kozlova, C. Levy, E.A. Mangus, M. Mooney, J. Mueller, G.R.C. Rischbieter, A.K. Schwartz
AArticle
A Review of Basic Energy Reconstruction Techniques inLiquid Xenon and Argon Detectors for Dark Matter andNeutrino Physics Using NEST
M. Szydagis * , G.A. Block , C. Farquhar , A.J. Flesher , E.S. Kozlova , C. Levy ,E.A. Mangus , M. Mooney , J. Mueller , G.R.C. Rischbieter , and A.K. Schwartz Department of Physics, University at Albany SUNY, 1400 Washington Ave., Albany, NY 12222-0100 USA Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, NY 12180 USA Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre “Kurchatov Institute”, Moscow,117218, Russian Federation Colorado State University, Department of Physics, Fort Collins, CO 80523 USA ANDRO Computational Solutions, LLC, Rome, NY 13440 and the College of St. Rose, Albany, NY 12203 USA Northrop Grumman, Goddard Space Flight Center, Greenbelt, MD 20771 USA Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854 USA National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, 115409, Russian Federation * Correspondence: [email protected]: December 1, 2020;
Abstract:
Detectors based upon the noble elements, especially liquid xenon as well as liquid argon,as both single- and dual-phase types, require reconstruction of the energies of interacting particles,both in the field of direct detection of dark matter (WIMPs, axions, et al.) and in neutrino physics.Experimentalists, as well as theorists who reanalyze/reinterpret experimental data, have used a fewdifferent techniques over the past few decades. In this paper, we review techniques based on solely theprimary scintillation channel, the ionization or secondary channel available at non-zero drift electricfields, and combined techniques that include a simple linear combination and weighted averages, witha brief discussion of the application of profile likelihood, maximum likelihood, and machine learning.Comparing results for electron recoils (beta and gamma interactions) and nuclear recoils (primarilyfrom neutrons) from the NEST simulation to available data, we confirm that combining all availableinformation generates higher-precision means, lower widths (energy resolution), and more symmetricshapes (approximately Gaussian) especially at keV-scale energies, with the symmetry even greater whenthresholding is addressed. Near thresholds, bias from upward fluctuations matters. For MeV-GeV scales,if only one channel is utilized, an ionization-only-based energy scale outperforms scintillation; channelcombination remains beneficial. We discuss what major collaborations use.
Keywords: energy reconstruction; xenon; argon; dark matter; neutrino physics; particle detectors
1. Introduction
The noble elements especially xenon (Xe) and argon (Ar) as liquids have been instrumental in thefield of dark matter (DM) direct detection, focused on identifying the missing ∼
25% of the mass-energycontent of the universe. They have also been key for neutrinos. In the former case, Xe [1–3] and Ar [4,5]are each used by distinct large collaborations, and used both to search for continuous spectra, such asthe approximate falling exponential expected from the traditional WIMP (Weakly Interacting MassiveParticle) [6], or monoenergetic peaks expected from dark photons or bosonic super-WIMPs [7]. In thelatter case, argon is used in long- and short-baseline oscillation studies [8,9] and xenon in the search forneutrinoless double-beta decay, as either a liquid [10] or a gas [11]. In all of these cases, there is a clearneed for high accuracy and high precision in energy reconstruction and good energy resolution in orderto identify signals and backgrounds, and calibrate the detectors. Combining the data with high-fidelity a r X i v : . [ h e p - e x ] F e b of 44 Monte Carlo (MC) simulations can aid in this task. Xe and Ar produce scintillation light, and when anexternal electric field is applied then ionization electrons can be extracted as well. In a dual-phase timeprojection chamber (TPC) a gas stage converts the ionization into a secondary scintillation pulse [12] whilea single-phase TPC reads out the charge directly [13,14]. Energy scales have been based in the past andpresent on the scintillation, on the ionization, and on their combination.In this work, we will be reviewing each of these methods, contrasting them and enumerating theirstrengths and weaknesses, in terms of the mean, median, and mode ( e . g . Gaussian peak centroid) ofreconstructed energy best matching the true energy (MC truth energies and/or monoenergetic calibrationpeaks), the width, and the shape (symmetry). Multiple types of particles will be covered, addressingscattering from atomic electrons and nuclei, electron recoil (ER) and nuclear recoil (NR) respectively,and recoil energies from sub-keV up to GeV, from DM-WIMP-induced NR or coherent elastic neutrinonucleus scattering (CE ν NS), to neutrino-induced ER. The summaries in each section make idealizedrecommendations, with detector-dependent caveats, for future DM/neutrino projects.
2. Methods
Examples of usages of each of the possible energy scale definitions are taken from empirical datawherever possible, but also compared to NEST (Noble Element Simulation Technique), which is also usedby itself where data are lacking. NEST is a global, experiment- and detector-independent MC frameworkthat allows simulation of scintillation and ionization yield averages and resolutions as functions ofincoming or deposited energy, electric field, and interaction type [15].The values of detector-specific parameters also need to be known in order to permit NEST to simulatethe detectors effects for a specific experiment. The most important numbers are g , g , and the magnitudesof the drift and extraction electric fields, if applicable. g and g are respectively defined as the gains ofthe primary and secondary scintillation channels, the latter from ionization (again, only if applicable). g is always between 0 and 1, and is an efficiency which combines the quantum efficiencies of one’sphoto-sensors with the geometric light collection efficiency. (It is also known as the photon detectionefficiency.) It can include or exclude, depending on choice of units, the probability for certain photondetectors (especially in the vacuum ultraviolet or VUV) to produce more than one photoelectron (phe) fora single incoming photon [16]. Typical values across all experiments using Xe or Ar are ∼ g is a combination of the electron extraction efficiency for a two-phase TPC with the gasgain, i . e . the number of photons produced per extracted electron times the photon detection efficiency inthe gas phase [24]. A typical value is ∼ p e ), where p e is the probabilityof producing two (photo)electrons, typically 0.1-0.3, depending on the manufacturer, temperature, andindividual phototube: phd = phe / ( + p e ) , while a similar translation applies to the g . While takingthis effect into account is ideal for the resolving of peaks and achieving the best possible backgrounddiscrimination for one’s final analyses, the convention for how the final results are plotted varies byexperimental collaboration, making comparisons more difficult (XENON and DARWIN prefer phe or PEbut LUX and LZ prefer phd). PIXeY’s 2-phe probability was reported as 17.5% [25], implying that divisionby 1.175 would convert phe into phd.We define N ph and N e − , as the original numbers of photons and electrons generated from aninteraction site, determined by MC truth (integer) or empirical reconstruction (float). N q is their sum. of 44 In data, or advanced MC including detector effects like finite detection efficiencies not just mean yields: N ph = S c / g and N e − = S c / g . S1 and S2 are the primary and secondary scintillation pulse areas.Subscript ’c’ denotes correction, primarily for XYZ-position effects, as light collection efficiency maydepend significantly on 3D position, especially in a large-scale detector [26]. The energy dependence isintrinsic to the element, unrelated to the position inside a particular detector. It is thus useful to also definetwo additional terms, L y and Q y , which respectively refer to the N ph and N e − per unit of energy.Our default guiding formula, at least for combined energy-scale reconstruction, is therefore: ( ) E = N q W q L ( E ) = ( N ph + N e − ) W q L ( E ) = ( S c g + S c g ) W q L ( E ) . L is Lindhard factor, quantifying E “lost” (if a detector cannot see phonons) into heat (atomic motion)instead of observable quanta. Called also “quenching” historically, that word is not precise: quanta arenot being quenched per se but not being created ab initio , unlike in quenching by impurities or ionizationdensity. It depends on E , making Eqn. 1 circular. Circularity can be avoided by a good MC model likeNEST, and by quasi-monoenergetic NR data, as in the LUX D-D analysis [27]. For ER, L is taken to be 1.0,not implying no heat loss but an approximately constant loss as a function of E that can be “rolled into”the definition of work function, essentially raising it. For neutrino experiments, E depositions are tracksnot point-like, and dE / dx (energy loss per unit of distance) is more relevant.The L quantifies the effectiveness of an initial NR at producing more elastic recoils as secondaryinteractions not inelastic, i.e. , atomic excitations/ionizations. It can be modeled in other/better ways thanLindhard’s, expected to break down at low E ’s, as seen in Si/Ge [28]. It should not be confused with L e f f used for S1 [17,29–31] at zero field, and not accounting for Co 122 keV γ -rays not being representative ofeven ER yields, at different E ’s [32,33]. ( L e f f was the ratio of NR to ER light yields.) L ( E ) can be thought of as merging the scintillation and ionization efficiencies (whereas L e f f is onlythe scintillation efficiency, again compared to ER’s L y ). However, as with the word quenching, it is betterto avoid this terminology; it can be confused with the efficiency set in DAQ and/or data analysis, by forexample requiring a certain number of PMTs to fire to count an S1 (2-fold coincidence for example in LUX:see Fig. 4 later, ER, where this, g (cid:28)
1, and other effects lead to a threshold). The E within the L -factoris the true energy of a nucleus recoiling from a neutron (or ν coherently, or DM hopefully in the future).When quoting imperfect reconstructed energy using Eqn. 1, with 0 < L <
1, the standard unit is keV nr tocontrast with the unit defined assuming L = ee .The subscript ’q’ indicates that the W value is not based on scintillation or ionization alone. W q iseffectively an average over microphysical processes producing excited/ionized atoms. We do not describethem, as they are within other works [34–36], nor establish NEST’s accuracy here, using it for conveniencewhere data are lacking. The physical details and how NEST captures them are beyond the scope of thispaper. In this section in particular we summarize established methods [32,37].At zero field one only has access to the S1, and for specialized searches for (sub-)GeV DM [38,39] toonly S2 due to the low energies involved, as the ionization i . e . charge yield is typically larger and easier todetect, even as E goes to zero. The formula correspondingly morphs into one of these: ( ) E = N ph L y = S c g L y ( E , E ) OR ( ) E = N e − Q y = S c g Q y ( E , E ) ,where L y = N ph / E and Q y = N e − / E are functions of energy E and field E . Each differ for ER andNR; they are not fixed as W q was, for ER. The challenge of E reconstruction increases via an inherentnon-linearity: e . g . 2x the E does not mean 2x the light or charge as it does with N q at least for ER. Whenconsidering resolution, this causes deviation from the Poisson expectation of 1/ √ E improvement withhigher E , which only applies for the combined scale (1/ (cid:112) N q ). A more general power law then worksbest [40–42]. In LXe (liquid xenon) the fact L y is not flat vs. E was first demonstrated by Obodovskii of 44 & Ospanov [43] for ER (implying for fixed W that ER Q y is also not constant) and by Aprile et al.for NR Q y [44,45] but not well known in the DM field for ER background at least until much laterpublications [33,46]. In the case of experiments like EXO (0 νββ decay) and DUNE (long-baseline ν ’s) usingXe/Ar, only the first half of (3) applies, as they measure Q directly in liquid using wire readout planes,instead of in gas. Also, for combined E (Eqn. 1) especially, S2 can be defined using a subset of photonsensors instead of all. A cylindrical TPC typically has two arrays, one at each end. The bottom one alone(subscript ’b’ for differentiation from total S2) may be used for E reconstruction as in [47] to adjust forlight loss created by inoperative phototubes in the gas, or saturation. Lastly, g can be vastly smaller inkilotonne-scale ν experiments, unlike the range quoted earlier for DM: they rely on Q y .For the purposes of reproducibility we note that all of the work presented here uses the latest stableNEST release at time of writing: Version 2.2.0 [48] for which the default detector parameter file is designedto mimic the first science run of LUX [49] but which we modify as needed to reproduce other experiments,focusing again on g , g , and drift electric field E as the three most salient inputs. The main assumptions utilized in NEST to reproduce efficiencies are briefly explained below.
1. A Fano-like factor sets variation in total quanta, with a binomial distribution for differentiating excitons/ions(inelastic scattering). In LXe it is not sub-Poissonian as in GXe, as experimentally verified in each phase [50].2. Recombination fluctuations [51–53]: the “slosh” of N ph vs. N e − caused by recombination probability forionization e − ’s, which may either recombine to make more S1, or escape to make S2. These are worse ( i . e . larger)than expected naïvely (non-binomial). This is distinct from Fano factor, and canceled by combined E . The above are general, but the below depend on the detector, all combining into the final efficiency. g is used to define a binomial distribution for the S1 photon detection efficiency with < S > = g N ph .2. For an S1 to be above the trigger threshold, most experiments require that O (0.1) phe must be observed in N PMTs for N -fold coincidence, where usually N = O (0.1) phe is also modeled.3. The pulse areas of single phe are assumed to follow a truncated (negative phe are not possible) Gaussiandistribution, with O (10%) resolution differing by photon-sensor, but a detector-wide average is used for NEST,as an approximation. If single phe detection efficiency is reported, it can be used instead of a threshold appliedto a Gaussian random number generator, thus taking non-Gaussianity and other detector-specific idiosyncrasiesinto account. This and others numbers are collected from arXiv, publications, and theses.4. Drifting, diffusing electrons are removed via an exponential electron lifetime, and are assumed to follow abinomial extraction efficiency, while the number of photons produced per surviving extracted electron dependson the gas density, electroluminescence electric field, and gas gap size, in a 2-phase TPC [54,55].5. A special Fano factor, typically also > O (100) phe removes the lowest-energy events, to avoid few-electron backgrounds [57].6. S1 and S2 XYZ variation is simulated in NEST if provided in analytical form, then realistically corrected backout, based upon finite position resolution, not MC truth positions, thus allowing not only for correct means butcorrect widths. (Z or drift correction applies only to S1, handled for S2 by the electron lifetime.)7. N ph falls while N e − rises with drift field in anti-correlated fashion, and fields can be non-uniform. A final step of noise is applied as an empirical smearing to the S1 and S2 pulse areas to match realisticexperimental data; however, the above lists capture the vast majority of fluctuations that can shift thelow-energy efficiency higher or lower. Additional noise is typically at a level of O (1%) from unknownsources, but likely due to position correction imperfection and other analysis-specific effects, discussed in of 44 [24,36,58]. This is uncorrelated noise, as it is applied separately to S1 and S2, while the variation inducedby the Fano factor (Step 1 in first list) is correlated “noise” due to raising S1 and S2 together, and therecombination fluctuations constitute anti-correlated noise, as in raising S1 they lower S2, and vice versa.All fluctuations can move events above and/or below nominal thresholds.All steps above are uncertain especially when it comes to a simulation software package such asNEST. It would be infeasible to discuss and address all uncertainties. Thus, we will mention only one thatis often largest. The N ex and N i , followed by N ph and N e − , produced at Step (1.) in the first list above,depend on particle, energy, field, density via temperature and pressure, and phase, and at the lowestenergies (sub-keV especially, and in particular for NRs) there is a non-negligible systematic uncertaintyfrom the values assumed for the average yields ( L y and Q y ) which are always the first step in NESTmodeling. For ER Q y , the discrepancy between different data sets and models is as much as 20% below1 keV, as illustrated by contrasting NEST [58] with PIXeY Ar data [59], x-rays in LUX [60], and H inXENON100 [61]. L y = E threshold.”For the purposes of this review paper, what is of greatest importance is that the assumptions, of thedefault NEST yields models, are not varied, when comparing different energy reconstruction techniques,so that at the very least a robust comparison can be made among them. That being said, we stress theaccuracy of NEST in reproducing efficiency even for publications where the authors have no access to theoriginal data is high (not only LUX [62]). XENON1T is an excellent example [58].
3. Results
Xe is examined first (ER then NR) followed by Ar. For Xe, the present-day relevant experimentsseeking DM for whom this review is most pertinent include: LZ, XENON, PandaX. The use of LAris divided, present and past, across DEAP, CLEAN, ArDM, and DarkSide (first two single-phase andzero field, latter two dual-phase and non-zero electric field) on the DM front, and DUNE, MicroBooNE,ArgoNeuT, ICARUS, plus many others, studying neutrinos. Enriched LXe is used by nEXO, a TPC butonly one phase, and NEXT (GXe) for the hunt for 0 νββ decays. α ’s and heavier ions different from themedium, with properties like additional quenching, modify the E reconstruction formulae, but we willonly focus on basic ER and NR; other recoil types are already covered elsewhere [15,63]. Low Energy: keV-scale (Dark Matter Background, Signal) Basic Recon of Mono- E Peaks
The term electron recoil or ER refers to interactions with the electron cloud, such as from betaemissions and the Compton scattering or photoabsorption of gamma rays. In a WIMP search, ER is theprimary background, but in a more general DM (or exotic physics) search a monoenergetic peak or evencontinuous ER spectrum can be the signal [64]. To illustrate the differences among the S1-only, S2-only orQ-only, and combined- E scales for reconstruction the first example is the lowest-energy ER calibrationpeak available at time of writing for LXe where we have S1 and S2 still: the electron capture decay of Arat 2.82 keV. It is also a timely example due to the recent XENON1T ER result [42,58].While this E is not often in the regime of efficiency drop, we do address it in this section. Our source ofdata here was the seminal work led by McKinsey et al. at Yale/Berkeley [59] who constructed a small-scalecalibration chamber, PIXeY, with g = ± g = ( ± ) ∗ = ± e − (extraction efficiency times the single- e − pulse area). To replicate PIXeY preciselywith NEST in Fig. 1, we use g = g = σ higher. We studied only 198 V/cm. W q was taken to be 13.5 eV, between Dahl [36] and neriX [65] measurements. In all plots, keV ee means of 44 reconstructed energy ( ee standing for electron equivalent, for when NR is translated into this scale) asopposed to MC truth, or a known single E from a peak, reported in keV sans subscript.While lower- E calibrations exist than 2.8 keV, this is the lowest where S1 and S2 are identifiedseparately. Others become S2-only [60]. Fig. 1a demonstrates that the S1-only scale, used primarily onXENON10 [29] and continuing on in a subset of XENON100 analyses [66], performs the poorest, with anenergy resolution σ / µ of 38.63% for data (38.59 NEST) in red. (Both XENON10/100 had similar g ’s toPIXeY, but slightly lower, at ∼ E ’s being comprised of upward S1 fluctuations above nominal S1 threshold, due to finite g .An experimenter measures the right tail of S1s essentially.Nevertheless, it is possible to mitigate S1 effects, still include S1 in the E calculation, and obtain thebest possible resolution. One way is to fit a skew Gaussian (parameters explained in [53] and [58]): ( ) y = Ae − ( x − ξ ) ω [ + er f ( α x − ξω √ )] While this has been done for bins in S2 vs. S1 [53] and once for combined E [58] it is most effectivefor S1: see the improvement in Fig. 1a (blue vs. red). A skew fit, while including an error function er f and similar to the equation used in [59] that should account for triggering, still misses some points, askeV-level S1 becomes non-Gaussian and non-symmetric due to trigger efficiency dropping below 100%.In plot (c) however, the reduced χ drops from O (100) for both data and NEST to 2.6 for the 1.5-5 keV ee range, still too high due to features in the data not captured even by a skew-normal fit, but more sensible.Asymmetries arise from both thresholding bias [27] and microphysics [53,58].3.1.2. More Advanced Energy Reconstruction Strategies, from keV to MeV Scales, and Resolution
A superior mitigation strategy can be found upon realization that the optimal weights for the S1and S2 pulse areas are no longer simply g and g at the O (keV) scale. We can recast this statement interms of the (n)EXO-style combined-energy scale first developed by Conti [51]: instead of using a g and g it defines what is known as an angle of anti-correlation for summing S1 plus Q or S2. As energydecreases the angle becomes energy-dependent instead of being fixed as tan − ( g / g ) [40] and thus nolonger respecting “perfect” anti-correlation of quanta, with N ph and N e − always summing to N q = E / W q .Note there is no evidence of anti-correlation breakdown at least in LXe above 1 keV: this effect is caused byinability to reconstruct N ph well in data due to dropping S1 efficiency, as first suggested by Szydagis (2012)and first publicly applied in the PIXeY Ar paper [59]. ( ) E (cid:48) = ( w ( E ) S c g + S c g ) W q × w ( w ) Parameter w decreases the weight assigned to S1 for low E ’s, countering thresholding; one couldincrease the S2 weight, but this is equivalent. Multiplying S1 by one weight, and S2 by another wouldbe redundant. Instead, one weight is applied to S1, and a second weight w to the formula as a wholeto bring the average of the energy being reconstructed back to the correct mean after the shift caused byadding w , while simultaneously correcting for any efficiency bias near the S1 and/or S2 thresholds. It isnot technically independent then, thus written in Eqn. 5 as a function of w , which itself is a function ofenergy. To avoid a circular reference, Eqn. 1 can be used to determine its energy dependence, for use in5, and the process can be iterative, defining E” after E’, etc. Knowledge of the proper weights a priori isachievable via MC. of 44 (a) (b)(c) (d) data NEST data
NEST
Figure 1.
Reconstruction of the 2.8224 keV Ar peak in the PIXeY detector [59] compared to NEST. Realdata always hollow black circles, NEST MC green squares. Gaussian fits in red, skew Gaussian (better fit)in blue, with the fits to data in long dash and NEST in short (indistinguishable due to NEST’s fidelity).Number of events in data 7.4 × , while 9.3 × in the MC, after all cuts ( i . e . all thresholds). (a.) Original,non-linear S1-only E scale used for LXe. Bins with non-zero counts begin very suddenly at the left inboth NEST and data due to a cut-off created by triggering only on 3-fold PMT coincidence, and otherthreshold requirements. The results are highly skewed, driving the asymmetry within the combined-energyfit later. (b.) S2-only, which is quite symmetric, so that Gaussian and skew-Gaussian fits overlap. (c.) Thecombined-energy scale in common use now for LXe DM detectors. Gaussian fits in red are clearly poorercompared to skew fits, diverging from the histogram in the cases of NEST and data alike. (d.) An optimizedcombination for energy, as done on PIXeY. Both NEST and data, and Gaussian and skew-Gaussian fits alike,have all become indistinguishable for this stage. The best-fit mean energy has shifted from 3.03 keV in (c)to 2.82 keV for (d). This improvement in precision is also reflected in the sum of the mean quanta from (a)and (b) matching (d), but not (c), which is too high. The skew parameter α decreases from 3 for S1 only (a)to 2 for the combined scale in (c) and 1 in (b,d) of 44 Without an MC like NEST tuned on earlier calibration data, it is possible to empirically determine thetwo weights by calibrating an experiment with monoenergetic peaks ( e − capture, x-ray, gamma-ray). In thecase of PIXeY’s Ar measurement, the values which minimize the width of the Ar peak in reconstructedenergy (optimum resolution) are w = w = ∼ ee (again, higher because of triggering on high-S1 fluctuations) to 2.83(2.81) much closer to the true value of 2.82, while the asymmetry in the histogram has nearly vanished,with the best-fit skew Gaussian possessing a positive (right-hand) skewness parameter α < ∼ i . e . plot 1c’s method, but a PLR(Profile Likelihood Ratio) analysis effectively takes into account energy bias by relying on NEST to producenon-analytic 2D PDFs for both background and signal, relying on MC truth energy converted to S1 andS2, not reconstructed energy [67]. XENON’s own MCs for its PLR perform the same function, taking MCtruth and/or calibrations as input, and outputting (S1, S2) PDFs mimicking data [68].Many possible enhancements exist, like Maximum Likelihood [69] and Machine Learning [70]. Thesecan take more than S1 and S2 into account, e . g . bypassing calibrated 3D corrections, feeding raw S1 & S2plus positions into an artificial neural network (ANN) or Boosted Decision Tree (BDT) from which XYZdependence emerges, given sufficient training. Ernst and Carrera suggest that it is possible to determinehow much is sufficient [71]. Some examples of additional training variables include the E -dependent S1pulse shape, usable given sufficient statistics [54,72], as well as breakdown of pulse areas into top andbottom arrays, capitalizing on anti-correlation of top vs. bottom light similar to that of S1 vs. S2, as usedearly on LUX [73], good for detectors sans S2 (0 V/cm). However, idiosyncrasies of individual detectorsmake it difficult to review such methods, which still rely on S1 and S2 as the two most important variablesregardless. ANNs/BDTs are best trained by a combination of S1s and S2s from data and MC, per analysis,and have so far never been applied at < E (cid:48) (Eqn. 5). To broaden applicability to more detectors, wealso consider variants. Fig. 2a shows S1-only in red and S2-only in cyan. The dashed red line illustrateshow the S1 scale is poorer (the effect propagates into combined energy) when one does not account forthe so-called “2-phe effect,” mentioned earlier [16]. Accounting for this via dividing it out improves theresolution, as the additional phe do not provide any new information on the original number of photonsproduced N ph , even though they may be useful in lowering threshold and increasing the sensitivity tolower-mass DM [74]. The solid red NEST line demonstrates the improvement achieved in doing this, plusattempting to reconstruct the integer numbers of photons hitting the photomultiplier tubes (PMTs), insteadof only reporting S1 pulse areas. This technique is known as photon counting or spike counting [62] and iseasy/feasible only at low E . More importantly than the slight improvement in energy resolution, at onlythe lowest energies ( <
10 keV), this reduces the leakage of background ER events into the WIMP (NR)region in S2 vs. S1 [18]. All points plotted are defined as raw σ / µ , but comparable results can be achievedwith Gaussian/skew-fit centroids or medians.Cyan lines represent S2, which as seen before can be better than S1 or even combined- E scales, butonly at O (1) keV. It is at least comparable, which is important given the historical use of only S1 for E evenin 2-phase TPCs with both channels, and continued usage for gas-less regions like the skin vetos of LZ and of 44 (a) S1 (photoelectrons) NESTS1 (spike counting)S2 (O(1) ms e - lifetime)S2 (100 μ s e - lifetime)data (LUX 2016) ~180 V/cm combined- E scale combined (comb) NESTcomb (no noise)comb (uniform field)optimized comb NEST data (neriX)480 V/cm E-fieldNEST (b) Figure 2.
Review of E resolutions and means. (a.) Resolution vs. E for LUX monoenergetic calibration plusbackground [52]. Only combined resolutions published (black) but S1 (red) and S2 (cyan) scales includedfrom NEST to show they are mutually comparable at O (10-1000) keV. The lowest- E point is optimizedas done in PIXeY, so anomalously good (low). NEST combined scale blue (below S2 only in cyan exceptfor Ar) and optimized gold. w in optimal scale varies from 0.26 to 1.0 from 2.8 to 662 keV, while w falls from 1.45 to 1.00. (Lines are guides not fits.) (b.) Data from neriX (Columbia’s small-scale calibrationchamber, like PIXeY) as black points vs. measured recoil energies from Compton scatters [65] comparedto NEST in blue vs. true energy known from MC, showing consistent deviation for both in reconstructedenergies for a combined but non-optimized scale due to threshold bias (weights as used for NEST in goldin (a) correcting for this not applied purposely in blue in (b) to show this effect). XENONnT. For S2, it is critical to understand the limitations, especially in low-mass-DM experiments likeLBECA, where it is the only channel used. It can suffer from poor drift e − lifetime (impurities), incompleteextraction at a liquid-gas interface due to fields being too low, or both. The former effect (same as latter) isshown by the dash vs. solid cyan. Even when lifetime and extraction are known, along with single- e − pulse size, low values lead to high S2 area variation, although the effect is muted above 50 keV. The41.55 keV “hiccups” are m Kr, a combination of 2 decays, at 9.4 and 32.1 keV [75]. An inverse square rootis not a good fit to the S2 or S1 alone and not included; it is due to incomplete accounting of quanta, also tolinear noise flattening the curves. Such noise impacts higher E ’s more and is defined in detail in Section 4.3of [36] and Section III.A of [58]. As seen in the ∼ straight lines in log-log, a power law (often plus constantfor noise) is reasonable for combined E (blue) but below ∼ E − breaks down, unless the poweris free, preventing extrapolation from 10-100+ keV down to where behavior may even be non-analytic,and E resolution ill-defined.The NEST combined scale is in solid blue in Fig. 2a compared to LUX data from its first science runas black circles. LUX used the same combined scale, which again is clearly advantageous compared tosingle-channel methods, with g = ± g = ± e.g. ,imperfect position corrections). This is modeled as only 1.4% for LUX. It is typically O (1%) [36,58]. Second,respectively, by simulating a uniform electric field, when the real field varied with position, though notsignificantly in LUX’s first WIMP search run (180 V/cm average) and the (much larger) variation wastaken into account in the second [77]. The last few highest-energy points in data (black) do not overlapwith MC due to not fully accounting for PMT saturation (S2 clipping) above 500 keV.The advantages of the optimal scale (gold) disappear rapidly above 10 keV, comparing gold to blue.There is a benefit to this. It means that at sufficiently high energies the rotating/re-weighting of a peak in S1 and S2 to find the optimal resolution results in a derivation of g and g [49]. This abrogates the need formultiple peaks, arranged in S2 vs. S1 (means) in what is known as the Doke plot. Such a plot is a straightline due to the anti-correlation between N ph and N e − for ER [78] shown to work across at least four ordersof magnitude in energy, and different fields [36,62,79,80]. Alternatively, if studies of anti-correlation bothwithin peaks and across peaks for a given analysis in a certain experiment are possible, then these twomethods for deriving the S1 and S2 gains can serve as cross-checks, on top of NEST comparisons andknown-spectrum reproduction such as that from tritium betas [76]. As explained in the caption of Fig. 2,the S1 weight w is decreasing toward 0 with decreasing E ’s while w increases to compensate, but withincreasing E ’s both w ’s asymptote to 1.0, as expected.In the second plot plane (b) we focus on the mean instead of the width (resolution) demonstratingexplicitly with both data from Compton scattering in black [65] and our NEST MCs (despite significantuncertainties) that the thresholding effects raise the reconstructed energy significantly above the truevalue. This phenomenon becomes most prevalent in the sub-keV regime, however, where resolutionbecomes ill-defined due to individual photon and electron quanta becoming resolvable, generating amultiple-peak structure [27]. The peaks become not just skewed-Gaussian, but entirely non-Gaussian, oreven non-analytic [81]. For this reason, Fig. 2a stops at 2 keV on the x-axis. But Fig. 2b continues belowthat, focused on mean ( i . e . ratio of reconstructed over known energy) not width however. We switch toneriX from LUX here, as LUX does not have a relevant plot published with which we can compare, anddid not have direct, quasi-monoenergetic measurements below 1 keV. (Nevertheless, due to similar g ’sand g ’s in these and most experiments the results should be quite general.) Data uncertainties are drivenin x ( E axis) by finite resolution in the Ge detector used for independent energy determination, and in yby uncertainties in neriX’s g and g (0.105 ± + − phe/ e − ). NEST uncertaintiesare large only at sub-keV, and are not statistical due to large simulations. Instead they are due to theuncertainty on how to define a central value, using a mean or median or attempted Gaussian fit, due tothe multi-peak effect mentioned (photon and e − discretization).At low energy the benefits of not just a combined but optimally-combined (re-weighted) scale aresignificant: not just a built-in erasure due to w of the growing discrepancy between the reconstructedand real values of energy illustrated effectively in Fig. 2b (see also neriX’s Fig. 7 [65]) but a reduction inwidth that was 50% (relative) for Ar in both PIXeY and LUX. Lastly, as illustrated in Fig. 1d the shapebecomes more symmetric at individual energies, with the skew nearly disappearing. While this mattersmore for monoenergetic ER peak searches (for axion-like particles or ALPs, bosonic WIMPs, et al.) a benefitfor a WIMP search, or for any analysis in fact, is better determination of the g and g through tighterwindowing around single-energy calibration lines in 2D, in S2 vs. S1, which can occur iteratively, reducingthe errors on g and g (5-10% typical) that often drive systematic uncertainties on both yield analysesand final physics results, especially in terms of S1 and S2 thresholds [18,58,76]. The only disadvantageis loss of the field-independence a combined scale usually has, as the yields change with field. As mostexperiments run at only one electric field however, that is not a true drawback.3.1.3. High Energy: The MeV Scale (Neutrinoless Double-Beta Decay)
Far from the hard thresholds, we turn our attention next to 0 νββ decay. Searches for this require greatresolution for good background discrimination, at Q ββ = Xe specifically [82]. Whileresolution naturally improves with E due to the greater numbers of quanta produced, effects such as PMTsaturation and different noise sources, including position-dependent effects, become more prominent.While machine learning can help a great deal as done on EXO-200 especially with detector-specificidiosyncrasies [70] the analytic optimum scale becomes degenerate with combined E above 0.1 MeV evenalready as illustrated earlier. Table 1 reviews the resolutions achieved in actual experiments: projections of future performance e . g . for LZ [83] are not included, in order to showcase only what has been demonstrated,or extrapolated with σ / E ∝ √ E (+ optional constant).In EXO, in its references cited below, a richer formulation was adopted: σ = a + bE + cE . Itconsiders more detector noise sources. For a = c =
0, it simplifies to σ = bE or σ / E = √ b / E . Table 1.
Survey of experimentally achieved energy resolutions at Q ββ or very close to it (for instance,2.6 MeV calibration). Entries marked with * are exceptions: extrapolations from power-law fits to muchlower energies. Error bars are included whenever they were reported for the analyses. EXO made bothhardware upgrades (Phase I, II) as well as many software enhancements. Experiment Resolution [%] Gaussian 100*1 σ /mean Uncertainty XENON10 [40] 0.89*XENON100 [84] 1.21*XENON1T [41] 0.80 0.02EXO-200 [85] single-scatter only 4.5 for QEXO-200 [86] ibid . 1.9641 0.0039EXO-200 [87] 1.84 (6.0-7.9 S1, 3.5 Q) 0.03EXO-200 [82] 1.67EXO-200 [86,88,89] 1.5820 or 1.6(0) 0.0044EXO-200 [13,90–93] 1.53 0.06EXO-200 [10,94] 1.38 then 1.23 then 1.15 0.02 (last)EXO-200 [70] 0.94(1)-1.38(2) comb and 3.44(6)-4.08(4) for QKamLAND-ZEN [95,96] 4.0-4.3 (GXe dissolved in liquid scintillator)KamLAND-ZEN [97–100] 4.2 ∼ The reader must be cautioned not to conclude that one technology (XENON is two-phase, but otherssingle) is better, as fiducial mass and total exposure time, position resolution, overall background rate inthe region of interest and self-shielding, and enrichment in
Xe come into play. The XENON series ofdetectors have focused primarily on DM not 0 νββ and so were not enriched. Their intrinsically betterresolutions are due not necessarily to the addition of a gas stage (converting Q into S2) but the use of PMTswith single-photon resolution, while EXO used silicon photo-multipliers (SiPMs) with poorer single-pheresolution (not needed at MeV energies) required for their lower radioactivity that is superior to even thecustom PMTs for LZ/LUX and XENON [93,102–106]. Lastly, we do not explore GXe, for which there ismuch data: NEXT has achieved better resolution than reported here, 0.1-0.3% (0.30-0.74 FWHM) due tolower total-quanta Fano and lower recombination fluctuations [107,108] both accounted for in NEST [48].(The question of high mass vs. superior resolution is beyond our scope.)What we can do is perform detailed MC scans to predict the best potential LXe resolution, for 2458 keV,but differing conditions; real experiments measure it at a nearby
E e.g.
Tl. Validations arenot overlaid, but we point to successes in predicting resolution for XENON1T [41,42,58] and postdictingLUX. To narrow the enormous parameter space, infinite e − lifetime and 100% extraction efficiency (or,all-LXe detector like n/EXO) are assumed, with 0% noise in Q readout from the grids, but varying S1 noiselevel and wide E-field range for completeness. Second, an assumption is made of fixed medium g = g , from a pessimistic scenario of 1%, all the way up to 100%.Higher E-field is only better at low g , due to NEST’s strictly empirical Fano factor F q increasing withfield. It is unphysical, but needed to match data claimed to be de-noised or low in noise [109]. This isimportant, given the rush to achieve higher field for better resolution [110] similar to the rush in the DMfield, for lower leakage of ER backgrounds into the NR regime [53,56,111]. While L y and Q y are changing (a) (b)
10 V/cm E-field betas (NEST)501005001000500 V/cm gamma rays500 V/cm alt beta model
Figure 3. (a.) 2.5 MeV resolution in LXe according to NEST vs. g and fields. For one reasonable field,500 V/cm, systematic uncertainty due to model choice shown: dashed cyan is NEST ER model based onphotoabsorption gamma data, solid is ER model from gamma Compton scattering and betas, and dottedline is a different beta model, based on [24]. The differences are most significant at low g , where the exact L y value is more important. It is a key question for nEXO whether yields are more beta- or gamma-like. (b.)The middle-of-the-road default beta model was selected, and g and field frozen at 0.1 and 500 V/cm, andthe resolution as a function of the Fano factor assumed is presented, for different levels of noise in the S1(primary scintillation) signal. As at left, combined E used, except for the dashed line (S1) and dotted (S2 orQ) for comparison to more detectors, as close to the max (worst) possible. with E-field thus changing combined resolution, higher g is naturally better, at least for non-zero fieldand combined E , due to more photons being collected. XENON1T, with its g ≈ g ’s and field rises slightly to match at 0.8when applying XENON’s e − lifetime and e − extraction efficiency [58].In Fig. 3b is resolution’s dependence on Fano factor, from a theoretical value [112] (sub-Poissonian, (cid:28)
1) up to the largest experimental one, of Conti et al. [51]. This governs standard deviation: (cid:112) F q N q .While the best-fit (world data) NEST value, for 2.5 MeV and 500 V/cm, is 14 by default, we treat the Fanofactor as free in Fig. 3b, extending down to 0.2 due to NEST possibly absorbing detector-specific noises bymistake into the Fano value (even if this is not likely due to matching data across decades [41,109]). All thevarious EXO-200 results can be explained, as being between ∼ Q y and L y asymptote to constants [24,32,113]. Thedashed line is too high to explain EXO’s S1-only values, but S1 resolution improves with more light atlower E-field (higher E-field increases charge, at expense of light).Regardless of whether it is achieved through ramping up g (not unrealistic for the future given 100%QE devices [114] and high-quality reflectors [115]) or F q dropping to zero (it is not tuneable, at least notwithout doping of Xe with other materials; only feasible if the intrinsic value is already below Poisson i . e .1) the best possible value for resolution appears to be 0.4%, a “basement” created by binomial fluctuationsin excitation and ionization, combined with non-binomial recombination fluctuations [52,79] if there is nonoise (versus fixed 2% example in pane b). Given realistic detector conditions a more reasonable estimateof the minimum possible here is 0.6% (comparable to gas). Even if the total number of quanta is higher than assumed here, due to W being lower, as recentlymeasured by EXO-200, 11.5 ± ± ± ± F q = nd order the fluctuation models in NEST would have to be revised, to 1 st order everything discussed herewould remain the same, but with g and g estimates decreasing by ∼ Energy Reconstruction and Efficiencies for a Continuous Spectrum
In searching for either 0 νββ decay or the dark matter, a continuous-spectrum background can obscureany potential signal of beta decay or dark matter respectively, in addition to peaks in the background, orcalibration peaks [90,117–120]. In our final ER analysis, we return to optimal combined E , but considera non-monoenergetic spectrum. A new challenge appears, as cross-contamination, e.g. , between binsin a histogram, makes it difficult to separate the upward fluctuations of lower E ’s from simultaneousdownward fluctuations from the higher bins.This difficulty is exacerbated by the fact that energy resolution is not fixed, so this is not a flat or lineareffect with which it is easy to deal analytically. The resolution of course degrades as energy goes to zero.Because the light and charge yields depend on energy, an additional problem is the fact a spectrum flatin (combined) energy is not flat in S1 nor in S2, and not all background spectra are going to be flat. Thatbeing said, this is approximately true at low energies for DM searches in LXe TPCs, after the contributionsfrom all background radioisotopes are summed together, from Compton plateaus, neutrinos, and/or betaspectra, as in [24,42,53,58].A naïve optimization attempt for a uniform spectrum that allows both w , w to vary distorts itmore than normal. Better results are obtained fixing w , unlike before. LUX is the example again: itis NEST’s default. A generic flat ER background is simulated from 0-20 keV in real energy (it shouldnot be taken to represent the true backgrounds found within [49,118]). An excellent analytic fit for thedetection efficiency vs. E for a continuous spectrum is a modified Gompertz function suggested by aLUX collaborator: 10 ( − m e − m ∗ Em − m e − m ∗ E − m ) /100%, which addresses both low-energy threshold andhigh-energy cut-off. (Typical values: m and m are O ( ) while m , m , m O ( ) and m O ( ) .)Fig. 4a shows how the optimal scale, in gold again, is closer to the correct energies known fromNEST MC in grey, relative to traditional combined energy in dark blue again. H (tritium) betas arenot flat in energy but their LUX trigger efficiency should be similar enough to a flat spectrum, so it isincluded in black to verify NEST’s reasonableness [76]. A H beta spectrum terminates ( Q β ) at an 18.6 keVendpoint, but finite resolution causes the fluctuations around that energy. In gold, the w is held constantat 1.0, but w = − e − E , basically adjusting for the growing deviation between reconstructedand real energies as showcased in Fig. 2b using an S-shaped curve asymptoting close to 1.0 (without ashrinking w , this weight w has the opposite trend compared to Fig. 2a). E in keV can stem from either thetraditional combined scale, or MC truth, which in an actual experiment can be validated with a series ofmonoenergetic calibration peaks. The χ /DOF = 2.65 for blue compared directly bin by bin with no fit togrey at 0.5-17.5 keV, versus 1.68 for gold. Bin widths are 0.1 keV. The 50% fall-off point at high E ’s (perfectstep function in true E in grey) shifts from 19.5 to 20 keV, and is thus more accurate in gold compared toblue, forcing the endpoint smearing to be symmetric.Fig. 4b reiterates once more how distorted S1/S2-only E scales can be, in red/cyan. While Fig. 1did show S2-only can be best for low- E peaks, this is not the case for a continuum. Both S1/S2-onlyare non-uniform, despite the underlying spectrum being flat, and accounting for non-linearities in the underlying S1 and S2 yields, fitting quadratic not linear functions vs. (true) E . The flat top should be 0.005as in the truth spectrum, due to normalization: bin width over range = (0.1 keV)/(20-0 keV) = 0.005. S1 ispulse area not spike, but in units of phd [16,19,62]. Despite this, there are unnatural peaks at both low andhigh E , caused by threshold and the maximum E simulated (20 keV) respectively. C o un t s (a) (b) - Figure 4. (a.) Histogram of 10 NEST uniform- E -spectrum events (0-20 keV true) binned using MCtruth energies (grey), reconstructed energy from the combined scale (blue), and re-weighted optimalreconstruction (gold). Gold outperforms blue even visually, correcting underestimation of efficiencysub-keV, plus overestimation near 1.5 keV (see the text for quantitative goodness of fit comparisons).Tritiated methane (CH T) is the black points, for validation against actual data. Its efficiency curve ismarkedly similar despite a non-flat spectrum. As it is continuous, the E is still only reconstructed, notknown to infinite precision as in MCs, although an attempt to empirically account for smearing was madeby LUX [76,79]. The solid black line is the Gompertz fit, superior to a more traditional er f , dashed, whilethe inset zooms on low energies for clarity, with a linear x-axis and log y now. (b.) The true E ’s repeatedin grey, but now compared to S1 (red) and S2-only (cyan) scales (Eqns. 2, 3), with the former possessingunnatural peaks at left and right, and the latter grossly underestimating efficiency at keV scales. The defaultpublic β model (v2.2.0) is used here but comparable results occur with γ -rays. Pivoting toward nuclear recoil, the first hurdle is that for this type of recoil the total number ofquanta per unit energy is not fixed, unlike what was shown for ER (first by Doke et al. at 1 MeV [78], andconfirmed for energies of greater interest to DM experiments by Dahl [36]). This would seem to implythere is no anti-correlation between photons and electrons for NR and thus no benefit to using a combinedenergy scale for them. However, this does not appear to be the case, as the sum of quanta in actual data iswell-fit by a power law, when combining all world data ever collected. This power law simply replacesthe flat line (or general linear function but with no y-offset, if not dividing by energy: twice the energymeans twice the N q ) that works so well for ER, given a fixed work function W q averaged over both flavorsof quantum. This fit is related simply to the L ( E ) from Eqn. 1.The mixing of units is possible, and depending upon whether one uses an S1-only, S2-only, orcombined-energy scale, for NR the unit of keV ee can mean the beta, Compton, or photoabsorption eventequivalent energy at which NR produces the same amount of S1, amount of S2, or the sum. In none ofthese three cases however is the conversion a simple constant or linear function, and can differ wildly,from keV ee being 2-10x smaller than keV nr , depending also on energy [15]. The reason it is smaller: it takesless energy for ER to produce the same number of quanta compared to NR for the same energy deposit( L < L should not depend on field, only the recoil energy, and the E resolution may be best via combination of information from both S1 andS2 again. (For additional clarity: some authors refer to L as f n [35].)Fig. 5 has all data available on N ph + N e − , from which we extract L . The plots suggest combined E may still be beneficial even for NR, due to anti-correlation. The evidence is indirect, but strong: > >
20 experiments across nearly 2 decades were combined, respecting the systematics ofeach (typically driven by how well g and g were known). Remarkably, within uncertainty at least at the2-sigma level the vast majority of the the hundreds of data points lie along the same straight line in log-logspace. Publications reporting continuous lines stemming from e . g . a modified NEST version or their owncustom MCs are not ignored, but a few sample points at discrete energies are plotted. Fig. 5’s plot style issimilar to that pioneered by Sorensen & Dahl in [35] as well as in later works.Uncovering direct evidence of anti-correlation in NR is challenging: monoenergetic neutron (n)sources exist, but internal monoenergetic NR sources do not. The common sources used such as AmBeand Cf produce n’s at energies O (1-10) MeV which lead to Xe recoils O (1-100) keV for calibrating DMdetectors. While n’s can be background [136] they are sub-dominant compared to ER [137,138] and appearmore commonly as the stand-in for DM used to calibrate WIMPs, being neutral particles that primarilyscatter elastically, as DM should do [6,139]. The closest one can get to separable recoil energies comes fromdetermination of neutron angle and double scattering as done in LUX using a D-D neutron generator,but even in this most optimum situation the direct testing of anti-correlation was not possible: Q y , L y were reported at energies that did not match, and the former data included x-axis ( E ) error bars driven byuncertainty in angle, while the energy error for (single-scatter) L y data stemmed in turn from uncertaintyfrom the Q y used to establish an in situ S2-only E scale [27,140].As this is not a paper presenting any novel models (in NEST for instance) we do not focus onbreakdown of the total quanta into N ph or L y and N e − or Q y , which numerous papers already discussat great length [141]. We also pass over the Migdal Effect, which could increase the light and/or chargeat keV scales due to additional ER from initial NR; there is no evidence of its existence at present, butit is predicted to describe the behavior of electrons “left over” after a nucleus recoils [142]. Additionalphenomena like it are secondary when combining all individual channels. Returning our attention toFigs. 5a-c, the empirical total number of quanta is described by the following power law (black line): ( ) N q = α E β , where α = ± β = ± N q / E = α E β − ∼ quantakeV Not only can summed data from [27,30,36,38,68,121,122,125–129,131–135] be described simply with apower fit but with an exponent near 1, implying a nearly fixed number of quanta/keV, ∼ c f . 73 forER, coming from 1/ W ) i . e . fixed L of ∼ L , re-arranging Eqn. 1, is: ( ) L ( E ) = N q E W q = α E β − W q = ( ± ) E ± ≈ + EW q = × − keV is assumed here with no uncertainty as just an example, while the last term isthe Taylor expansion to first order at 10 keV. In Figs. 5d-e, the fit to N q from data is compared to severalmodels, starting with the traditional Lindhard approach [139,143]: ( ) L ( (cid:101) ) = kg ( (cid:101) ) + kg ( (cid:101) ) , k = Z A ≈ g ( (cid:101) ) = (cid:101) + (cid:101) + (cid:101) , (cid:101) = E Z − ≈ E Where Z = 54, A = 131.293 (average) for Xe. (cid:101) is called “reduced energy.” It allows dimensionless L comparison across different elements. A Taylor expansion for Eqn. 8 at 10 keV is L ( E ) = + E .At this E , the value of L for the expansion of Eqn. 7 is close, <
5% lower than the one for Lindhard (8).Eqn. 7’s linear approximation is lower for both of its terms, but this can be explained by bi-excitonic and/orPenning quenching, which increases with higher dE / dx , which occurs with increasing E ’s for keV NR. Energy [keV] T o t a l Q u a n t a (a) Fit to Data (All)LUX DD 190 V/cmneriX 190 V/cmLUX DD 200 V/cm neriX 490 V/cmManzur 1000 V/cmneriX 1020 V/cmManzur 4000 V/cm
Energy [keV] (Corr*) T o t a l Q u a n t a ( C o rr * ) (b) Fit to Data (All)Dahl 60 V/cmDahl 522 V/cmDahl 876 V/cmDahl 1951 V/cmDahl 4060 V/cm
Energy [keV] (Corr*) T o t a l Q u a n t a ( C o rr * ) (c) Fit to Data (All)XENON1T 82 V/cmXENON1T 117 V/cmPandaX-II 300-400 V/cmXENON100 530 V/cmXENON10 730 V/cmZEPLIN-III 3400 V/cmZEPLIN-III 3900 V/cm
Energy [keV] T o t a l Q u a n t a (d) Fit to Data (All)NEST v 2.0.1NEST v 2.0.1 (no sigmoid roll-offs)Lindhard: k=0.110 (Hitachi)Lindhard: k=0.1735 (LUX Run03 DD)
Energy [keV] T o t a l Q u a n t a (e) Fit to Data (All)Sorensen 2015: q=1.1×10 Bezrukov, Kahlhoefer, and LindnerMu, Xiong, and Ji
Energy [keV] T o t a l Q u a n t a (f) XENON1T 82 V/cmXENON1T 117 V/cmLUX DD 190 V/cmLUX DD 200 V/cmPandaX-II 300-400 V/cm XENON100 530 V/cmXENON10 730 V/cmManzur 1000 V/cmZEPLIN-III 3400 V/cmZEPLIN-III 3900 V/cmFit to DataNEST v 2.0.1NEST v 2.0.1 (no sigmoid roll-offs)Lindhard: k=0.110 (Hitachi)Lindhard: k=0.1735 (LUX Run03 DD)Sorensen 2015: q=1.1×10 Bezrukov, Kahlhoefer, and LindnerMu, Xiong, and JiFit to DataNEST v 2.0.1NEST v 2.0.1 (no sigmoid roll-offs)Lindhard: k=0.110 (Hitachi)Lindhard: k=0.1735 (LUX Run03 DD)Sorensen 2015: q=1.1×10 Bezrukov, Kahlhoefer, and LindnerMu, Xiong, and Ji
Figure 5.
All available world data on LXe NR at time of writing summarized in one place, with N ph and N e − combined into N q . Where the E ’s did not match up (sometimes even within the same data set), asimple power law was used to spline (only interpolate not extrapolate) the numbers of photons first to addthem to electrons. E-field does not cause measurable differences. (a.) Only directly measured yields usingangular measurements to determine E [27,30,121,122]. These are handled as more “trustworthy” in thecommunity due to being quasi-monoenergetic analyses, and thus given the most weight in the fit even ifthere were fewer points. One simple power law appears to describe the data points across over three ordersof magnitude in E , depicted as the black line, dashed or solid, within every plot pane. For (a), an uncertaintyband was included (2 σ for clear visualization in green, not 1 σ ). (b.) Dahl’s thesis data from the Xed detectortaken from broad-spectrum shape spline fits ( Cf) [36]. *Corr(ected) on the y-axis refers to correctingthe data in our global meta-re-analysis for effects often not known at the time of data-taking, such as the2-phe effect, or the extraction efficiency being much less than 100% than the data-takers had originallyestimated [16,123,124]. The former can lower the L y measurements, depending on the analysis technique,while the latter raises Q y data points typically. The x-axis was corrected in the sense of energy estimatesupdated with a more modern combined- E scale whenever possible. (c.) More (indirect) measurementsfrom continuous source bands, from XENON, ZEPLIN, and PandaX [35,68,80,125–130]. Errors in data usedwhenever reported. For PandaX, L y was not provided, only Q y . The former was estimated using theirAmBe bands, by the authors of this work. (d. plus e.) A review of models [27,48,131–135]. (f.) Low- E zoomof models, with data included, as larger-size points. Colliding pairs of excitons may lead to de-excitation, and thus less S1 [131]. Some fraction of excitationmay also be converted into ionization, adding to Q. Using the values in [30] or [133] it is even possibleto show that NEST, similar to the data fit, follows Lindhard closely above O (1 keV) as long as additionalquenching is added, for photons (see NR analysis note [15]).This is remarkable given that it was not expected that Lindhard would work even that high inenergy [28,131,132]. Yet data, once summed, exhibit no significant deviation from the Lindhard model,down to sub-keV even. At higher energy, the work of Hitachi [45,131], who incorporates quenching, maybe more appropriate however; it can be approximated using Lindhard but with k = σ level between 0.7-74 keV, given k = ± k Lindhard at high E ’s, and an atomic-physicsmotivated roll-off below 1 keV, with a free parameter q (in same units as (cid:101) ) we chose to best match allcontemporary data, 1.1 × − or 10.5 eV. Only the min (blue) and max (green) k (which is uncertain andcan range from 0.1-0.2 according to [28,35,134]) easiest to justify are depicted (Fig. 5d). k = k = ≥ E (red, Fig. 5d) matching Eqn. 6 with rounding,but more importantly different because of considering not just raw yields but log ( S c / S c ) bandmeans, and giving greater weight to the lowest- E data, of greatest importance to a DM search [139].(Previously 12.6 E , before all statistical and systematic uncertainties were properly considered.) Thedash purple line of Fig. 5d is not just the power law but the full NEST that also since v2.0.1 to todayincludes sigmoidal corrections, separate in both L y and Q y , to allow for modeling of NR violating strictmacroscopic anti-correlation. These cause the N ph and N e − to realistically drop below the power law,conservatively accounting for non-Lindhard-like behavior below a few keV, and better matching data inthis regime such as from the D-D calibration of LUX’s second science run [122]. Nevertheless, all modelsagree very well at low energies, all of them extrapolating at 200 eV to 1-2 quanta (see inset). Below 0.2 keV,NEST conservatively assumes 0 quanta, justifiable from first principles [15,28,48,132].For greater readability several models have been omitted from Figs. 5d-e, which do not include thework of Sarkis, Aguilar-Arevalo, and D’Olivo [28] nor of Wang and Mei [141]. This is not to say theirapproaches are not valuable, but the former is markedly similar to Sorensen [132] and to the completeNEST equation with a sub-keV roll-off despite starting with different formulae, while the latter is fit tothe LUX data, and thus practically redundant with dashed green. In Fig. 5f we zoom in on energies < B solar neutrino CE ν NS is of great significance as well, interesting in its own right for the first detectionof the recently measured coherent scattering [146,147] but from solar neutrinos, and as a background tonext-generation LXe-based WIMP experiments [1,148].In following the ER section, the next step should be a discussion of the energy resolution as afunction of energy. This has never been published for the combined scale with NR, however, to the bestof our knowledge, except for plotting of the S1- and S2-only scales only once each as far as we know, byPlante [31,149] (but only at zero field, in a dissertation) and Verbus [27,140] respectively. In both situationsthese were only quasi-monoenergetic reconstructions, tagging neutron scatter angle with a Ge detector inthe former case, as typical for all L e f f measurements, and in situ in the same Xe volume (LUX) in the latter.For NEST comparisons to both of these, see Figure 3 bottom in the LZ simulation paper [150]. We alsopoint to potential examples of threshold bias “lifting” E ’s above correct values (or, Eddington bias, forcontinuous spectra), as manifesting in light yields [112,151,152] seen much earlier for ER in Fig. 2b but it ishandled in later works [140,153] and thus not shown explicitly pre-correction. (a) (b) . Figure 6. (a.) Combined (blue) and optimal (yellow) scales for a 50 GeV standard WIMP spectrum, the MCtruth for which is grey. Above 2 keV, bins are omitted in log fashion for clarity. LUX detector parameters ( i . e .Run03, first WIMP search) used as earlier for similar ER plot, again for illustrative purposes ( ∼
180 V/cm).Yellow corrects for sub-keV efficiency underestimation, and an overestimation at several keV, comparingyellow to grey and blue to grey. (These effects can change from detector to detector, with signal shape.)While a distinct functional form vis-à-vis ER, w is again S-shaped. Better results may be possible withlower w , kept fixed at 1.0 again here for simplicity. In actual data, with ER and NR mixed, backgroundswith potential signals, it is impossible to know a priori if applying keV nr or ee is more appropriate by event.(b.) True spectrum is repeated, but now compared with S1 / S2 in red / cyan. Power laws in legend arecrude, detector-specific approximations, but can be converted using S c = g N ph , S c = g N e − ( g = g = ∼
1, please see Eqn. 6.
Lacking truly monoenergetic peaks, continuous spectra present an opportunity still for contrastingthe S1, S2, combined, and optimized- E scales. Those from all known n sources are highly dependent ongeometry, however; thus NEST is insufficient: a full-fledged Geant4 MC [154,155] would be required tomodel detectors. Instead, an example of a 50 GeV/ c mass WIMP will be shown with an unrealisticallylarge cross-section of interaction (1 pb, and 1 kg-day exposure). While artificial, this illustrative exampleis valid given underlying assumptions for not just total quanta but individual photons and electrons,and resolution in both channels, verified by NEST comparison with data elsewhere [32,34,144] and realexperiments will be able to test the ideas presented in future NR calibrations, in XENONnT and LZ.Fig. 6 is a repeat of Fig. 4, but is for NR. The WIMP spectrum is more relevant than a uniform- E spectrum would be, as even for a massive (multi-TeV mass-scale) WIMP it is a poor approximation towhat is inherently an exponential spectrum, falling as energy increases. The drop off on the left is of coursecaused as before by a combination of separate threshold effects that remove the lowest-energy S1s and S2s.The optimal scale shows improvement again over combined, but by itself combined E is not dissimilarfrom S1- or S2-only for NR, because the lower-quantum/area signals are dominated by detector specificssuch as (binomial or Poisson) light collection efficiency. S1 only is most common, used in every experimentstarting with the seminal XENON10 result [29] due not to a better energy reconstruction, but signal (NR)versus background (ER) discrimination [36,53]. S2 only may be as good for discrimination if not betterhowever, according to the work of Arisaka, Ghag, Beltrame, et al. [156]. The key points of the LXe (ER) section (with detector-specific caveats) are:• A combined scale reconstructs monoenergetic ER peaks best for DM/ ν projects, but below 3 keV atleast this is not true according to an Ar study with S2-only best (outperforming S1 as well) if e − lifetime is high. A combination can be established with two numbers, S1 and S2 gains, leading to a1D histogram (XENON/LUX style) or equivalently a 2D rotation angle (Conti/EXO method).• An optimal weighting of S1 and S2 can result in better resolution than simple combined energy, downto O ( ) keV even, and mitigation of threshold bias and skew. Higher, the best resolution occurs whenthe weights applied to the S1 and S2 are 1/ g and 1/ g , but machine learning is likely to outperformanalytic methods, if more parameters (beyond S1, S2) are considered.• For neutrinoless double-beta decay, O (1%) resolution has been achieved in the relevant energy rangeby a multitude of different experiments and technologies, while the best feasible may be 0.4-0.6%, inliquid, which may be limited by a Fano factor (often confused with recombination fluctuations) thatis higher than in gas. But no one experiment has yet reached its full potential.• For a continuous ER spectrum, the combined scale is a clear winner over S1-only and S2-only alike,at least for a uniform energy distribution (uniform in neither S1 nor S2, as L y and Q y are functions ofenergy, not flat). But optimization with re-weighting is still possible, just in a different manner thandone for monoenergetic peaks, because of cross-contamination between bins.Next we summarize NR; there is good agreement on total yield from different experimentalists.• While impossible to obtain from truly monoenergetic lines, a summation of separate N ph and N e − data sets results in strong evidence of NR anti-correlation akin to ER’s and no statistically significantdifference from Lindhard even sub-keV, at least given additional high- E quenching.• Despite the point above, the advantages of a combined scale are not significant compared to theS1-only default (but S2 comparable) as so much E is lost to heat ( > Low Energy: keV-scale (Dark Matter Backgrounds / Calibrations) Monoenergetic Peaks
For ER in LAr the best example of a low-energy calibration line is the m Kr peak, at 41.5 keV,commonly used to calibrate both LXe and LAr experiments, but in this latter case there exists no evidenceof the yields depending on the separation time between the individual 32.1 and 9.4 keV peaks [157], unlikein LXe [75], so the MC comparison is easier. The 2.82 keV electron capture from Ar has also been studiedin LAr but most commonly at zero electric field in single-phase (liquid) detectors, making it a less idealchoice for complete NEST comparisons to S1, S2, and combined- E histograms [158]. For a WIMP searchER is again the main background, due to Ar in DarkSide-50 (DS-50) at Gran Sasso [159], DEAP-3600 (andformerly CLEAN precursors) at SNOLab [160,161], and ArDM (at Canfranc). Underground Ar depleted inthis isotope reduces the background, but it remains dominant [162]. In neutrino experiments, ER is thesignal, via neutral-current, charged-current, and elastic-scattering interactions. In this section, we beginby focusing on dark matter at the keV scale, later moving on to cover the GeV scale more relevant foraccelerator neutrino experiments like DUNE [163], with the intermediate scale at MeV also important forsupernova or solar neutrinos [164,165].Predictions of NEST’s LAr ER model in comparison to experimental data are shown in Fig. 7.The source of data here is DarkSide (DS), specifically several PhD theses of its students [21–23]. Forthis experiment, g = ± g = ± stat ± syst [23]. On the S2 side, g = ± ± stat ± syst according to [23]. Note thatthe gain factors g and g are called (cid:101) and (cid:101) by DS; others call them α and α .To most closely center NEST with respect to DS data in Fig. 7, we set g = g = W q was assumed to be 19.3 eV, a valuejustified later when discussing reconstruction for neutrino detectors. Reconstructed energy is again keV ee as opposed to keV (without the subscript) for known individual energies.Unlike in LXe, the S1-only energy scale does not necessarily perform the poorest. Our particular m Kr example has an energy resolution σ / µ of 6.5%, in Fig. 7a. The S1-based scale is more reliable inLAr due to its greater linearity, wherein the light yield for different betas and gamma rays is quite flatin energy, starting at 40-50 photons/keV and falling as the electric field rises and more energy goes intocharge production [78,157,169–174]. Next, in Fig. 7b the S2-only scale is plotted, leading to a resolution of25%. Reproducing this large width was done artificially by setting the linear noise in the S2 channel to25.0% (only 2.9% for S1 to match that width, an effectively negligible value). Compare this to 6.0% (S2, sohigh due to e − trains/tails/bursts [57]) and 1.4% (S1) assumed by default for LUX Run03 within NEST.We interpret the cause of the large value for S2 in LAr as stemming from a lack of full 3D corrections inthe initial DS analysis. There is also a clear offset in skew compared to the MC which may come fromDS-specific effects difficult to fully capture in a custom MC like NEST that does not account for all detectoridiosyncrasies. No (statistical) errors are depicted as they are negligible from this high-statistics calibration.Fig. 7c shows a combined resolution of 7.5%, not improving on the S1-only resolution, but still amarked improvement over S2-only, suggestive of anti-correlation of charge and light in LAr (more robustlyestablished later in this section). The agreement is even worse with MC here, however, than in the S2plot, but this can be explained by the peak being from a different analysis from (a) and (b), with the Krcalibration sitting on top of a large background, from Ar inside natural Ar, which we did not model. (Butthis is the only example of a DS combined-energy peak we were able to locate.) In the original source thepeak was not centered on 41.5 keV ee , likely due to a systematic offset in g and/or g (see contradictoryvalues above) but we had no difficulty in NEST with this. For ease of comparison for at least the width,2.5 keV ee was added to data, to force alignment to a 41.5 keV(ee) mean [23].Fig. 7d is the combined- E resolution vs. E . NEST is in blue. The data have full position correctionsfrom high-statistics m Kr calibrations [21–23] as in LXe. They are most crucial for S2, in XY (or radius andangle) as Z is already handled by electron lifetime. NEST points for comparison are at semi-log steps in E = − g , g , and E-field. The combined- E resolution drops from the 7.5% in (c)to below 5% in this case at 41.5 keV in (d). The empirical S2 noise term was thus likely accounting forimperfect correction for the (2D) position-dependent S2 light collection.There is no equivalent of Fig. 2b for LAr, as no example of Eddington-like bias could be found. Anopposite effect (lower instead of higher reconstructed E ) is recorded in Figure 3.11 of [23]. However, thiscan easily be interpreted as E “loss” into charge when using only S1, which while more linear in LArcompared to LXe, is still not a fixed flat L y at all energies, not even at null electric field [158,175].3.4.2. High Energies: The MeV and GeV Scales (Neutrino Physics)
In moving from the keV scale of DM experiments to the GeV scale of the accelerator neutrinoexperiments, we study the MeV scale as a boundary case. A 1 MeV beta was chosen as an example of an ERinteraction energy just beyond what is considered relevant for a DM search, but on the other hand at theextremely low-energy end for neutrino physics, potentially just barely above threshold in an experiment (a) (b)(c) (d)
Figure 7.
Reconstruction of the 41.5 keV m Kr peak in DS [23] compared to NEST, with data as black dots,NEST grey squares. For clarity, no fits overlaid, although most data are ∼ Gaussian. (a.) S1-only E scalemost common for LAr-based DM detectors [22]. Our work/conclusions for such a scale should apply notonly to TPCs where ionization e − ’s are drifted but also to 0 V/cm 1-phase detectors, where these electronsfail to recombine to add to the S1 in LAr for both ER and NR [158,166,167] just as in LXe [32], with the L y having the same shape vs. E as for non-zero fields as field goes to 0 in TPCs (see Doke et al. as well asWang and Mei for possible reasons [78,141,168,169]). (b.) S2-only, with the slight right-hand asymmetrynearly reproduced by NEST [21]. (c.) Combined- E scale, now standard at least in DS. Optimization as donein LXe could be possible, but not shown. Resolution is poorer than in (a) instead of better due to poor S2resolution in (b) and that S2 is being combined with S1, on top of Ar. This is explained in the text, aslikely due to lack of XY correction creating noise not correlated with S1. For E ’s below 1 MeV like herethis is not likely due to delta rays not being simulated by NEST by itself, as no S2 noise (and little in S1) isneeded in the next plot (d) and S1 is not as wide as S2 in (a), while delta rays would affect both. Combined E , canceling them, should still be better in general in Ar as in Xe. (d.) Resolution vs. E for monoenergeticcalibrations/backgrounds studied on DS [23]. Only one set of resolutions covering a broad E range wasfound (black) to compare to combined E from NEST (blue). like DUNE [176]. This is of the same order of magnitude but just slightly above the Ar beta spectrumendpoint (565 keV), and is also near the same energies (976 keV and 1.05 MeV internal-conversion electronand gamma ray, respectively, from
Bi) studied by Doke et al. in their seminal 1989-2002 papers [78,169].Our own re-analysis shows that if one sums L y and Q y vs. electric field, it is a constant number ofquanta/keV within experimental uncertainties, and consistent with 1 / W q , given reasonable assumptionson g and g . Table 2.
Best (lowest) possible resolution of a 1 MeV electron recoil at 0.5 kV/cm as a function of theS1 photon detection efficiency g and wire noise (in semi-log steps). Each entry is averaged over 10 simulations in stand-alone NEST, with the effect of delta rays approximated analytically (based on G4). Allphotons and electrons are included from the interaction, which is thus being treated as a single site. g [ % ] Q noise 1% 2% 5% 10% 20% 50% 100% < dE / dx is also at the cusp of the minimally ionizing regime, making a 1 MeVelectron a MIP (Minimally Ionizing Particle) like electrons from GeV-scale neutrino interactions prior toshowering [177]. In neutrino detectors there is no g however, as electron charge is directly measured, ason EXO, by wire planes instead of S2. They are 1-phase liquid TPCs with unit gain for charge readout.Table 2 scans different levels of energy resolution associated with noise from the wire readout, showing thebest (lowest) resolution for different values of g . Combined-energy and even S1-only resolution appear inthe table, for high g paired with high wire noise.Resolution in a DUNE-like detector can be halved already at g = F q drives combined- E results. Its theoretical value 0.1 was assumed, given no other data [168]. ForS1 only, a g -based binomial drives what is possible. 0% noise was assumed for S1.Unfortunately, large LArTPC neutrino experiments like DUNE will achieve much lower values of g [178], though g =
2% is already much lower than any Xe or Ar DM experiment has achieved. Athigher levels of noise, still realistic for future experiments but energy-dependent, even lower g suffices formaking combined energy superior to Q-only. When reading this table from the top down, if the value startschanging this means that the minimum resolution being quoted is from the combination of scintillationand ionization, and no longer just the ionization. If reading across: when the values stop changing thatmeans (at high g ) an S1-only scale is best, as at higher levels of wire noise not only does the Q-only energyscale become unreliable, but the benefit in utilizing the anti-correlation of charge and light washes out forthe combined scale, leaving the S1-only scale. The small-scale LArTPC R&D detector, LArIAT (Liquid Argon In A Test beam), has investigatedthe claim that the combined-energy scale, making use of both ionization charge and scintillation light, ismore precise [179,180]. While not targeting the removal of the wire noise, it does effectively cancel outthe exciton-ion and recombination fluctuations, shown using a sample of Michel electrons (from muondecay) at a scale of tens of MeV. Here, the definition of combination is more appropriately set for neutrinointeractions using differential energy loss along the particle track, updating our earlier equations, startingwith (1) but with L = ( ) E = ( L y E + Q y E ) W q = ( dSdE E + dQdE E ) W q → dEdx = ( dSdE dEdx + dQdE dEdx ) W q = ( dSdx + dQdx ) W q ,where the number of photons N ph and number of electrons N e − are replaced for the first step by L y and Q y , specific yields per unit energy, each multiplied by energy.Next, to align our terminology with what is more common in the neutrino field we rewrite L y as dS / dE and Q y as dQ / dE [181] (instead of N ph / E and N e − / E , with S and Q standing respectively forscintillation and charge, the quantum values). S is used for the scintillation light instead of L to avoidconfusion with Lindhard factor. The resultant formula above is still not what is most commonly used inthe field. Instead, that is: ( ) dEdx = dQdx dEdQ = dQdx Q − y ( E , E ) .This is equivalent to the S2-only scale for two-phase TPCs in Eqn. (3) where E = N e − / Q y ( E , E ) , exceptdivided by dx and g = 1, given no need for extraction from liquid to gas, nor any photons created byelectrons as a secondary process in gas (S2 i . e . electroluminescence). Although, the electron lifetime muststill be high, ideally much larger than the full drift time across a TPC, and also well-measured, so that theQ can be corrected in the same way as S2. Q y ( N e − / E ) is often parameterized with Birks’ Law [32,175,182]in terms of dE / dx instead of E : ( ) Q y ( dEdx , E ) = A W i +( k B / E )( dE / dx ) = A Q ( E ) / E +( k B / E )( dE / dx ) ,where W i (sometimes called W e ) is not the same as the work function W q defined much earlier, but triviallyrelated. Being defined as E / N i , not E / ( N ex + N i ) , the convention of ionization W is related to the overallor total work function by W i = ( + N ex / N i ) W q . ( N ex / N i are excitons/ions).For LAr, this means W i = ( + ) W q = 1.21 * (19.5 eV) = 23.6 eV, approximately [78,183]. NoteLAr’s W q has been labeled W maxph [78], as it is related to the maximum possible L y , when Q y =
0, but this isnot possible even at 0 V/cm (it does become possible as ionization density from interactions goes to ∞ andforces recombination in both LXe and LAr [78,184]). Drift electric field is E while k B is known as Birks’constant, and A is the correction factor explained later. Q is effectively the maximum possible charge, atinfinite E , defined as E / W i or N i . While Birks is not the only possible parameterization ( e . g . there is alsothe Thomas-Imel box model [185,186]) the focus of this work is on energy reconstruction not the variousmicrophysics models. We take this to be only one, representative example here.Another approach, taking into account not just excitation vs. ionization, but e − -ion recombination,begins the same as for LXe [35,36,144], and LAr experiments used for DM instead of neutrinos: ( ) E = N q W q = ( N ph + N e − ) W q where N ph = N ex + r ( E , E ) N i and N e − = [ − r ( E , E )] N i .Here r refers to the recombination probability and depends not only on energy and electric field butalso the particle or interaction type, N ex is the number of excited atoms initially produced, and N i thenumber of e − -ion pairs. In this case, N ph + N e − is also N ex + N i . Applying the same revision to Birks’ Lawsuggested in 2011 by Szydagis et al. for Xe [32] to Ar recasts it in terms of first principles: ( ) r ( E , E ) = k ( E ) dE / dx + k ( E ) dE / dx , N e − = ( − r ) N i → N e − E = Q y = ( − r ) N i E = − rW i = W i + k ( E ) dE / dx , with k ( E ) = k B / E only one possible parameterization of recombination’s E-field dependence, and inturn charge and light yields, with a more general negative power law possible [32,187]. Only the A fromICARUS [188] is lacking in terms of robust justification, but it is likely a correction needed only whenthe secondary particle production range cut in the Geant simulation is set too high to allow for delta-rayformation down to keV-scale energies. Delta rays are lower-energy, higher- dE / dx tracks with greaterrecombination, hence more light, at the expense of charge, explaining why A <
1. Increased simulationtime and memory usage associated with lowering the secondary particle production range cut often leadthis cut to be set too high in Geant simulations to capture this effect.In Fig. 8a the number of ionization electrons produced from 1 MeV primary electrons is plotted versusboth the Geant4 secondary production range cut (“length scale factor”) as well as the associated energythreshold for delta rays. The ratio between the values of the two plateaus at the left and right extremes inQ is almost exactly equal to the ICARUS best-fit value of the renormalization constant A (0.800 ± ∼ (a) (b)(c) Figure 8. (a.) Lack of delta rays in Geant4 altering median Q at 1 MeV in a large 500 V/cm LAr volume,more so as the threshold in track length set by the user for creation of secondary e − ’s increases past thevalue from Mozumder [190]. The default threshold is typically too high by >
10 times, in length and/or E ,in neutrino simulations [189]. (b.) Demonstration of S versus Q anti-correlation from our reanalysis of Dokeet al. 1988 and 2002 [78,169], confirmed by the recent LArIAT study [180]. 1 MeV ER at different E-fields,as opposed to many E ’s at one field (as done for a contemporary “Doke plot”). (c.) Noiseless charge-onlyresolution vs. fixed electron E using Geant4, with G4 secondary production range cuts of 1 µ m (blue) and0.7 mm (black, in LArSoft), compared to data points at isolated E ’s on recombination fluctuations withdelta rays from [186] (red) and [191] (green, no measurement uncertainty provided). Fig. 8b (upper right) shows that the lower plateau in the large left plot (a) in its lower left corner iscloser to correct. The zero-electric-field light yield for a 1 MeV beta, or other electron, is approximately41 photons/keV [169] while the red line in (b) shows a reduction to ∼ ± + − quanta/keV (an S value different than 41, potentially higher, onlystrengthens our following arguments by lowering Q). The charge yield is total minus light, leading us to 51.3 − = + − e − /keV. The NEST (2012) value is thus very much within the error envelope ofactual data for the lower level, but outside it for the higher one, which also never quite flattens (Fig. 8aupper right). Including more, relevant measurement uncertainties does not sufficiently explain thisdiscrepancy. A similar conclusion can be reached by converting relative charge (green curve in Fig. 8b) toabsolute, pointing again toward the lower value of Q being the more correct one. Fig. 8c demonstratesfully accounting for delta rays is also important for correctly predicting ionization-only E resolution forprimary electrons at these energies ( ∼ · cm )/g driven primarily by Birks, as givenby Eqn. 13 (with the Thomas-Imel box still called for any accompanying delta rays). There was no need forrenormalization as in Eqn. 11 (so A =
1) due to using a significantly smaller secondary production rangecut in Geant4, and the Birks constant electric field dependence was k ( E ) = E ( c f . Amoruso’s k ( E ) = ( ± ) / E ). The different power on the electric field dependence, less than 1, on topof the different constant within the numerator is likely due to using Birks to model the recombinationdirectly instead of R = − r or QQ . In addition, it was based on higher-LET dark matter detector dataand extrapolated lower. This is also nearly identical to Equation 8 from Obodovskiy’s comprehensivereport [187].One point of confusion to address is the most common quantity used for data/MC comparison inthe neutrino field, the recombination factor, R . It is actually an “escape” factor for electrons from ionizedatoms: Q = ( − r ) N i → R = − r = Q / N i = QW i / E , where W i = ± dE / dx ) because at time of writing the ER model for LAr in the latest NESTversion has not been recast yet into a dE / dx basis for a robust comparison [192,193] assuming a typicalLAr density of 1.4 g/cm . Minor discrepancies are observed at low dE / dx , which will be addressed withplanned improvements to the NEST LAr ER model in the near future.The corrections discussed here are important not only for energy reconstruction considerations butalso for background discrimination, such as for differentiating neutral pions, photons, and e + e − pairproduction from single electrons which comprise the signal of interest for accelerator neutrino experiments.This particle identification can be carried out with the use of dE / dx by first measuring dQ / dx [194].Potentially one can add in dS / dx for a low-enough energy threshold, if the g is high enough, as discussedearlier. The exclusion of delta rays common in typical Geant4 simulations for LArTPC neutrino experimentsaffects not only the mean yields, which can still be simulated accurately with a 20% correction almostindependently of electric field and LET, but also resolution: delta rays will degrade the energy resolutionand require more complicated corrections if they are deactivated in Monte Carlo simulations (in Fig. 8c).Incorrectly-modeled energy, and thus dE / dx , resolution can lead to potential biases between data andsimulation when using reconstructed dE / dx for particle identification: electron/photon discrimination inLArTPC neutrino experiments for example. The final topic is low-energy (keV-scale) nuclear recoil or NR within LAr, which is important not onlyfor dark matter in experiments such as DS [195] but also for CE ν NS on collaborations like COHERENT [196].The sum of quanta in data is again fit well by a power law, combining all global data on total yields, relatedto L ( E ) from the beginning, Eqn. 1.The fit in Fig. 10 is quite similar to that from LXe earlier in Fig. 5 in both the base and exponent. Herewe plot total quanta/keV instead of just quanta for greater clarity: in terms of quanta the power would be Figure 9. R vs. dE / dx in ICARUS data (stopping muons, protons) [188] at fields 500, 350, 200 V/cm. Datain black/white, as white circle, black circle, and black star, while results of a Geant4 MC making use of theNEST 2013 LAr ER model are colored red, green, blue respectively with decreasing field; protons, muons,electrons, and their respective antiparticles, while varying in R at the 5% level, are sufficiently consistentto combine. The x-axis here is LET (linear energy transfer), or, dE / dx divided by density. (NEST pointsextracted by individual secondary track from 1 GeV total- E simulations.) c f . 1.068-1.1 for xenon). Data are scarce for N q in Fig. 10a, as most LAr data for DM traditionallywere 0 V/cm ( e . g . microCLEAN, DEAP) thus lacking N e − to add to N ph . L e f f data exist from many sources,collected in [161,197–199] but these do not directly inform L , being just L y .Lindhard works surprisingly well according to Fig. 10b, staying within 2 σ for the power fit to databelow 50 keV. Deviation below Lindhard at high E is easy to understand as bi-excitonic quenching againas per Hitachi, while (some) deviation at sub-keV is also understandable, as Lindhard’s approach shouldbreak down at < L y increasing in energy, while Q y decreases [175,200]. Confusion between L y and total yield hasled to past claims Lindhard does not fit well [200,201]. Regardless of whether Lindhard fits well or doesnot in some energy regime, Fig. 10a is indicative of a combined- E scale being worthwhile (in place of S1only) as in LXe, as argued both by DS [23] and LArIAT [180].The final plot, Fig. 11, displays the breakdown into the S1 and S2 pulse areas for one example energycoming from the same quasi-monoenergetic technique cited earlier for table-top LXe yield measurements(for both ER and NR) relying upon coincidence between a noble-element detector and a second detector,typically Ge [31,65,175]. For NEST MC, the means of their values for the gains have been assumed: g = ± g = ± e − . The drift electric field was 193 V/cm and sampleenergy 16.9 keV, selected due to being the lowest value for which the S1 and S2 histograms are displayedat an identical energy anywhere within the existing literature.NEST seems to overestimate the L y , but a larger issue is at play: contradictory data exist for NRfrom over the past ∼ two decades: some experiments showed the amount of scintillation staying flat,others decreasing, and several even increasing with decreasing recoil energy [161,197,198], physicallypossible if one adapts the logic from Bezrukov, Kahlhoefer, and Lindner from LXe on screening [133].Those showing increase cannot be easily explained as caused by threshold bias, as several distinct setsof results agreed upon the increase [195,200]. Other hypotheses include different collection efficiencies, especially as wavelength shifters are generally used in LAr, and different ones [204], some of which mayhave efficiencies higher than 100% effectively due to creation of multiple visible photons per individualinput photon in the extreme UV, though the data on the existence of this are also contradictory [205]. Arelated effect may be something in photo-sensors exposed to LAr analagous to the 2-PE effect seen in LXe.A compounding problem is the discrepancy for the zero-field L y for Co (or m Kr) used as in LXe toset L e f f . Historically, it is stated as near 40 photons/keV [169] but more recent work, with g known byDoke plot, suggests closer to 50, nearer the max (1/ W q ) if Q y →
0, sensible for
E → e − ’s remain). Systematic uncertainty in L y at ∼
20 keV may be as high as40% ( L e f f = L y building into a mild increase with increasing NR energy, but at a higher level than the traditional ∼
10 photons/keV (0.25 L e f f x40), better matching the claims of high L y at low E [175]. (Earlier versionswould switch between differing, mutually exclusive solutions.)Fig. 11b suggests an S2-only scale may ironically be more reliable for (NR-based) DM searcheswith LAr. Contradictions are fewer between data and different models, including NEST, even at otherenergies, and multi-ms e − lifetime may be easier to achieve through high-level purification [159,206];however, a note of caution that this may be due to the paucity of non-zero-field data, for measuring Q y , atmultiple E-fields. Columnar recombination, not currently simulated, which changes the yield dependingon electric field orientation, is a further complication [200]. The combined- E scale essentially removes (fit to all data) Figure 10. (a.) The (E-field-independent) total number of quanta N q per keV for NR in liquid argon: L y + Q y , or ( N ph + N e − ) / E . The best-fit power law, used in the current NEST’s NR model for LAr, is ( ± ) E ± , surprisingly similar to LXe, with 1 σ /2 σ error bands in green/yellow. Kimuradata [167] are given as fit to data in original paper; SCENE and ARIS points are taken from [200] and[175]. (b.) A model review, collected from [132,143,201] of Lindhard/Lindhard-like approaches. Solid linesassume 45 photons/keV for the (0 V/cm) L y of ER in LAr, with upper and lower dashes covering 50 and 40respectively to span the uncertainty in light, before addition with Q y . (c.) As in (a, b) NEST repeated here,with two additional model comparisons, from PARIS (used by DS [202]) and [203]. (a) (SCENE) (b) (SCENE) Figure 11. (a.) S1 peak and (b.) S2 peak for 16.9 keV NR in LAr from Cao et al. [200]. Data are in black witherrors, with original MC in red (fit borders for it as vertical blue lines) and NEST overlaid in grey overoriginal paper plots: defaults solid, while altered to match data in dash. Large noise levels needed in NESTare comparable to those assumed by SCENE ( R and R in legends imply S1 30%, S2 25%). the effect of these and any other recombination fluctuations, which cause the variance in the originalnumbers of photons and electrons to be identical “at birth” prior to any fluctuations due to propagationand/or detection [36,51]. Such a scale will also remove the effect of delta rays (ER) on the ultimate energyresolution achievable, if driven by anti-correlated fluctuations (recombination).S2 is generally easier to measure, however, than the S1 is: electrons drift upward in a TPC alongnearly-straight lines (slight diffusion occurs) from the liquid to the wires or to the wires followed by gas,where many photons are produced per electron. Losses due to the impurities along the drift length canbe quantified simply, with an exponential. On the other hand, scintillation photons are produced in alldirections and are affected by not only attenuation (not necessarily exponential, but difficult to quantifyanalytically) but geometric collection efficiency driven by reflection and refraction, and QE. As energydecreases, Q y increases for both NR and ER, for both LAr and LXe, at least down to the keV level beforeturning around, while L y appears to decrease toward 0. For this reason, NEST models are created usingthe total yield first, then charge yield, and light reconstructed by subtraction in the code. (The same is truefor LXe.) In conclusion, the key points of the LAr ER section, coupled to reasonable/common detectorparameter values including/especially g and E-field E , are:• A combined S1 + S2 scale continues to reconstruct ER energies best for DM/neutrino experiments,due to anti-correlation between channels, but not if g is very low ( (cid:28) g very high ( e . g ., 2-phaseTPC). An additional challenge is created by sitting on top of a continuous background like the betadecay of Ar for combined energies, but noise in Q can make S1 more favorable.• dE / dx is more important than just E at the GeV scales of greatest relevance to neutrino projects andit is most commonly reconstructed utilizing dQ / dx (ignoring dS / dx ).• A correction ( ∼ e − -ion thermalization radius O(1 µ m) in MC. Energy resolution may also be affected, not just meanyields, and high-energy, low- dE / dx (MIP) interactions are not immune to this problem due tosecondary particle production, handled with e . g . Geant4.• Due to differences in delta rays and other secondaries, an analytical fit may be impossible across allparticle types, leading to different recombination probabilities even if you consider only the averagesversus dE / dx or energy. • Either escape probability or recombination can be modeled as a function of the dE / dx (or the LET,which includes the effects of density).Next, we summarize the key points of the LAr NR section. We note that because yields change slowlywith increasing field especially for the dense tracks of NR that our S1 examples from two-phase TPCs (DS,ARIS, SCENE) should be relevant/applicable to 0 V/cm single-phase detectors as well.• While possible to measure for only approximately monoenergetic peaks, a summation of the fewavailable N ph plus N e − data sets results in evidence for NR anti-correlation (akin to ER’s) and modestagreement with Lindhard. This is important for both DM and CE ν NS.• Due to uncertainty in the scintillation yield, an S2-only scale may be beneficial, but exploration ofcombined E may still be interesting in the future (as stated above). Non-zero-field measurements arenot as plentiful for charge yields as zero-field light-only ones for NR in liquid argon.
4. Discussion and General Conclusions
We have reviewed mainly LXe and LAr, in 2-phase TPCs, and manage to extract insights spanningdark matter and neutrinos, proving once again the remarkable consistency obtained across numerousdata sets, and the utility of NEST to probe at least the simple reconstruction methods reviewed. Froman historical perspective, it is intriguing that the usage of noble elements in the DM field began withscintillation-only E measurements, with charge primarily used for position reconstruction, while forneutrinos the opposite occurred: ionization-only E scale, with initial scintillation used as a trigger forevent activity of interest. Moving forward in both fields, it will be interesting to see how charge and lightare combined together to improve E measurements further than what has already been achieved.The new insights we have gleaned from our review and meta-analyses with our own simulations,based on the global, cross-experiment framework of NEST, first for liquid xenon, include:
1. The first comparison as far as we know of the same one monoenergetic ER peak ( Ar calibration) across S1-only, S2-only, andtwo versions of combined energy (standard and optimized) with both real data and NEST, with skew-Gaussians adjusting fordetection efficiency and other effects. Width for S1 only was shown to be ∼
4x worse than the best possible.2. The only full explanation published for an optimized (weighted) combined- E scale (not in a thesis or an internal report).3. While the combined- E scale has already been established as superior to S1-only in past work, we explore also an S2-only scaleand show it may outperform combined energy at the keV level, but only for monoenergetic peaks and high g .4. Demonstration that combined energies (even non-optimal) improve not just the widths and thus energy resolution, as alreadyestablished in the community, but also reconstructed mean energies, and shape ( i.e. symmetry or skewness).5. Replication of measured upward bias in E reconstruction with NEST, suggesting it is due to both thresholds and physics.6. A summary of energy resolutions from 0 νββ experiments, with MCs suggesting where to make improvements.7. Clear delineation of the difference between recombination fluctuations, which affect S1 vs. S2, and the Fano factor, thatcontrols their total, as the literature is currently unclear on this, with one term often being used incorrectly for the other.8. A complete comparison analagous to (1) above for the efficiency vs. reconstructed E , for both ER/NR, as reconstructed by S1,S2, and both (standard and optimum combination) compared together for a simple continuous spectrum (box/WIMP).9. The most complete compilation to date of NR Q y + L y , showing also a Lindhard-like power law matches the total yield For liquid argon, items of interest presented here that were new, to the best of our knowledge:
1. The first comparisons of NEST performed for LAr, in plots for dark matter at low energies and neutrino physics for high E ’s(vs. dE / dx ) never presented before, demonstrating a new understanding of mean yields and widths, requiring G4.2. An exhaustive simulated table relevant to neutrino physics that goes beyond existing data, and predicts a significantimprovement in E reconstruction at an energy (1 MeV, low LET) still relevant to neutrinos, for sufficiently high g .3. A demonstration that anti-correlation was “hiding” in seminal work by Doke et al. with an explicit reanalysis of the originalpaper showing photons and electrons sum to a constant for a MIP in LAr as a function of E-field at fixed E .4. A clarification of confusing/conflicting definitions of work function, recombination probability, and charge yield.5. Quantitative proof confirming the hypothesis ICARUS’ data required a correction specifically for not having delta-raysactivated in simulation, plus the first evidence not just mean reconstruction of charge is affected but also the width.0 of 446. A comprehensive compilation of all existing data and models for NR in terms of total yield not just light, beyond 0 V/cm. Funding:
The research of Prof. Levy and Szydagis at the University at Albany SUNY (the State University of NewYork) was funded by the U.S. Department of Energy (DOE) under grant number DE-SC0015535. Prof. Mooney and hisstudents, Alex Flesher and Justin Mueller, were funded through university start-up funds. Ms. Kozlova was fundedthrough the Russian Science Foundation (contract number 18-12-00135) and Russian Foundation for Basic Research(projs. 20-02-00670a).
Acknowledgments:
The authors wish to thank these members of the LZ and/or LUX collaborations who reviewed adraft of the Xe section informally and provided helpful comments: Prof. Henrique Araújo of Imperial College London,Andrew Stevens from Oxford University, and Prof. Chamkaur Ghag of University College London. We also thankProf. Dan McKinsey and all of his students and postdocs who worked on PIXeY, with whom we have had very fruitfuldiscussions over the years. Lastly, Szydagis thanks Jason Sokaris and Steve Cifarelli for early work on the optimizedenergy scale, as well as Prof. Dmitri Akimov of MEPhI, for allowing his advisee E. Kozlova to work on NEST, and onthis paper.
References
1. Akerib, D.; Akerlof, C.; Alsum, S.; Araújo, H.; Arthurs, M.; Bai, X.; Bailey, A.; Balajthy, J.; Balashov, S.; Bauer, D.;et al.. Projected WIMP sensitivity of the LUX-ZEPLIN dark matter experiment.
Physical Review D , .doi:10.1103/physrevd.101.052002.2. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Amaro, F.; Anthony, M.; Arneodo, F.; Barrow, P.; Baudis, L.;Bauermeister, B.; et al.. First Dark Matter Search Results from the XENON1T Experiment. Physical ReviewLetters , . doi:10.1103/physrevlett.119.181301.3. Cui, X.; Abdukerim, A.; Chen, W.; Chen, X.; Chen, Y.; Dong, B.; Fang, D.; Fu, C.; Giboni, K.; Giuliani, F.; Gu, L.;Gu, Y.; Guo, X.; Guo, Z.; Han, K.; He, C.; Huang, D.; He, S.; Huang, X.; Huang, Z.; Ji, X.; Ju, Y.; Li, S.; Li, Y.;Lin, H.; Liu, H.; Liu, J.; Ma, Y.; Mao, Y.; Ni, K.; Ning, J.; Ren, X.; Shi, F.; Tan, A.; Wang, C.; Wang, H.; Wang, M.;Wang, Q.; Wang, S.; Wang, X.; Wang, X.; Wu, Q.; Wu, S.; Xiao, M.; Xie, P.; Yan, B.; Yang, Y.; Yue, J.; Zhang, D.;Zhang, H.; Zhang, T.; Zhang, T.; Zhao, L.; Zhou, J.; Zhou, N.; Zhou, X. Dark Matter Results from 54-Ton-DayExposure of PandaX-II Experiment. Phys. Rev. Lett. , , 181302. doi:10.1103/PhysRevLett.119.181302.4. Li, C.Y.; Si, Z.G.; Zhou, Y.F. Constraints on dark matter interactions from the first results of DarkSide-50. Nuclear Physics B , , 114678. doi:10.1016/j.nuclphysb.2019.114678.5. Ajaj, R.; Amaudruz, P.A.; Araujo, G.; Baldwin, M.; Batygov, M.; Beltran, B.; Bina, C.; Bonatt, J.; Boulay, M.;Broerman, B.; et al.. Search for dark matter with a 231-day exposure of liquid argon using DEAP-3600 atSNOLAB. Physical Review D , . doi:10.1103/physrevd.100.022004.6. McCabe, C. Astrophysical uncertainties of dark matter direct detection experiments. Physical Review D , . doi:10.1103/physrevd.82.023530.7. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Althueser, L.; Amaro, F.; Anthony, M.; Arneodo, F.; Barrow, P.;Baudis, L.; et al.. Search for bosonic super-WIMP interactions with the XENON100 experiment. Physical ReviewD , . doi:10.1103/physrevd.96.122002.8. Abi, B.; others. Deep Underground Neutrino Experiment (DUNE), Far Detector Technical Design Report,Volume I: Introduction to DUNE, 2020, [arXiv:physics.ins-det/2002.02967].9. Abratenko, P.; others. A Convolutional Neural Network for Multiple Particle Identification in the MicroBooNELiquid Argon Time Projection Chamber, 2020, [arXiv:hep-ex/2010.08653].10. Anton, G.; Badhrees, I.; Barbeau, P.; Beck, D.; Belov, V.; Bhatta, T.; Breidenbach, M.; Brunner, T.; Cao, G.; Cen,W.; et al.. Search for Neutrinoless Double-Beta Decay with the Complete EXO-200 Dataset. Physical ReviewLetters , . doi:10.1103/physrevlett.123.161802.11. Woodruff, K.; Baeza-Rubio, J.; Huerta, D.; Jones, B.; McDonald, A.; Norman, L.; Nygren, D.; Adams, C.; Álvarez,V.; Arazi, L.; et al.. Radio frequency and DC high voltage breakdown of high pressure helium, argon, andxenon. Journal of Instrumentation , , P04022–P04022. doi:10.1088/1748-0221/15/04/p04022.12. Akerib, D.; Bai, X.; Bedikian, S.; Bernard, E.; Bernstein, A.; Bolozdynya, A.; Bradley, A.; Byram, D.; Cahn,S.; Camp, C.; et al.. The Large Underground Xenon (LUX) experiment. Nuclear Instruments and Methods in
Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment , , 111–126.doi:10.1016/j.nima.2012.11.135.13. Albert, J.; others. Search for Majorana neutrinos with the first two years of EXO-200 data. Nature , , 229–234. doi:10.1038/nature13432.14. Fernandes, L.M.P.; Freitas, E.D.C.; Ball, M.; Gómez-Cadenas, J.J.; Monteiro, C.M.B.; Yahlali, N.; Nygren, D.;Santos, J.M.F.d. Primary and secondary scintillation measurements in a Xenon Gas Proportional ScintillationCounter. Journal of Instrumentation , , P09006–P09006. doi:10.1088/1748-0221/5/09/p09006.15. Szydagis, M.; et al.. NEST: Noble Element Simulation Technique, A Symphony of Scintillation, 2020.16. Faham, C.; Gehman, V.; Currie, A.; Dobi, A.; Sorensen, P.; Gaitskell, R. Measurements of wavelength-dependentdouble photoelectron emission from single photons in VUV-sensitive photomultiplier tubes. Journal ofInstrumentation , , P09010–P09010. doi:10.1088/1748-0221/10/09/p09010.17. Aprile, E.; Arisaka, K.; Arneodo, F.; Askin, A.; Baudis, L.; Behrens, A.; Bokeloh, K.; Brown, E.; Cardoso, J.M.R.;Choi, B.; et al.. First Dark Matter Results from the XENON100 Experiment. Physical Review Letters , .doi:10.1103/physrevlett.105.131302.18. Akerib, D.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein, A.; Biesiadzinski, T.;Boulton, E.; et al.. Improved Limits on Scattering of Weakly Interacting Massive Particles from Reanalysis of2013 LUX Data. Physical Review Letters , . doi:10.1103/physrevlett.116.161301.19. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein, A.;Biesiadzinski, T.; et al.. Results from a Search for Dark Matter in the Complete LUX Exposure. Physical ReviewLetters , . doi:10.1103/physrevlett.118.021303.20. Abe, K.; Hieda, K.; Hiraide, K.; Hirano, S.; Kishimoto, Y.; Ichimura, K.; Kobayashi, K.; Moriyama, S.; Nakagawa,K.; Nakahata, M.; et al.. Search for Bosonic Superweakly Interacting Massive Dark Matter Particles with theXMASS-I Detector. Physical Review Letters , . doi:10.1103/physrevlett.113.121301.21. Hackett, B.R. The DarkSide-50 Experiment: Electron Recoil Calibrations and A Global Energy Variable. PhDthesis, Hawaii U., 2017. doi:10.2172/1422185.22. Agnes, P. Direct Search for Dark Matter with the DarkSide Experiment. PhD thesis, APC, Paris, 2016.23. Pagani, L. Direct dark matter detection with the DarkSide-50 experiment. PhD thesis, University of Genoa,2017.24. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Balajthy, J.; Baxter, A.; Bernard, E.; Bernstein, A.; Biesiadzinski, T.;Boulton, E.; et al.. Improved modeling of beta electronic recoils in liquid xenon using LUX calibration data. Journal of Instrumentation , , T02007–T02007. doi:10.1088/1748-0221/15/02/t02007.25. Boulton, E. Applications of Two-Phase Xenon Time Projection Chambers: Searching for Dark Matter andSpecial Nuclear Materials. PhD thesis, Yale U., 2019.26. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein, A.;Biesiadzinski, T.; et al.. Kr83m calibration of the 2013 LUX dark matter search. Physical Review D , .doi:10.1103/physrevd.96.112009.27. Akerib, D.S.; et al.. Low-energy (0.7-74 keV) nuclear recoil calibration of the LUX dark matter experimentusing D-D neutron scattering kinematics, 2016, [arXiv:physics.ins-det/1608.05381].28. Sarkis, Y.; Aguilar-Arevalo, A.; D’Olivo, J.C. Study of the ionization efficiency for nuclear recoils in purecrystals. Physical Review D , . doi:10.1103/physrevd.101.102001.29. Angle, J.; Aprile, E.; Arneodo, F.; Baudis, L.; Bernstein, A.; Bolozdynya, A.; Brusov, P.; Coelho, L.C.C.; Dahl,C.E.; DeViveiros, L.; et al.. First Results from the XENON10 Dark Matter Experiment at the Gran Sasso NationalLaboratory. Physical Review Letters , . doi:10.1103/physrevlett.100.021303.30. Manzur, A.; Curioni, A.; Kastens, L.; McKinsey, D.; Ni, K.; Wongjirad, T. Scintillation efficiency and ionizationyield of liquid xenon for mono-energetic nuclear recoils down to 4 keV. Phys. Rev. C , , 025808,[arXiv:physics.ins-det/0909.1063]. doi:10.1103/PhysRevC.81.025808.31. Plante, G.; Aprile, E.; Budnik, R.; Choi, B.; Giboni, K.L.; Goetzke, L.W.; Lang, R.F.; Lim, K.E.;Melgarejo Fernandez, A.J. New measurement of the scintillation efficiency of low-energy nuclear recoilsin liquid xenon. Physical Review C , . doi:10.1103/physrevc.84.045805.
32. Szydagis, M.; Barry, N.; Kazkaz, K.; Mock, J.; Stolp, D.; Sweany, M.; Tripathi, M.; Uvarov, S.; Walsh, N.; Woods,M. NEST: a comprehensive model for scintillation yield in liquid xenon.
Journal of Instrumentation , , P10002–P10002. doi:10.1088/1748-0221/6/10/p10002.33. Aprile, E.; Budnik, R.; Choi, B.; Contreras, H.A.; Giboni, K.L.; Goetzke, L.W.; Koglin, J.E.; Lang, R.F.; Lim, K.E.;Melgarejo Fernandez, A.J.; et al.. Measurement of the scintillation yield of low-energy electrons in liquid xenon. Physical Review D , . doi:10.1103/physrevd.86.112004.34. Szydagis, M.; Fyhrie, A.; Thorngren, D.; Tripathi, M. Enhancement of NEST capabilities forsimulating low-energy recoils in liquid xenon. Journal of Instrumentation , , C10003–C10003.doi:10.1088/1748-0221/8/10/c10003.35. Sorensen, P.; Dahl, C.E. Nuclear recoil energy scale in liquid xenon with application to the direct detection ofdark matter. Physical Review D , . doi:10.1103/physrevd.83.063501.36. Dahl, C.E. The physics of background discrimination in liquid xenon, and first results from Xenon10 in thehunt for WIMP dark matter. PhD thesis, Princeton U., 2009.37. Szydagis, M.; et al.. A Detailed Look at the First Results from the Large Underground Xenon (LUX) DarkMatter Experiment, 2014, [arXiv:hep-ex/1402.3731].38. Angle, J.; Aprile, E.; Arneodo, F.; Baudis, L.; Bernstein, A.; Bolozdynya, A.I.; Coelho, L.C.C.; Dahl, C.E.;DeViveiros, L.; Ferella, A.D.; et al.. Search for Light Dark Matter in XENON10 Data. Physical Review Letters , . doi:10.1103/physrevlett.107.051301.39. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Althueser, L.; Amaro, F.; Antochi, V.; Angelino, E.; Arneodo, F.;Barge, D.; et al.. Light Dark Matter Search with Ionization Signals in XENON1T. Physical Review Letters , . doi:10.1103/physrevlett.123.251801.40. Aprile, E.; Angle, J.; Arneodo, F.; Baudis, L.; Bernstein, A.; Bolozdynya, A.; Brusov, P.; Coelho, L.; Dahl, C.;DeViveiros, L.; et al.. Design and performance of the XENON10 dark matter experiment. Astroparticle Physics , , 679–698. doi:10.1016/j.astropartphys.2011.01.006.41. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Althueser, L.; Amaro, F.D.; Antochi, V.C.; Angelino, E.;Angevaare, J.; Arneodo, F.; et al.. Energy resolution and linearity of XENON1T in the MeV energy range. TheEuropean Physical Journal C , . doi:10.1140/epjc/s10052-020-8284-0.42. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Althueser, L.; Amaro, F.; Antochi, V.; Angelino, E.;Angevaare, J.; Arneodo, F.; et al.. Excess electronic recoil events in XENON1T. Physical Review D , . doi:10.1103/physrevd.102.072004.43. Obodovskii, I.; Ospanov, K. Scintillation output of liquid xenon for low-energy gamma-quanta. Instrumentsand Experimental Techniques , , 42–45.44. Aprile, E.; Giboni, K.L.; Majewski, P.; Ni, K.; Yamashita, M.; Hasty, R.; Manzur, A.; McKinsey, D.N.Scintillation response of liquid xenon to low energy nuclear recoils. Phys. Rev. D , , 072006.doi:10.1103/PhysRevD.72.072006.45. Aprile, E.; Dahl, C.E.; de Viveiros, L.; Gaitskell, R.J.; Giboni, K.L.; Kwong, J.; Majewski, P.; Ni, K.; Shutt, T.;Yamashita, M. Simultaneous Measurement of Ionization and Scintillation from Nuclear Recoils in LiquidXenon for a Dark Matter Experiment. Phys. Rev. Lett. , , 081302. doi:10.1103/PhysRevLett.97.081302.46. Baudis, L.; Dujmovic, H.; Geis, C.; James, A.; Kish, A.; Manalaysay, A.; Marrodán Undagoitia, T.;Schumann, M. Response of liquid xenon to Compton electrons down to 1.5 keV. Physical Review D , . doi:10.1103/physrevd.87.115015.47. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Althueser, L.; Amaro, F.; Anthony, M.; Arneodo, F.; Baudis, L.;Bauermeister, B.; et al.. Dark Matter Search Results from a One Ton-Year Exposure of XENON1T. PhysicalReview Letters , . doi:10.1103/physrevlett.121.111302.48. Szydagis, M.; Balajthy, J.; Brodsky, J.; Cutter, J.; Huang, J.; Kozlova, E.; Lenardo, B.; Manalaysay, A.; McKinsey,D.; Mooney, M.; Mueller, J.; Ni, K.; Rischbieter, G.; Tripathi, M.; Tunnell, C.; Velan, V.; Zhao, Z. Noble ElementSimulation Technique, 2018. doi:10.5281/zenodo.4062516.
49. Akerib, D.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Bedikian, S.; Bernard, E.; Bernstein, A.; Bolozdynya, A.;Bradley, A.; et al.. First Results from the LUX Dark Matter Experiment at the Sanford Underground ResearchFacility.
Physical Review Letters , . doi:10.1103/physrevlett.112.091303.50. Yahlali, N.; Ball, M.; Cárcel, S.; Díaz, J.; Gil, A.; Gómez Cadenas, J.; Martín-Albo, J.; Monrabal, F.; Serra, L.; Sorel,M. NEXT: Neutrino Experiment with high pressure Xenon gas TPC. Nuclear Instruments and Methods in PhysicsResearch Section A: Accelerators, Spectrometers, Detectors and Associated Equipment , , 520 – 522. 11th PisaMeeting on Advanced Detectors, doi:https://doi.org/10.1016/j.nima.2009.10.076.51. Conti, E.; DeVoe, R.; Gratta, G.; Koffas, T.; Waldman, S.; Wodin, J.; Akimov, D.; Bower, G.; Breidenbach, M.;Conley, R.; et al.. Correlated fluctuations between luminescence and ionization in liquid xenon. Physical ReviewB , . doi:10.1103/physrevb.68.054201.52. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein, A.;Biesiadzinski, T.; et al.. Signal yields, energy resolution, and recombination fluctuations in liquid xenon. Physical Review D , . doi:10.1103/physrevd.95.012008.53. Akerib, D.S.; et al.. Discrimination of electronic recoils from nuclear recoils in two-phase xenon time projectionchambers, 2020, [arXiv:physics.ins-det/2004.06304].54. Mock, J.; Barry, N.; Kazkaz, K.; Stolp, D.; Szydagis, M.; Tripathi, M.; Uvarov, S.; Woods, M.; Walsh, N.Modeling pulse characteristics in Xenon with NEST. Journal of Instrumentation , , T04002–T04002.doi:10.1088/1748-0221/9/04/t04002.55. Chepel, V.; Araújo, H. Liquid noble gas detectors for low energy particle physics. Journal of Instrumentation , , R04001–R04001. doi:10.1088/1748-0221/8/04/r04001.56. Araújo, H. Revised performance parameters of the ZEPLIN-III dark matter experiment, 2020,[arXiv:physics.ins-det/2007.01683].57. Akerib, D.S.; Alsum, S.; Araújo, H.M.; Bai, X.; Balajthy, J.; Baxter, A.; Bernard, E.P.; Bernstein, A.; Biesiadzinski,T.P.; Boulton, E.M.; Boxer, B.; Brás, P.; Burdin, S.; Byram, D.; Carmona-Benitez, M.C.; Chan, C.; Cutter, J.E.;de Viveiros, L.; Druszkiewicz, E.; Fan, A.; Fiorucci, S.; Gaitskell, R.J.; Ghag, C.; Gilchriese, M.G.D.; Gwilliam,C.; Hall, C.R.; Haselschwardt, S.J.; Hertel, S.A.; Hogan, D.P.; Horn, M.; Huang, D.Q.; Ignarra, C.M.; Jacobsen,R.G.; Jahangir, O.; Ji, W.; Kamdin, K.; Kazkaz, K.; Khaitan, D.; Korolkova, E.V.; Kravitz, S.; Kudryavtsev, V.A.;Leason, E.; Lenardo, B.G.; Lesko, K.T.; Liao, J.; Lin, J.; Lindote, A.; Lopes, M.I.; Manalaysay, A.; Mannino,R.L.; Marangou, N.; McKinsey, D.N.; Mei, D.M.; Moongweluwan, M.; Morad, J.A.; Murphy, A.S.J.; Naylor, A.;Nehrkorn, C.; Nelson, H.N.; Neves, F.; Nilima, A.; Oliver-Mallory, K.C.; Palladino, K.J.; Pease, E.K.; Riffard, Q.;Rischbieter, G.R.C.; Rhyne, C.; Rossiter, P.; Shaw, S.; Shutt, T.A.; Silva, C.; Solmaz, M.; Solovov, V.N.; Sorensen,P.; Sumner, T.J.; Szydagis, M.; Taylor, D.J.; Taylor, R.; Taylor, W.C.; Tennyson, B.P.; Terman, P.A.; Tiedt, D.R.; To,W.H.; Tvrznikova, L.; Utku, U.; Uvarov, S.; Vacheret, A.; Velan, V.; Webb, R.C.; White, J.T.; Whitis, T.J.; Witherell,M.S.; Wolfs, F.L.H.; Woodward, D.; Xu, J.; Zhang, C. Investigation of background electron emission in the LUXdetector, 2020, [arXiv:physics.ins-det/2004.07791].58. Szydagis, M.; Levy, C.; Blockinger, G.M.; Kamaha, A.; Parveen, N.; Rischbieter, G.R.C. Investigating theXENON1T Low-Energy Electronic Recoil Excess Using NEST, 2020, [arXiv:hep-ex/2007.00528].59. Boulton, E.; Bernard, E.; Destefano, N.; Edwards, B.; Gai, M.; Hertel, S.; Horn, M.; Larsen, N.; Tennyson, B.;Wahl, C.; et al.. Calibration of a two-phase xenon time projection chamber with a 37Ar source. Journal ofInstrumentation , , P08004–P08004. doi:10.1088/1748-0221/12/08/p08004.60. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein, A.;Biesiadzinski, T.; et al.. Ultra-low energy calibration of LUX detector using Xe127 electron capture. PhysicalReview D , . doi:10.1103/physrevd.96.112011.61. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Amaro, F.; Anthony, M.; Arneodo, F.; Barrow, P.; Baudis, L.;Bauermeister, B.; et al.. Signal yields of keV electronic recoils and their discrimination from nuclear recoils inliquid xenon. Physical Review D , . doi:10.1103/physrevd.97.092007.62. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein, A.;Biesiadzinski, T.; et al.. Calibration, event reconstruction, data analysis, and limit calculation for the LUX darkmatter experiment. Physical Review D , . doi:10.1103/physrevd.97.102008.
63. Cutter, J. The Noble Element Simulation Technique v2, NorCal HEP-EXchange December 2, 2017.64. Akerib, D.; Alsum, S.; Aquino, C.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein,A.; et al.. First Searches for Axions and Axionlike Particles with the LUX Experiment.
Physical Review Letters , . doi:10.1103/physrevlett.118.261301.65. Goetzke, L.; Aprile, E.; Anthony, M.; Plante, G.; Weber, M. Measurement of light and charge yield of low-energyelectronic recoils in liquid xenon. Physical Review D , . doi:10.1103/physrevd.96.103007.66. Aprile, E.; Agostini, F.; Alfonsi, M.; Arisaka, K.; Arneodo, F.; Auger, M.; Balan, C.; Barrow, P.; Baudis, L.;Bauermeister, B.; et al.. First axion results from the XENON100 experiment. Physical Review D , .doi:10.1103/physrevd.90.062009.67. Akerib, D.; Bai, X.; Bedikian, S.; Bernard, E.; Bernstein, A.; Bradley, A.; Cahn, S.; Carmona-Benitez, M.;Carr, D.; Chapman, J.; et al.. LUXSim: A component-centric approach to low-background simulations. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment , , 63–77. doi:10.1016/j.nima.2012.02.010.68. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Althueser, L.; Amaro, F.; Antochi, V.; Arneodo, F.; Baudis, L.;Bauermeister, B.; et al.. XENON1T dark matter data analysis: Signal and background models and statisticalinference. Physical Review D , . doi:10.1103/physrevd.99.112009.69. Bloch, I.M.; Caputo, A.; Essig, R.; Redigolo, D.; Sholapurkar, M.; Volansky, T. Exploring New Physics withO(keV) Electron Recoils in Direct Detection Experiments, 2020, [arXiv:hep-ph/2006.14521].70. Delaquis, S.; Jewell, M.; Ostrovskiy, I.; Weber, M.; Ziegler, T.; Dalmasson, J.; Kaufman, L.; Richards, T.; Albert,J.; Anton, G.; et al.. Deep neural networks for energy and position reconstruction in EXO-200. Journal ofInstrumentation , , P08023–P08023. doi:10.1088/1748-0221/13/08/p08023.71. Carrara, N.; Ernst, J.A. On the Upper Limit of Separability, 2017, [arXiv:hep-ex/1708.09449].72. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein, A.;Biesiadzinski, T.; et al.. Liquid xenon scintillation measurements and pulse shape discrimination in the LUXdark matter detector. Physical Review D , . doi:10.1103/physrevd.97.112002.73. Akerib, D.; Bai, X.; Bernard, E.; Bernstein, A.; Bradley, A.; Byram, D.; Cahn, S.; Carmona-Benitez, M.; Chapman,J.; Coffey, T.; et al.. Technical results from the surface run of the LUX dark matter experiment. AstroparticlePhysics , , 34–43. doi:10.1016/j.astropartphys.2013.02.001.74. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Balajthy, J.; Baxter, A.; Beltrame, P.; Bernard, E.; Bernstein, A.;Biesiadzinski, T.; et al.. Extending light WIMP searches to single scintillation photons in LUX. Physical ReviewD , . doi:10.1103/physrevd.101.042001.75. Manalaysay, A.; Undagoitia, T.M.; Askin, A.; Baudis, L.; Behrens, A.; Ferella, A.D.; Kish, A.; Lebeda, O.;Santorelli, R.; Vénos, D.; et al.. Spatially uniform calibration of a liquid xenon detector at low energies using83mKr. Review of Scientific Instruments , , 073303. doi:10.1063/1.3436636.76. Akerib, D.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein, A.; Biesiadzinski,T.; Boulton, E.; et al.. Tritium calibration of the LUX dark matter experiment. Physical Review D , .doi:10.1103/physrevd.93.072009.77. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein, A.;Biesiadzinski, T.; et al.. 3D modeling of electric fields in the LUX detector. Journal of Instrumentation , , P11022–P11022. doi:10.1088/1748-0221/12/11/p11022.78. Doke, T.; Hitachi, A.; Kikuchi, J.; Masuda, K.; Okada, H.; Shibamura, E. Absolute Scintillation Yieldsin Liquid Argon and Xenon for Various Particles. Japanese Journal of Applied Physics , , 1538–1545.doi:10.1143/jjap.41.1538.79. Dobi, A. Measurement of the Electron Recoil Band of the LUX Dark Matter Detector With a Tritium CalibrationSource. PhD thesis, Maryland U., College Park, 2014. doi:10.13016/M24P5P.80. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Althueser, L.; Amaro, F.; Antochi, V.; Arneodo, F.; Baudis, L.;Bauermeister, B.; et al.. XENON1T dark matter data analysis: Signal reconstruction, calibration, and eventselection. Physical Review D , . doi:10.1103/physrevd.100.052014.
81. Lenardo, B.; Xu, J.; Pereverzev, S.; Akindele, O.A.; Naim, D.; Kingston, J.; Bernstein, A.; Kazkaz, K.; Tripathi,M.; Awe, C.; Li, L.; Runge, J.; Hedges, S.; An, P.; Barbeau, P.S. Measurement of the ionization yieldfrom nuclear recoils in liquid xenon between 0.3 – 6 keV with single-ionization-electron sensitivity, 2019,[arXiv:physics.ins-det/1908.00518].82. Auger, M.; Auty, D.J.; Barbeau, P.S.; Beauchamp, E.; Belov, V.; Benitez-Medina, C.; Breidenbach, M.; Brunner, T.;Burenkov, A.; Cleveland, B.; et al.. Search for Neutrinoless Double-Beta Decay in Xe136 with EXO-200.
PhysicalReview Letters , . doi:10.1103/physrevlett.109.032505.83. Akerib, D.S.; Akerlof, C.W.; Alqahtani, A.; Alsum, S.K.; Anderson, T.J.; Angelides, N.; Araújo, H.M.; Armstrong,J.E.; Arthurs, M.; Bai, X.; et al.. Projected sensitivity of the LUX-ZEPLIN experiment to the 0neutrinoBetaBetadecay of Xe136. Physical Review C , . doi:10.1103/physrevc.102.014602.84. Aprile, E.; Alfonsi, M.; Arisaka, K.; Arneodo, F.; Balan, C.; Baudis, L.; Behrens, A.; Beltrame, P.; Bokeloh, K.;Brown, E.; et al.. Analysis of the XENON100 dark matter search data. Astroparticle Physics , , 11–24.doi:10.1016/j.astropartphys.2013.10.002.85. Ackerman, N.; Aharmim, B.; Auger, M.; Auty, D.J.; Barbeau, P.S.; Barry, K.; Bartoszek, L.; Beauchamp, E.; Belov,V.; Benitez-Medina, C.; et al.. Observation of Two-Neutrino Double-Beta Decay in Xe136 with the EXO-200Detector. Physical Review Letters , . doi:10.1103/physrevlett.107.212501.86. Davis, C.; Hall, C.; Albert, J.; Barbeau, P.; Beck, D.; Belov, V.; Breidenbach, M.; Brunner, T.; Burenkov, A.; Cao,G.; et al.. An optimal energy estimator to reduce correlated noise for the EXO-200 light readout. Journal ofInstrumentation , , P07015–P07015. doi:10.1088/1748-0221/11/07/p07015.87. Albert, J.B.; Auger, M.; Auty, D.J.; Barbeau, P.S.; Beauchamp, E.; Beck, D.; Belov, V.; Benitez-Medina, C.; Bonatt,J.; Breidenbach, M.; et al.. An improved measurement of the 2nuBetaBeta half-life of 136Xe with the EXO-200detector. Physical Review C , . doi:10.1103/physrevc.89.015502.88. Albert, J.; Anton, G.; Badhrees, I.; Barbeau, P.; Bayerlein, R.; Beck, D.; Belov, V.; Breidenbach, M.; Brunner,T.; Cao, G.; et al.. Searches for double beta decay of Xe134 with EXO-200. Physical Review D , .doi:10.1103/physrevd.96.092001.89. Auger, M.; Auty, D.J.; Barbeau, P.S.; Bartoszek, L.; Baussan, E.; Beauchamp, E.; Benitez-Medina, C.; Breidenbach,M.; Chauhan, D.; Cleveland, B.; et al.. The EXO-200 detector, part I: detector design and construction. Journal ofInstrumentation , , P05010–P05010. doi:10.1088/1748-0221/7/05/p05010.90. Albert, J.B.; Auty, D.J.; Barbeau, P.S.; Beck, D.; Belov, V.; Benitez-Medina, C.; Breidenbach, M.; Brunner, T.;Burenkov, A.; Cao, G.F.; Chambers, C.; Cleveland, B.; Coon, M.; Craycraft, A.; Daniels, T.; Danilov, M.;Daugherty, S.J.; Davis, C.G.; Davis, J.; Delaquis, S.; Der Mesrobian-Kabakian, A.; DeVoe, R.; Didberidze, T.;Dolgolenko, A.; Dolinski, M.J.; Dunford, M.; Fairbank, W.; Farine, J.; Feldmeier, W.; Fierlinger, P.; Fudenberg,D.; Giroux, G.; Gornea, R.; Graham, K.; Gratta, G.; Hall, C.; Herrin, S.; Hughes, M.; Jewell, M.J.; Jiang, X.S.;Johnson, A.; Johnson, T.N.; Johnston, S.; Karelin, A.; Kaufman, L.J.; Killick, R.; Koffas, T.; Kravitz, S.; Kuchenkov,A.; Kumar, K.S.; Leonard, D.S.; Licciardi, C.; Lin, Y.H.; Ling, J.; MacLellan, R.; Marino, M.G.; Mong, B.;Moore, D.; Nelson, R.; Odian, A.; Ostrovskiy, I.; Piepke, A.; Pocar, A.; Prescott, C.Y.; Rivas, A.; Rowson, P.C.;Russell, J.J.; Schubert, A.; Sinclair, D.; Smith, E.; Stekhanov, V.; Tarka, M.; Tolba, T.; Tsang, R.; Twelker, K.;Vuilleumier, J.L.; Waite, A.; Walton, J.; Walton, T.; Weber, M.; Wen, L.J.; Wichoski, U.; Wood, J.; Yang, L.; Yen,Y.R.; Zeldovich, O.Y. Investigation of radioactivity-induced backgrounds in EXO-200. Phys. Rev. C , , 015503. doi:10.1103/PhysRevC.92.015503.91. Albert, J.; Auty, D.; Barbeau, P.; Beck, D.; Belov, V.; Breidenbach, M.; Brunner, T.; Burenkov, A.; Cao, G.;Chambers, C.; et al.. Cosmogenic backgrounds to ZeroNuBetaBeta in EXO-200. Journal of Cosmology andAstroparticle Physics , , 029–029. doi:10.1088/1475-7516/2016/04/029.92. Albert, J.; Barbeau, P.; Beck, D.; Belov, V.; Breidenbach, M.; Brunner, T.; Burenkov, A.; Cao, G.; Chambers, C.;Cleveland, B.; et al.. First search for Lorentz and CPT violation in double beta decay with EXO-200. PhysicalReview D , . doi:10.1103/physrevd.93.072001.93. Leonard, D.; Auty, D.; Didberidze, T.; Gornea, R.; Grinberg, P.; MacLellan, R.; Methven, B.; Piepke, A.;Vuilleumier, J.L.; Albert, J.; et al.. Trace radioactive impurities in final construction materials for EXO-200. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment , , 169–179. doi:10.1016/j.nima.2017.04.049.94. Albert, J.; Anton, G.; Badhrees, I.; Barbeau, P.; Bayerlein, R.; Beck, D.; Belov, V.; Breidenbach, M.; Brunner, T.;Cao, G.; et al.. Search for Neutrinoless Double-Beta Decay with the Upgraded EXO-200 Detector. PhysicalReview Letters , . doi:10.1103/physrevlett.120.072701.95. Asakura, K.; et al. Results from KamLAND-Zen, 2014, [arXiv:physics.ins-det/1409.0077].96. Shirai, J. KamLAND-Zen Experiment. Proceedings of Science , HQL2018 .97. Asakura, K.; Gando, A.; Gando, Y.; Hachiya, T.; Hayashida, S.; Ikeda, H.; Inoue, K.; Ishidoshiro, K.; Ishikawa,T.; Ishio, S.; et al.. Search for double-beta decay of 136Xe to excited states of 136Ba with the KamLAND-Zenexperiment.
Nuclear Physics A , , 171–181. doi:10.1016/j.nuclphysa.2015.11.011.98. Gando, A.; Gando, Y.; Hanakago, H.; Ikeda, H.; Inoue, K.; Ishidoshiro, K.; Kato, R.; Koga, M.;Matsuda, S.; Mitsui, T.; et al.. Limit on Neutrinoless Beta Beta Decay of Xe136 from the First Phaseof KamLAND-Zen and Comparison with the Positive Claim in Ge76. Physical Review Letters , .doi:10.1103/physrevlett.110.062502.99. Gando, A.; Gando, Y.; Hanakago, H.; Ikeda, H.; Inoue, K.; Kato, R.; Koga, M.; Matsuda, S.; Mitsui, T.; Nakada,T.; et al.. Limits on Majoron-emitting Double-Beta Decays of 136Xe in the KamLAND-Zen experiment. PhysicalReview C , . doi:10.1103/physrevc.86.021601.100. Gando, A.; Gando, Y.; Hanakago, H.; Ikeda, H.; Inoue, K.; Kato, R.; Koga, M.; Matsuda, S.; Mitsui, T.; Nakada, T.;et al.. Measurement of the double-beta decay half-life of 136Xe with the KamLAND-Zen experiment. PhysicalReview C , . doi:10.1103/physrevc.85.045504.101. Gando, A.; Gando, Y.; Hachiya, T.; Hayashi, A.; Hayashida, S.; Ikeda, H.; Inoue, K.; Ishidoshiro, K.; Karino, Y.;Koga, M.; et al.. Search for Majorana Neutrinos Near the Inverted Mass Hierarchy Region with KamLAND-Zen. Physical Review Letters , . doi:10.1103/physrevlett.117.082503.102. Leonard, D.S.; Grinberg, P.; Weber, P.; Baussan, E.; Djurcic, Z.; Keefer, G.; Piepke, A.; Pocar, A.; Vuilleumier,J.L.; Vuilleumier, J.M.; Akimov, D.; Bellerive, A.; Bowcock, M.; Breidenbach, M.; Burenkov, A.; Conley, R.;Craddock, W.; Danilov, M.; DeVoe, R.; Dixit, M.; Dolgolenko, A.; Ekchtout, I.; au2, W.F.J.; Farine, J.; Fierlinger,P.; Flatt, B.; Gratta, G.; Green, M.; Hall, C.; Hall, K.; Hallman, D.; Hargrove, C.; Herbst, R.; Hodgson, J.; Jeng, S.;Kolkowitz, S.; Kovalenko, A.; Kovalenko, D.; LePort, F.; Mackay, D.; Moe, M.; Díez, M.M.; Neilson, R.; Odian,A.; O’Sullivan, K.; Ounalli, L.; Prescott, C.Y.; Rowson, P.C.; Schenker, D.; Sinclair, D.; Skarpaas, K.; Smirnov, G.;Stekhanov, V.; Strickland, V.; Virtue, C.; Wamba, K.; Wodin, J. Systematic study of trace radioactive impuritiesin candidate construction materials for EXO-200, 2008, [arXiv:physics.ins-det/0709.4524].103. Gallina, G.; Giampa, P.; Retière, F.; Kroeger, J.; Zhang, G.; Ward, M.; Margetak, P.; Li, G.; Tsang, T.; Doria,L.; et al.. Characterization of the Hamamatsu VUV4 MPPCs for nEXO. Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment , , 371–379.doi:10.1016/j.nima.2019.05.096.104. Nakarmi, P.; Ostrovskiy, I.; Soma, A.; Retière, F.; Kharusi, S.A.; Alfaris, M.; Anton, G.; Arnquist, I.; Badhrees, I.;Barbeau, P.; et al.. Reflectivity and PDE of VUV4 Hamamatsu SiPMs in liquid xenon. Journal of Instrumentation , , P01019–P01019. doi:10.1088/1748-0221/15/01/p01019.105. Akerib, D.; Bai, X.; Bernard, E.; Bernstein, A.; Bradley, A.; Byram, D.; Cahn, S.; Carmona-Benitez, M.; Carr,D.; Chapman, J.; et al.. An ultra-low background PMT for liquid xenon detectors. Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment , , 1–6.doi:10.1016/j.nima.2012.11.020.106. Aprile, E.; Agostini, F.; Alfonsi, M.; Arazi, L.; Arisaka, K.; Arneodo, F.; Auger, M.; Balan, C.; Barrow, P.; et al..Lowering the radioactivity of the photomultiplier tubes for the XENON1T dark matter experiment. TheEuropean Physical Journal C , . doi:10.1140/epjc/s10052-015-3657-5.107. Alvarez, V.; others. Near-Intrinsic Energy Resolution for 30 to 662 keV Gamma Rays in a High PressureXenon Electroluminescent TPC. Nucl. Instrum. Meth. A , , 101–114, [arXiv:physics.ins-det/1211.4474].doi:10.1016/j.nima.2012.12.123. α X-rays.
Journal of Instrumentation , , P10007–P10007.doi:10.1088/1748-0221/9/10/p10007.109. Aprile, E.; Mukherjee, R.; Suzuki, M. Performance of a liquid xenon ionization chamber irradiated with electronsand gamma-rays. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers,Detectors and Associated Equipment , , 177 – 185. doi:https://doi.org/10.1016/0168-9002(91)90507-M.110. Anton, G.; Badhrees, I.; Barbeau, P.S.; Beck, D.; Belov, V.; Bhatta, T.; Breidenbach, M.; Brunner, T.; Cao, G.F.; Cen,W.R.; et al.. Measurement of the scintillation and ionization response of liquid xenon at MeV energies in theEXO-200 experiment. Physical Review C , . doi:10.1103/physrevc.101.065501.111. Lebedenko, V.N.; Araújo, H.M.; Barnes, E.J.; Bewick, A.; Cashmore, R.; Chepel, V.; Currie, A.; Davidge, D.;Dawson, J.; Durkin, T.; Edwards, B.; Ghag, C.; Horn, M.; Howard, A.S.; Hughes, A.J.; Jones, W.G.; Joshi, M.;Kalmus, G.E.; Kovalenko, A.G.; Lindote, A.; Liubarsky, I.; Lopes, M.I.; Lüscher, R.; Majewski, P.; Murphy, A.S.J.;Neves, F.; Pinto da Cunha, J.; Preece, R.; Quenby, J.J.; Scovell, P.R.; Silva, C.; Solovov, V.N.; Smith, N.J.T.; Smith,P.F.; Stekhanov, V.N.; Sumner, T.J.; Thorne, C.; Walker, R.J. Results from the first science run of the ZEPLIN-IIIdark matter search experiment. Phys. Rev. D , , 052010. doi:10.1103/PhysRevD.80.052010.112. Aprile, E.; Bolotnikov, A.E.; Bolozdynya, A.I.; Doke, T., Front Matter. In Noble Gas Detectors ; John Wiley& Sons, Ltd, 2006; pp. I–XVI, [https://onlinelibrary.wiley.com/doi/pdf/10.1002/9783527610020.fmatter].doi:10.1002/9783527610020.fmatter.113. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Balajthy, J.; Baxter, A.; Beltrame, P.; Bernard, E.; Bernstein, A.;Biesiadzinski, T.; et al.. Improved measurements of the beta-decay response of liquid xenon with the LUXdetector.
Physical Review D , . doi:10.1103/physrevd.100.022002.114. You, L. Superconducting nanowire single-photon detectors for quantum information. Nanophotonics
01 Sep.2020 , , 2673 – 2692. doi:https://doi.org/10.1515/nanoph-2020-0186.115. Kravitz, S.; Smith, R.; Hagaman, L.; Bernard, E.; Mckinsey, D.; Rudd, L.; Tvrznikova, L.; Gann, G.; Sakai, M.Measurements of angle-resolved reflectivity of PTFE in liquid xenon with IBEX. The European Physical Journal C , , 1–20.116. Escobar, C.O.; Rubinov, P.; Tilly, E. Near-infrared scintillation of liquid argon: recent resultsobtained with the NIR facility at Fermilab. Journal of Instrumentation , , C03031–C03031.doi:10.1088/1748-0221/13/03/c03031.117. Araújo, H.; Akimov, D.; Barnes, E.; Belov, V.; Bewick, A.; Burenkov, A.; Chepel, V.; Currie, A.; DeViveiros,L.; Edwards, B.; et al.. Radioactivity backgrounds in ZEPLIN–III. Astroparticle Physics , , 495–502.doi:10.1016/j.astropartphys.2011.11.001.118. Akerib, D.; Araújo, H.; Bai, X.; Bailey, A.; Balajthy, J.; Bernard, E.; Bernstein, A.; Bradley, A.; Byram, D.; Cahn, S.;et al.. Radiogenic and muon-induced backgrounds in the LUX dark matter detector. Astroparticle Physics , , 33–46. doi:10.1016/j.astropartphys.2014.07.009.119. Li, S.; Chen, X.; Cui, X.; Fu, C.; Ji, X.; Lin, Q.; Liu, J.; Liu, X.; Tan, A.; Wang, X.; Xiao, M.; Xie, P. Krypton andradon background in the PandaX-I dark matter experiment. Journal of Instrumentation , , T02002–T02002.doi:10.1088/1748-0221/12/02/t02002.120. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Amaro, F.D.; Anthony, M.; Arneodo, F.; Barrow, P.; Baudis, L.;et al.. Intrinsic backgrounds from Rn and Kr in the XENON100 experiment. The European Physical Journal C , . doi:10.1140/epjc/s10052-018-5565-y. Physical Review D , . doi:10.1103/physrevd.98.112003.122. Huang, D. Ultra-Low Energy Calibration of the LUX and LZ Dark Matter Detectors. PhD thesis, Brown U.,2020. doi:10.26300/zvs6-fx07.123. Edwards, B.; Bernard, E.; Boulton, E.; Destefano, N.; Gai, M.; Horn, M.; Larsen, N.; Tennyson, B.; Tvrznikova,L.; Wahl, C.; et al.. Extraction efficiency of drifting electrons in a two-phase xenon time projection chamber. Journal of Instrumentation , , P01005–P01005. doi:10.1088/1748-0221/13/01/p01005.124. Xu, J.; Pereverzev, S.; Lenardo, B.; Kingston, J.; Naim, D.; Bernstein, A.; Kazkaz, K.; Tripathi, M. Electronextraction efficiency study for dual-phase xenon dark matter experiments. Physical Review D , .doi:10.1103/physrevd.99.103024.125. Sorensen, P.; Manzur, A.; Dahl, C.; Angle, J.; Aprile, E.; Arneodo, F.; Baudis, L.; Bernstein, A.; Bolozdynya, A.;Coelho, L.; et al.. The scintillation and ionization yield of liquid xenon for nuclear recoils. Nuclear Instrumentsand Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment , , 339–346. doi:10.1016/j.nima.2008.12.197.126. Sorensen, P. A coherent understanding of low-energy nuclear recoils in liquid xenon. Journal of Cosmology andAstroparticle Physics , , 033–033. doi:10.1088/1475-7516/2010/09/033.127. Sorensen, P.; Angle, J.; Aprile, E.; Arneodo, F.; Baudis, L.; Bernstein, A.; Bolozdynya, A.; Brusov, P.; Coelho,L.C.C.; Dahl, C.E.; DeViveiros, L.; Ferella, A.D.; Fernandes, L.M.P.; Fiorucci, S.; Gaitskell, R.J.; Giboni, K.L.;Gomez, R.; Hasty, R.; Kastens, L.; Kwong, J.; Lopes, J.A.M.; Madden, N.; Manalaysay, A.; Manzur, A.; McKinsey,D.N.; Monzani, M.E.; Ni, K.; Oberlack, U.; Orboeck, J.; Plante, G.; Santorelli, R.; dos Santos, J.M.F.; Shagin, P.;Shutt, T.; Schulte, S.; Winant, C.; Yamashita, M. Lowering the low-energy threshold of xenon detectors, 2010,[arXiv:astro-ph.IM/1011.6439].128. Horn, M.; Belov, V.; Akimov, D.; Araújo, H.; Barnes, E.; Burenkov, A.; Chepel, V.; Currie, A.; Edwards, B.; Ghag,C.; et al.. Nuclear recoil scintillation and ionisation yields in liquid xenon from ZEPLIN-III data. Physics LettersB , , 471–476. doi:10.1016/j.physletb.2011.10.038.129. Aprile, E.; Alfonsi, M.; Arisaka, K.; Arneodo, F.; Balan, C.; Baudis, L.; Bauermeister, B.; Behrens, A.; Beltrame,P.; Bokeloh, K.; et al.. Response of the XENON100 dark matter detector to nuclear recoils. Physical Review D , . doi:10.1103/physrevd.88.012006.130. Wang, Q.; Abdukerim, A.; Chen, W.; Chen, X.; Chen, Y.; Cheng, C.; Cui, X.; Fan, Y.; Fang, D.; Fu, C.; Fu, M.;Geng, L.; Giboni, K.; Gu, L.; Guo, X.; Han, K.; He, C.; He, S.; Huang, D.; Huang, Y.; Huang, Y.; Huang, Z.; Ji, X.;Ju, Y.; Li, S.; Liu, H.; Liu, J.; Ma, W.; Ma, Y.; Mao, Y.; Meng, Y.; Ni, K.; Ning, J.; Ning, X.; Ren, X.; Shang, C.; Si,L.; Shen, G.; Tan, A.; Wang, A.; Wang, H.; Wang, M.; Wang, S.; Wang, W.; Wang, X.; Wang, Z.; Wu, M.; Wu, S.;Wu, W.; Xia, J.; Xiao, M.; Xie, P.; Yan, B.; Yang, J.; Yang, Y.; Yu, C.; Yuan, J.; Yuan, Y.; Yue, J.; Zeng, X.; Zhang,D.; Zhang, T.; Zhao, L.; Zheng, Q.; Zhou, J.; Zhou, N.; Zhou, X. Results of Dark Matter Search using the FullPandaX-II Exposure, 2020, [arXiv:astro-ph.CO/2007.15469].131. Hitachi, A. Properties of liquid xenon scintillation for dark matter searches. Astropart. Phys. , , 247–256.doi:10.1016/j.astropartphys.2005.07.002.132. Sorensen, P. Atomic limits in the search for galactic dark matter. Physical Review D , .doi:10.1103/physrevd.91.083509.133. Bezrukov, F.; Kahlhoefer, F.; Lindner, M. Interplay between scintillation and ionization in liquid xenon DarkMatter searches. Astroparticle Physics , , 119–127. doi:10.1016/j.astropartphys.2011.06.008.134. Mu, W.; Xiong, X.; Ji, X. Scintillation Efficiency for Low-Energy Nuclear Recoils in Liquid-Xenon Dark MatterDetectors, 2013, [arXiv:physics.ins-det/1306.0170].135. Mu, W.; Ji, X. Ionization Yield from Nuclear Recoils in Liquid-Xenon Dark Matter Detection, 2013,[arXiv:physics.ins-det/1310.2094].136. Aprile, E.; Alfonsi, M.; Arisaka, K.; Arneodo, F.; Balan, C.; Baudis, L.; Bauermeister, B.; Behrens, A.; Beltrame,P.; Bokeloh, K.; et al.. The neutron background of the XENON100 dark matter search experiment. Journal ofPhysics G: Nuclear and Particle Physics , , 115201. doi:10.1088/0954-3899/40/11/115201. Astroparticle Physics , , 102391. doi:10.1016/j.astropartphys.2019.102391.139. Lewin, J.; Smith, P. Review of mathematics, numerical factors, and corrections for darkmatter experiments based on elastic nuclear recoil. Astroparticle Physics , , 87 – 112.doi:https://doi.org/10.1016/S0927-6505(96)00047-3.140. Verbus, J.R. An Absolute Calibration of Sub-1 keV Nuclear Recoils in Liquid Xenon Using D-D NeutronScattering Kinematics in the LUX Detector. PhD thesis, Brown U., 2016. doi:10.7301/Z01G0JQ7.141. Wang, L.; Mei, D.M. A comprehensive study of low-energy response for xenon-based dark matter experiments. Journal of Physics G: Nuclear and Particle Physics , , 055001. doi:10.1088/1361-6471/aa6403.142. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Althueser, L.; Amaro, F.; Antochi, V.; Angelino, E.; Arneodo, F.;Barge, D.; et al.. Search for Light Dark Matter Interactions Enhanced by the Migdal Effect or Bremsstrahlung inXENON1T. Physical Review Letters , . doi:10.1103/physrevlett.123.241803.143. Lindhard, J. Range concepts and heavy ion ranges. Mat. Fys. Medd. K. Dan. Vidensk. Selsk. , .144. Lenardo, B.; Kazkaz, K.; Manalaysay, A.; Mock, J.; Szydagis, M.; Tripathi, M. A Global Analysis ofLight and Charge Yields in Liquid Xenon. IEEE Transactions on Nuclear Science , , 3387–3396.doi:10.1109/tns.2015.2481322.145. Akerib, D.; Alsum, S.; Araújo, H.; Bai, X.; Balajthy, J.; Beltrame, P.; Bernard, E.; Bernstein, A.; Biesiadzinski, T.;Boulton, E.; et al.. Results of a Search for Sub-GeV Dark Matter Using 2013 LUX Data. Physical Review Letters , . doi:10.1103/physrevlett.122.131301.146. Akimov, D.; others. Observation of Coherent Elastic Neutrino-Nucleus Scattering. Science , , 1123–1126,[arXiv:nucl-ex/1708.01294]. doi:10.1126/science.aao0990.147. Akimov, D.; others. First Detection of Coherent Elastic Neutrino-Nucleus Scattering on Argon. ,[arXiv:nucl-ex/2003.10630].148. Aprile, E.; et al. Projected WIMP Sensitivity of the XENONnT Dark Matter Experiment, 2020,[arXiv:physics.ins-det/2007.08796].149. Plante, G. The XENON100 Dark Matter Experiment: Design, Construction, Calibration and 2010 Search Resultswith Improved Measurement of the Scintillation Response of Liquid Xenon to Low-Energy Nuclear Recoils.PhD thesis, Columbia U. (main), 2012.150. Akerib, D.; Akerlof, C.; Alqahtani, A.; Alsum, S.; Anderson, T.; Angelides, N.; Araújo, H.; Armstrong, J.; Arthurs,M.; Bai, X.; et al.. Simulations of events for the LUX-ZEPLIN (LZ) dark matter experiment. Astroparticle Physics , , 102480. doi:10.1016/j.astropartphys.2020.102480.151. Bernabei, R.; Belli, P.; Cappella, F.; Cerulli, R.; Montecchia, F.; Nozzoli, F.; Incicchitti, A.; Prosperi, D.; Dai, C.The DAMA pure liquid xenon experiment. International Workshop on Technique and Application of XenonDetectors, 2001, pp. 50–57.152. Chepel, V.; Solovov, V.; Neves, F.; Pereira, A.; Mendes, P.; Silva, C.; Lindote, A.; Pinto da Cunha, J.; Lopes,M.; Kossionides, S. Scintillation efficiency of liquid xenon for nuclear recoils with the energy down to 5 keV. Astroparticle Physics , , 58–63. doi:10.1016/j.astropartphys.2006.05.001.153. Verbus, J.; others. Proposed low-energy absolute calibration of nuclear recoils in a dual-phase nobleelement TPC using D-D neutron scattering kinematics. Nucl. Instrum. Meth. A , , 68–81,[arXiv:physics.ins-det/1608.05309]. doi:10.1016/j.nima.2017.01.053. Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment , , 250 – 303.doi:https://doi.org/10.1016/S0168-9002(03)01368-8.155. Allison, J.; others. Geant4 developments and applications. IEEE Trans. Nucl. Sci. , , 270.doi:10.1109/TNS.2006.869826.156. Arisaka, K.; Beltrame, P.; Ghag, C.; Lung, K.; Scovell, P. A new analysis method forWIMP searches with dual-phase liquid Xe TPCs. Astroparticle Physics , , 51 – 59.doi:https://doi.org/10.1016/j.astropartphys.2012.07.003.157. Lippincott, W.H.; Cahn, S.B.; Gastler, D.; Kastens, L.W.; Kearns, E.; McKinsey, D.N.; Nikkel, J.A. Calibration ofliquid argon and neon detectors with Kr83m. Physical Review C , . doi:10.1103/physrevc.81.045803.158. Kimura, M.; Aoyama, K.; Tanaka, M.; Yorita, K. Liquid argon scintillation response to electronicrecoils between 2.8–1275 keV in a high light yield single-phase detector. Physical Review D , .doi:10.1103/physrevd.102.092008.159. Agnes, P.; Alexander, T.; Alton, A.; Arisaka, K.; Back, H.; Baldin, B.; Biery, K.; Bonfini, G.; Bossa, M.; Brigatti,A.; et al.. First results from the DarkSide-50 dark matter experiment at Laboratori Nazionali del Gran Sasso. Physics Letters B , , 456–466. doi:10.1016/j.physletb.2015.03.012.160. Amaudruz, P.A.; Baldwin, M.; Batygov, M.; Beltran, B.; Bina, C.E.; Bishop, D.; Bonatt, J.; Boorman, G.; Boulay,M.G.; Broerman, B.; Bromwich, T.; Bueno, J.F.; Burghardt, P.M.; Butcher, A.; Cai, B.; Chan, S.; Chen, M.;Chouinard, R.; Cleveland, B.T.; Cranshaw, D.; Dering, K.; DiGioseffo, J.; Dittmeier, S.; Duncan, F.A.; Dunford,M.; Erlandson, A.; Fatemighomi, N.; Florian, S.; Flower, A.; Ford, R.J.; Gagnon, R.; Giampa, P.; Golovko, V.V.;Gorel, P.; Gornea, R.; Grace, E.; Graham, K.; Gulyev, E.; Hakobyan, R.; Hall, A.; Hallin, A.L.; Hamstra, M.;Harvey, P.J.; Hearns, C.; Jillings, C.J.; Kamaev, O.; Kemp, A.; Ku´zniak, M.; Langrock, S.; Zia, F.L.; Lehnert, B.;Lidgard, J.J.; Lim, C.; Lindner, T.; Linn, Y.; Liu, S.; Majewski, P.; Mathew, R.; McDonald, A.B.; McElroy, T.;McGinn, T.; McLaughlin, J.B.; Mead, S.; Mehdiyev, R.; Mielnichuk, C.; Monroe, J.; Muir, A.; Nadeau, P.; Nantais,C.; Ng, C.; Noble, A.J.; O’Dwyer, E.; Ohlmann, C.; Olchanski, K.; Olsen, K.S.; Ouellet, C.; Pasuthip, P.; Peeters,S.J.M.; Pollmann, T.R.; Rand, E.T.; Rau, W.; Rethmeier, C.; Retière, F.; Seeburn, N.; Shaw, B.; Singhrao, K.;Skensved, P.; Smith, B.; Smith, N.J.T.; Sonley, T.; Soukup, J.; Stainforth, R.; Stone, C.; Strickland, V.; Sur, B.; Tang,J.; Taylor, J.; Veloce, L.; Vázquez-Jáuregui, E.; Walding, J.; Ward, M.; Westerdale, S.; Woolsey, E.; Zielinski, J. Firstresults from the DEAP-3600 dark matter search with argon at SNOLAB, 2018, [arXiv:astro-ph.CO/1707.08042].161. Gastler, D.; Kearns, E.; Hime, A.; Stonehill, L.C.; Seibert, S.; Klein, J.; Lippincott, W.H.; McKinsey, D.N.; Nikkel,J.A. Measurement of scintillation efficiency for nuclear recoils in liquid argon. Physical Review C , .doi:10.1103/physrevc.85.065811.162. Galbiati, C.; Acosta-Kane, D.; Acciarri, R.; Amaize, O.; Antonello, M.; Baibussinov, B.; Ceolin, M.B.; Ballentine,C.J.; Bansal, R.; Basgall, L.; Bazarko, A.; Benetti, P.; Benziger, J.; Burgers, A.; Calaprice, F.; Calligarich, E.;Cambiaghi, M.; Canci, N.; Carbonara, F.; Cassidy, M.; Cavanna, F.; Centro, S.; Chavarria, A.; Cheng, D.; Cocco,A.G.; Collon, P.; Dalnoki-Veress, F.; de Haas, E.; Pompeo, F.D.; Fiorillo, G.; Fitch, F.; Gallo, V.; Gaull, M.; Gazzana,S.; Grandi, L.; Goretti, A.; Highfill, R.; Highfill, T.; Hohman, T.; Ianni, A.; Ianni, A.; LaCava, A.; Laubenstein,M.; Lee, H.Y.; Leung, M.; Loer, B.; Loosli, H.H.; Lyons, B.; Marks, D.; McCarty, K.; Meng, G.; Montanari, C.;Mukhopadhyay, S.; Nelson, A.; Palamara, O.; Pandola, L.; Pietropaolo, F.; Pivonka, T.; Pocar, A.; Purtschert,R.; Rappoldi, A.; Raselli, G.; Resnati, F.; Robertson, D.; Roncadelli, M.; Rossella, M.; Rubbia, C.; Ruderman,J.; Saldanha, R.; Schmitt, C.; Scott, R.; Segreto, E.; Shirley, A.; Szelc, A.M.; Tartaglia, R.; Tesileanu, T.; Ventura,S.; Vignoli, C.; Visnjic, C.; Vondrasek, R.; Yushkov, A. Discovery of underground argon with a low level ofradioactive 39Ar and possible applications to WIMP dark matter detectors. Journal of Physics: Conference Series , , 042015. doi:10.1088/1742-6596/120/4/042015.163. Abi, B.; others. Deep Underground Neutrino Experiment (DUNE), Far Detector Technical Design Report,Volume IV Far Detector Single-phase Technology. JINST , , T08010, [arXiv:physics.ins-det/2002.03010].doi:10.1088/1748-0221/15/08/T08010.164. Abratenko, P.; Alrashed, M.; An, R.; Anthony, J.; Asaadi, J.; Ashkenazi, A.; Balasubramanian, S.; Baller, B.;Barnes, C.; Barr, G.; Basque, V.; Bathe-Peters, L.; Rodrigues, O.B.; Berkman, S.; Bhanderi, A.; Bhat, A.; Bishai, M.; Blake, A.; Bolton, T.; Camilleri, L.; Caratelli, D.; Terrazas, I.C.; Fernandez, R.C.; Cavanna, F.; Cerati, G.;Chen, Y.; Church, E.; Cianci, D.; Cohen, E.O.; Conrad, J.M.; Convery, M.; Cooper-Troendle, L.; Crespo-Anadon,J.I.; Tutto, M.D.; Devitt, D.; Diurba, R.; Domine, L.; Dorrill, R.; Duffy, K.; Dytman, S.; Eberly, B.; Ereditato, A.;Sanchez, L.E.; Evans, J.J.; Fadeeva, A.A.; Aguirre, G.A.F.; Fitzpatrick, R.S.; Fleming, B.T.; Foppiani, N.; Franco,D.; Furmanski, A.P.; Garcia-Gamez, D.; Gardiner, S.; Gollapinni, S.; Goodwin, O.; Gramellini, E.; Green, P.;Greenlee, H.; Gu, L.; Gu, W.; Guenette, R.; Guzowski, P.; Hall, E.; Hamilton, P.; Hen, O.; Horton-Smith, G.A.;Hourlier, A.; Huang, E.C.; Itay, R.; James, C.; de Vries, J.J.; Ji, X.; Jiang, L.; Jo, J.H.; Johnson, R.A.; Jwa, Y.J.; Kamp,N.; Karagiorgi, G.; Ketchum, W.; Kirby, B.; Kirby, M.; Kobilarcik, T.; Kreslo, I.; LaZur, R.; Lepetic, I.; Li, K.; Li, Y.;Littlejohn, B.R.; Lorca, D.; Louis, W.C.; Luo, X.; Marchionni, A.; Marcocci, S.; Mariani, C.; Marsden, D.; Marshall,J.; Martin-Albo, J.; Caicedo, D.A.M.; Mason, K.; Mastbaum, A.; McConkey, N.; Meddage, V.; Mettler, T.; Miller,K.; Mills, J.; Mistry, K.; Mohayai, T.; Mogan, A.; Moon, J.; Mooney, M.; Moor, A.F.; Moore, C.D.; Mousseau, J.;Murphy, M.; Naples, D.; Navrer-Agasson, A.; Neely, R.K.; Nienaber, P.; Nowak, J.; Palamara, O.; Paolone, V.;Papadopoulou, A.; Papavassiliou, V.; Pate, S.F.; Paudel, A.; Pavlovic, Z.; Piasetzky, E.; Ponce-Pinto, I.; Porzio,D.; Prince, S.; Qian, X.; Raaf, J.L.; Radeka, V.; Rafique, A.; Reggiani-Guzzo, M.; Ren, L.; Rochester, L.; Rondon,J.R.; Rogers, H.E.; Rosenberg, M.; Ross-Lonergan, M.; Russell, B.; Scanavini, G.; Schmitz, D.W.; Schukraft, A.;Shaevitz, M.H.; Sharankova, R.; Sinclair, J.; Smith, A.; Snider, E.L.; Soderberg, M.; Soldner-Rembold, S.; Soleti,S.R.; Spentzouris, P.; Spitz, J.; Stancari, M.; John, J.S.; Strauss, T.; Sutton, K.; Sword-Fehlberg, S.; Szelc, A.M.;Tagg, N.; Tang, W.; Terao, K.; Thornton, R.T.; Thorpe, C.; Toups, M.; Tsai, Y.T.; Tufanli, S.; Uchida, M.A.; Usher,T.; Pontseele, W.V.D.; de Water, R.G.V.; Viren, B.; Weber, M.; Wei, H.; Williams, Z.; Wolbers, S.; Wongjirad, T.;Wospakrik, M.; Wu, W.; Yang, T.; Yarbrough, G.; Yates, L.E.; Zeller, G.P.; Zennamo, J.; Zhang, C. The ContinuousReadout Stream of the MicroBooNE Liquid Argon Time Projection Chamber for Detection of Supernova BurstNeutrinos, 2020, [arXiv:physics.ins-det/2008.13761].165. Abi, B.; others. Supernova Neutrino Burst Detection with the Deep Underground Neutrino Experiment. ,[arXiv:hep-ex/2008.06647].166. Kimura, M.; Tanaka, M.; Washimi, T.; Yorita, K. Measurement of the scintillation efficiency for nuclear recoils inliquid argon under electric fields up to 3 kV/cm.
Physical Review D , . doi:10.1103/physrevd.100.032002.167. Kimura, M.; Aoyama, K.; Takeda, T.; Tanaka, M.; Yorita, K. Measurements of argon-scintillation and-electroluminescence properties for low mass WIMP dark matter search. Journal of Instrumentation , , C08012–C08012. doi:10.1088/1748-0221/15/08/c08012.168. Doke, T.; Hitachi, A.; Kubota, S.; Nakamoto, A.; Takahashi, T. Estimation of Fano factors in liquid argon,krypton, xenon and xenon-doped liquid argon. Nuclear Instruments and Methods , , 353 – 357.doi:https://doi.org/10.1016/0029-554X(76)90292-5.169. Doke, T.; Crawford, H.J.; Hitachi, A.; Kikuchi, J.; Lindstrom, P.J.; Masuda, K.; Shibamura, E.; Takahashi, T. LETdependence of scintillation yields in liquid argon. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment , . doi:10.1016/0168-9002(88)90892-3.170. Alexander, T.; Alton, D.; Arisaka, K.; Back, H.O.; Beltrame, P.; Benziger, J.; Bonfini, G.; Brigatti, A.; Brodsky, J.;Bussino, S.; Cadonati, L.; Calaprice, F.; Candela, A.; Cao, H.; Cavalcante, P.; Chepurnov, A.; Chidzik, S.; Cocco,A.G.; Condon, C.; Angelo, D.D.; Davini, S.; Vincenzi, M.D.; Haas, E.D.; Derbin, A.; Pietro, G.D.; Dratchnev, I.;Durben, D.; Empl, A.; Etenko, A.; Fan, A.; Fiorillo, G.; Franco, D.; Fomenko, K.; Forster, G.; Gabriele, F.; Galbiati,C.; Gazzana, S.; Ghiano, C.; Goretti, A.; Grandi, L.; Gromov, M.; Guan, M.; Guo, C.; Guray, G.; Hungerford,E.V.; Ianni, A.; Ianni, A.; Joliet, C.; Kayunov, A.; Keeter, K.; Kendziora, C.; Kidner, S.; Klemmer, R.; Kobychev,V.; Koh, G.; Komor, M.; Korablev, D.; Korga, G.; Li, P.; Loer, B.; Lombardi, P.; Love, C.; Ludhova, L.; Luitz,S.; Lukyanchenko, L.; Lund, A.; Lung, K.; Ma, Y.; Machulin, I.; Mari, S.; Maricic, J.; Martoff, C.J.; Meregaglia,A.; Meroni, E.; Meyers, P.; Mohayai, T.; Montanari, D.; Montuschi, M.; Monzani, M.E.; Mosteiro, P.; Mount,B.; Muratova, V.; Nelson, A.; Nemtzow, A.; Nurakhov, N.; Orsini, M.; Ortica, F.; Pallavicini, M.; Pantic, E.;Parmeggiano, S.; Parsells, R.; Pelliccia, N.; Perasso, L.; Perasso, S.; Perfetto, F.; Pinsky, L.; Pocar, A.; Pordes,S.; Randle, K.; Ranucci, G.; Razeto, A.; Romani, A.; Rossi, B.; Rossi, N.; Rountree, S.D.; Saggese, P.; Saldanha,R.; Salvo, C.; Sands, W.; Seigar, M.; Semenov, D.; Shields, E.; Skorokhvatov, M.; Smirnov, O.; Sotnikov, A.;Sukhotin, S.; Suvarov, Y.; Tartaglia, R.; Tatarowicz, J.; Testera, G.; Thompson, J.; Tonazzo, A.; Unzhakov, E.; Vogelaar, R.B.; Wang, H.; Westerdale, S.; Wojcik, M.; Wright, A.; Xu, J.; Yang, C.; Zavatarelli, S.; Zehfus, M.;Zhong, W.; Zuzel, G. DarkSide search for dark matter.
Journal of Instrumentation , , C11021–C11021.doi:10.1088/1748-0221/8/11/c11021.171. Sangiorgio, S.; Joshi, T.; Bernstein, A.; Coleman, J.; Foxe, M.; Hagmann, C.; Jovanovic, I.; Kazkaz, K.;Mavrokoridis, K.; Mozin, V.; et al.. First demonstration of a sub-keV electron recoil energy threshold ina liquid argon ionization chamber. Nuclear Instruments and Methods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment , , 69–72. doi:10.1016/j.nima.2013.06.061.172. Aprile, E.; Aalbers, J.; Agostini, F.; Alfonsi, M.; Amaro, F.; Anthony, M.; Arneodo, F.; Barrow, P.; Baudis, L.;Bauermeister, B.; et al. XENON100 dark matter results from a combination of 477 live days. Physical Review D , . doi:10.1103/physrevd.94.122001.173. Zani, A.; et al.. The WArP Experiment: A Double-Phase Argon Detector for Dark Matter Searches. Advances inHigh Energy Physics , , 1–17. doi:10.1155/2014/205107.174. Agnes, P.; Albuquerque, I.; Alexander, T.; Alton, A.; Araujo, G.; Ave, M.; Back, H.; Baldin, B.; Batignani, G.;Biery, K.; et al.. DarkSide-50 532-day dark matter search with low-radioactivity argon. Physical Review D , . doi:10.1103/physrevd.98.102006.175. Agnes, P.; Dawson, J.; De Cecco, S.; Fan, A.; Fiorillo, G.; Franco, D.; Galbiati, C.; Giganti, C.; Johnson, T.; Korga,G.; et al.. Measurement of the liquid argon energy response to nuclear and electronic recoils. Physical Review D , . doi:10.1103/physrevd.97.112005.176. Weinstein, A.; et al. Supernova Neutrinos at the DUNE Experiment. Journal of Physics: Conference Series , , 012052. doi:10.1088/1742-6596/1342/1/012052.177. Aguilar-Arevalo, A.A.; Anderson, C.E.; Bazarko, A.O.; Brice, S.J.; Brown, B.C.; Bugel, L.; Cao, J.; Coney, L.;Conrad, J.M.; Cox, D.C.; et al. Search for core-collapse supernovae using the MiniBooNE neutrino detector. Physical Review D , . doi:10.1103/physrevd.81.032001.178. Acciarri, R.; others. Long-Baseline Neutrino Facility (LBNF) and Deep Underground NeutrinoExperiment (DUNE): Conceptual Design Report, Volume 1: The LBNF and DUNE Projects. ,[arXiv:physics.ins-det/1601.05471].179. Acciarri, R.; others. The Liquid Argon In A Testbeam (LArIAT) Experiment. JINST , , P04026,[arXiv:physics.ins-det/1911.10379]. doi:10.1088/1748-0221/15/04/P04026.180. Foreman, W.; others. Calorimetry for low-energy electrons using charge and light in liquid argon. Phys. Rev. D , , 012010, [arXiv:physics.ins-det/1909.07920]. doi:10.1103/PhysRevD.101.012010.181. Adams, C.; Alrashed, M.; An, R.; Anthony, J.; Asaadi, J.; Ashkenazi, A.; Balasubramanian, S.; Baller, B.;Barnes, C.; Barr, G.; et al.. Calibration of the charge and energy loss per unit length of the MicroBooNE liquidargon time projection chamber using muons and protons. Journal of Instrumentation , , P03022–P03022.doi:10.1088/1748-0221/15/03/p03022.182. BIRKS, J. CHAPTER 8 - ORGANIC LIQUID SCINTILLATORS. In The Theory and Practice of Scintillation Counting ;BIRKS, J., Ed.; International Series of Monographs in Electronics and Instrumentation, Pergamon, 1964; pp. 269– 320. doi:https://doi.org/10.1016/B978-0-08-010472-0.50013-6.183. Miyajima, M.; Takahashi, T.; Konno, S.; Hamada, T.; Kubota, S.; Shibamura, H.; Doke, T. Average energyexpended per ion pair in liquid argon.
Phys. Rev. A , , 1438–1443. doi:10.1103/PhysRevA.9.1438.184. Tanaka, M.; Doke, T.; Hitachi, A.; Kato, T.; Kikuchi, J.; Masuda, K.; Murakami, T.; Nishikido, F.; Okada, H.; Ozaki,K.; Shibamura, E.; Yoshihira, E. LET dependence of scintillation yields in liquid xenon. Nuclear Instrumentsand Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment , , 454 – 463. doi:https://doi.org/10.1016/S0168-9002(00)00785-3.185. Thomas, J.; Imel, D.A. Recombination of electron-ion pairs in liquid argon and liquid xenon. Phys. Rev. A , , 614–616. doi:10.1103/PhysRevA.36.614.186. Thomas, J.; Imel, D.A.; Biller, S. Statistics of charge collection in liquid argon and liquid xenon. Phys. Rev. A , , 5793–5800. doi:10.1103/PhysRevA.38.5793.187. Obodovskiy, I. Saturation curves and energy resolution of LRG ionization spectrometers. IEEE InternationalConference on Dielectric Liquids, 2005. ICDL 2005., 2005, pp. 321–324. doi:10.1109/ICDL.2005.1490090. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors andAssociated Equipment , , 275 – 286. doi:https://doi.org/10.1016/j.nima.2003.11.423.189. Snider, E.; Petrillo, G. LArSoft: toolkit for simulation, reconstruction and analysis of liquid argon TPC neutrinodetectors. Journal of Physics: Conference Series , , 042057. doi:10.1088/1742-6596/898/4/042057.190. Mozumder, A. Free-ion yield in liquid argon at low-LET. Chemical Physics Letters , , 143–148.doi:10.1016/0009-2614(95)00384-3.191. Aprile, E.; Hsin-Min Ku, W.; Park, J.; Schwartz, H. Energy resolution studies of liquid argon ionization detectors. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment , . doi:10.1016/0168-9002(87)90362-7.192. Kozlova, E.; Mueller, J. NEST liquid argon mean yields note, NEST collaboration website November 10, 2020.193. Berger, M.; Coursey, J.; Zucker, M.; Chang, J. ESTAR, PSTAR, and ASTAR: Computer Programs for CalculatingStopping-Power and Range Tables for Electrons, Protons, and Helium Ions, National Institute of Standards andTechnology, Gaithersburg, MD 2005.194. Acciarri, R.; Adams, C.; Asaadi, J.; Baller, B.; Bolton, T.; Bromberg, C.; Cavanna, F.; Church, E.; Edmunds,D.; Ereditato, A.; et al. Demonstration of MeV-scale physics in liquid argon time projection chambers usingArgoNeuT. Physical Review D , . doi:10.1103/physrevd.99.012002.195. Agnes, P.; Albuquerque, I.; Alexander, T.; Alton, A.; Araujo, G.; Asner, D.; Ave, M.; Back, H.; Baldin, B.;Batignani, G.; et al. Low-Mass Dark Matter Search with the DarkSide-50 Experiment. Physical Review Letters , . doi:10.1103/physrevlett.121.081307.196. Akimov, D.; others. COHERENT Collaboration data release from the first detection of coherent elasticneutrino-nucleus scattering on argon. , [arXiv:nucl-ex/2006.12659]. doi:10.5281/zenodo.3903810.197. Creus, W.; Allkofer, Y.; Amsler, C.; Ferella, A.; Rochet, J.; Scotto-Lavina, L.; Walter, M. Scintillation efficiencyof liquid argon in low energy neutron-argon scattering. Journal of Instrumentation , , P08002–P08002.doi:10.1088/1748-0221/10/08/p08002.198. Regenfus, C.; Allkofer, Y.; Amsler, C.; Creus, W.; Ferella, A.; Rochet, J.; Walter, M. Study of nuclearrecoils in liquid argon with monoenergetic neutrons. Journal of Physics: Conference Series , , 012019.doi:10.1088/1742-6596/375/1/012019.199. Alexander, T.; Back, H.O.; Cao, H.; Cocco, A.G.; DeJongh, F.; Fiorillo, G.; Galbiati, C.; Grandi, L.; Kendziora, C.;Lippincott, W.H.; Loer, B.; Love, C.; Manenti, L.; Martoff, C.J.; Meng, Y.; Montanari, D.; Mosteiro, P.; Olvitt,D.; Pordes, S.; Qian, H.; Rossi, B.; Saldanha, R.; Tan, W.; Tatarowicz, J.; Walker, S.; Wang, H.; Watson, A.W.;Westerdale, S.; Yoo, J. Observation of the dependence on drift field of scintillation from nuclear recoils in liquidargon. Phys. Rev. D , , 092006. doi:10.1103/PhysRevD.88.092006.200. Cao, H.; Alexander, T.; Aprahamian, A.; Avetisyan, R.; Back, H.O.; Cocco, A.G.; DeJongh, F.; Fiorillo, G.;Galbiati, C.; Grandi, L.; Guardincerri, Y.; Kendziora, C.; Lippincott, W.H.; Love, C.; Lyons, S.; Manenti, L.;Martoff, C.J.; Meng, Y.; Montanari, D.; Mosteiro, P.; Olvitt, D.; Pordes, S.; Qian, H.; Rossi, B.; Saldanha, R.; Sangiorgio, S.; Siegl, K.; Strauss, S.Y.; Tan, W.; Tatarowicz, J.; Walker, S.; Wang, H.; Watson, A.W.; Westerdale, S.;Yoo, J. Measurement of scintillation and ionization yield and scintillation pulse shape from nuclear recoils inliquid argon.