novel measurement method of heat and light detection for neutrinoless double beta decay

Accepted Manuscript Novel measurement method of heat and light detection for neutrinoless double beta decay G.B Kim, J.H Choi, H.S Jo, C.S Kang, H.L Kim, I.W Kim, S.R Kim, Y.H Kim, C Lee, H.J Lee, M.K Lee, J Li, S.Y Oh, J.H So PII: DOI: Reference: S0927-6505(17)30075-0 10.1016/j.astropartphys.2017.02.009 ASTPHY 2202 To appear in: Astroparticle Physics Received date: Revised date: Accepted date: 29 July 2016 23 January 2017 28 February 2017 Please cite this article as: G.B Kim, J.H Choi, H.S Jo, C.S Kang, H.L Kim, I.W Kim, S.R Kim, Y.H Kim, C Lee, H.J Lee, M.K Lee, J Li, S.Y Oh, J.H So, Novel measurement method of heat and light detection for neutrinoless double beta decay, Astroparticle Physics (2017), doi: 10.1016/j.astropartphys.2017.02.009 This is a PDF file of an unedited manuscript that has been accepted for publication As a service to our customers we are providing this early version of the manuscript The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain ACCEPTED MANUSCRIPT Novel measurement method of heat and light detection for neutrinoless double beta decay CR IP T G.B Kima,b , J.H Choia,b , H.S.Joa , C.S Kanga,b , H.L Kima , I.W Kima,b , S.R Kima,b , Y.H Kima,b,∗, C Leea , H.J Leea,b , M.K Leeb , J Lia , S.Y Oha,b , J.H Soa,b a AN US Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34047, Republic of Korea b Korea Research Institute of Standards and Science (KRISS), Daejeon 34113, Republic of Korea Abstract CE PT ED M We developed a cryogenic phonon-scintillation detector to search for 0νββ decay of 100 Mo The detector module, a proto-type setup of the AMoRE experiment, has a scintillating 40 Ca100 MoO4 absorber composed of 100 Mo-enriched and 48 Ca-depleted elements This new detection method employs metallic magnetic calorimeters (MMCs) as the sensor technology for simultaneous detection of heat and light signals It is designed to have high energy and timing resolutions to increase sensitivity to probe the rare event The detector, which is composed of a 200-g 40 Ca100 MoO4 crystal and phonon/photon sensors, showed an energy resolution of 8.7 keV FWHM at 2.6 MeV, with a weak temperature dependence in the range of 10-40 mK Using rise-time and mean-time parameters and light/heat ratios, the proposed method showed a strong capability of rejecting alpha-induced events from electron events with as good as 20σ separation Moreover, we discussed how the signal rise-time improves the rejection efficiency for random coincidence signals AC Keywords: neutrino, double beta decay, metallic magnetic calorimeter, low background ∗ Corresponding author Email address: yhk@ibs.re.kr (Y.H Kim) Preprint submitted to Elsevier March 1, 2017 ACCEPTED MANUSCRIPT Introduction AN US CR IP T Neutrinos are one of the elementary particles that compose the universe In the standard model (SM) of particle physics, they are considered to be massless and electric-chargeless and to have half-integer spin However, a series of observations on neutrino oscillation phenomena suggest that neutrinos have non-zero mass, and oscillate from one flavor state to others [1] The flavor states can be expressed by a neutrino mixing matrix with mass eigenstates Although the mixing angles in the matrix and square mass differences of the three mass eigenstates have been obtained recently [2], neutrino oscillation experiments not provide the absolute mass scale of neutrinos Moreover, their fundamental particle type (Dirac or Majorana) remains unanswered [3] Double beta (ββ) decay is an allowed nuclear transition for the isotopes for that the mass of the initial nucleus (A, Z) is larger than that of the final state nucleus (A, Z+2), but smaller than that of the intermediate state (A, Z+1) According to the SM, a ββ decay process is always accompanied by emission of two electrons and two neutrinos expressed as 2νββ, (1) M (A, Z) → (A, Z + 2) + 2e− + 2¯νe ED However, in the case that a neutrino is both massive and its own anti-particle (i.e., a Majorana particle), the following ββ decay process without neutrino emission can be allowed: (A, Z) → (A, Z + 2) + 2e− (2) AC CE PT Observation of this neutrinoless double beta (0νββ) decay would provide an unambiguous answer to the Dirac-or-Majorana question Allowing the physical process violating lepton number conservation would be a strong clue for matterantimatter asymmetry in the present universe Moreover, the absolute mass scale of neutrinos can be confined based on observation of 0νββ decay The half-life of the 0νββ process can be expressed as 0ν T 1/2 −1 = G0ν M 0ν m2ββ , (3) where G0ν is a phase space factor, M 0ν is a nuclear matrix element, and mββ is the effective Majorana neutrino mass defined as mββ ≡ mi Uei2 , i=1 (4) ACCEPTED MANUSCRIPT AN US CR IP T where Uei are the PMNS (Pontecorvo-Maki-Nakagawa-Sakata) matrix elements In the 0νββ process, the total decay energy (Q) is mostly carried by two electrons with negligible amount carried by a recoiled daughter nuclide Hence, the 0νββ process will result in a peak at the end point of the ββ spectrum Neutrinoless double beta decay is expected to be an extremely rare process A Majorana neutrino mass of 50 meV corresponds to a half-life of about 1026 years in 100 Mo 0νββ decay with some model dependance of the nuclear matrix element [4] One 0νββ event of 1-kg 100 Mo would occur in about 20 years One of the strategies to enhance the sensitivity is to increase the detector mass because a larger number of source elements provides a higher 0νββ decay event rate Reducing background events in the energy region of interest (ROI) is another key factor that increases the detection sensitivity for this rare process Moreover, the energy resolution of the detector that defines the ROI can be an efficient and crucial parameter High resolution measurement increases the accuracy of energy detection, and narrows the width of the ROI It results in reduction of number of background events in the ROI, particularly from irreducible 2νββ background events For a non-negligible background condition, the experimental sensitivity to the Majorana neutrino mass can be written as, M B∆E mββ ∝ Mt 1/4 (5) CE PT ED where B is the background rate, ∆E is the energy resolution of the detector, M is the mass of the detector, and t is the measurement time It is noted that the experimental sensitivity for Majorana neutrino mass is proportional to the 1/4 power of the quantities On the other hand, in the case that the expected background of the detector in the ROI is less than event during the measurement period, socalled zero-background case, the sensitivity for the Majorana neutrino mass can be expressed as 1/2 (6) mββ ∝ Mt AC In this zero-background case the mass sensitivity is inversely proportional to the square root of the mass and measurement time The advanced Mo-based rare process experiment (AMoRE) is an international effort to search for 0νββ of 100 Mo [5, 6, 7] AMoRE employs 40 Ca100 MoO4 as the target material of the 100 Mo decay in the source-equal-to-detector concept In order to increase the rate of 0νββ events, isotopically enriched 100 Mo is used to fabricate CaMoO4 crystals Moreover, enriched 40 Ca from 48 Ca depletion is ACCEPTED MANUSCRIPT AC CE PT ED M AN US CR IP T used to minimize interference from 2νββ signals of 48 Ca Consequently, doubly enriched 40 Ca100 MoO4 crystals are used The choice of 100 Mo as a 0νββ candidate is advantageous The Q-value of the 100 Mo decay is 3034.40(17) keV [8] which is sufficiently high to prevent interference from most of environmental γ-ray backgrounds The expected half-life of the 100 Mo 0νββ process is relatively short compared with other candidates [4, 9] Moreover, the high natural abundance of 100 Mo of about 9.6% does not require extraordinary enrichment cost Metallic magnetic calorimeters (MMCs) are used as the sensor technology for simultaneous measurement of heat and scintillation-light signals MMCs have demonstrated high energy resolutions in X-ray and alpha-particle detections [10, 11, 12, 13] The simultaneous measurement technique makes it possible to separate out background alpha signals in an event by event manner Moreover, the fast response time of MMC signals can minimize possible background from random coincidences of two 2νββ events Several Mo-containing crystals, such as Li2 MoO4 , CaMoO4 , MgMoO4 , and ZnMoO4 , have been used for suitability tests of large-scale 0νββ search experiments [14, 15, 16, 17, 18] Using semiconductor-based neutron transmutation doped (NTD) Ge thermistors as their thermal sensors of phonon and scintillation measurement, 6.3-keV FWHM resolution for the 2615 keV γ-line of 208 Tl was found with a 330-g ZnMoO4 detector, where 18σ and 19σ event discrimination capability were found from heat/light ratios and pulse shape parameters of β/γ and α signals, respectively [15] Although the phonon-scintillation detector with NTD Ge readout provides high energy resolution and discrimination power, it showed limited timing resolution where the rise-times of the phonon and light signals were 12 ms and 3.2 ms, respectively This limit on the rise-time of the signals originates from inefficient thermal coupling between phonons in the absorber crystal and conduction electrons in the thermistor Recently, another type of phononscintillation detector was tested for a CaMoO4 crystal with a NTD Ge sensor for heat signals and a millikelvin photomultiplier tube (PMT) readout for light signals where extreme timing resolution of the light signals was achieved [19], and two decay constants of 41 µs and 3.4 ms were found for CaMoO4 scintillation below 100 mK [20] The present experiment aims to develop a cryogenic phonon-scintillation detector based on a CaMoO4 crystal with MMC readout as the detector technology of the AMoRE project Taking advantage of the high energy and timing resolution of MMCs, simultaneous measurement of heat and light signals has been conducted using a 200-g 40 Ca100 MoO4 crystal in an above-ground laboratory This ACCEPTED MANUSCRIPT Gold wires MMC device OFHC holder CR IP T CaMoO4 crystal Light reflector Bottom side AN US Patterned gold film Photon detector Top side ED M Figure 1: The detector module with a 40 Ca100 MoO4 crystal and phonon/photon sensors The phonon sensor sits at the bottom of the module The connection between gold film and an MMC is shown in the top-left The light detector, which is made of a Ge wafer and another MMC, covers the top-side of the crystal CE PT paper focuses on detector performances and characteristics, such as energy and timing resolutions as well as event discriminations by pulse shapes and heat/light ratios These characteristics are empirically studied under various temperature conditions in an above-ground laboratory Other aspects of the AMoRE experiments are discussed elsewhere (e.g Monte Carlo background simulation [21], radioactive contamination of 40 Ca100 MoO4 crystals [22], and the overall status of the AMoRE project [7]) AC Detector setup The detector module is designed for simultaneous measurement of heat (phonon) and scintillation-light (photon) signals from a CaMoO4 crystal In this present experiment, a doubly enriched 40 Ca100 MoO4 was used as the target absorber The internal background of the crystal, named SB28, was previously studied with ACCEPTED MANUSCRIPT AC CE PT ED M AN US CR IP T room-temperature scintillation measurement at the YangYang Underground Laboratory (Y2L) [23] The module was structured using oxygen-free high conductivity (OFHC) copper for high thermal conductivity at low temperatures The crystal, with a mass of about 200 g, as an oval cylinder, was held by phosphorbronze springs that were firmly attached to the copper holder A patterned gold film of 2-cm diameter and 400-nm total thickness was evaporated on the bottom surface of the crystal This film collects phonons generated by particle detection in the crystal The phonon signals are read by a temperature sensor (i.e., an MMC sensor) placed on a copper plate with a superconducting quantum interference device (SQUID) The thermal connection between the gold phonon collector and the MMC sensor was made with annealed gold bonding wires The majority of the energy absorbed in the crystals is converted into heat signals in the form of phonons The excess phonons make net heat flow from the absorber crystal through the gold phonon collector film, gold wires and the MMC sensor The heat eventually releases to a thermal bath through a weak thermal link made of a couple of gold bonding wires connecting the MMC sensor and the copper sample holder The MMC with the SQUID read-out measures the temperature change at the MMC sensor in the heat flow sequence The details of the phonon sensing system are described in our previous reports [24, 25] A light detector composed of a 2-inch Ge wafer and an MMC sensor was employed to detect scintillation light from the CaMoO4 crystal This light detector was constructed in a manner similar to how the phonon sensor was made It has three circular gold films, mm in diameter and 300-nm thick, to collect phonons generated by light absorption in the wafer [26] A thermal connection between the gold films and an MMC sensor was also made using annealed gold wires A number of light detectors can be easily made with this patchable design MMCs and light absorbers can be made separately, and assembled in the final stage The intrinsic signal rise-time of the light detector was about 0.2 ms independent of operating temperature [26] The light detector was installed toward the top-side of the CaMoO4 crystal The crystal was mounted in a light cavity surrounded by VM2000 light reflector films to increase the collection efficiency of scintillation light The detector module was attached to the mixing chamber of a dilution refrigerator capable of cooling the system to mK The cryostat, which was installed in an above-ground laboratory, was surrounded by a 10-cm thick lead shield 10 mK 20 mK 10 0 30 mK 0.5 −20 40 mK 50 mK 10 20 30 40 50 60 Temperature (mK) AN US Signal (a.u.) 1.5 15 CR IP T FWHM (keV) ACCEPTED MANUSCRIPT 20 40 Time (ms) 60 80 ED M Figure 2: Averaged signals of full absorption of 2615 keV gammas measured in the heat channel at 10-50 mK The inset shows the FWHM resolution of the baseline noise without signals obtained by the amplitude-determining algorithm described in text to the baseline noise records Experimental Results AC CE PT 3.1 Signal Properties In the present experiment, the signals in both phonon and photon sensors originate from several sources Because the measurement was performed in an aboveground laboratory, events caused by muons passing the crystal appear over a wide energy range, up to about 30 MeV Radioactive decays of internal radio-impurities in the crystal also generated heat and light signals simultaneously Moreover, environmental gamma rays contributed to the background spectrum as a significant portion of electron-induced events, with energies up to 2615 keV An external 232 Th source was installed between the external lead shield and the cryostat The source was used for the energy calibration of the detector, in addition to detector resolution and signal shape studies at various temperatures Fig shows the signal shapes of 2615-keV gamma-rays fully absorbed in the 40 Ca100 MoO4 crystal, measured in 10-50 mK Lower temperatures result in larger ACCEPTED MANUSCRIPT AC CE PT ED M AN US CR IP T but slower signals due to the temperature dependence of the thermodynamic properties of the sub-thermal components of the detector A detector model of MMC measurement having a large crystal absorber was established [6, 27] It was further optimized for larger pulse height and faster signal rise [25] The inset shows the baseline resolution, which is the energy resolution of randomly triggered signals at each temperature The measured baseline resolutions represent the irreducible noise level of signal amplitudes corresponding to the signal-to-noise ratio for the measurement condition Determination of the signal amplitude for each measured pulse is one of most essential works in the analysis The optimal filtering method may provide the best energy estimation only if all signals are in the same shape but different proportionality [28, 29] However, this method is not practically applicable to the present measurement The event-rate of the measurement is relatively high compared to the long-decay-component of the pulse shape A following signal often appeared before the signal is fully decayed In this high event-rate condition that pile-up signals frequently appear, remained decay-component of a signal affects the signal shape of its subsequent events This makes optimal filtering inadequate to our measurement condition The pulse height parameter, the maximum of the pulse taking the high frequency noise into account, and the left area (LA) parameter [24], the weighted partial area of pulse, were considered as alternative amplitude parameters However, the pulse height parameter is also inadequate to represent the signal amplitude mainly because of the position dependence of the signal The position dependence appears because our signal is sensitive to athermal phonon signals with good timing resolutions The LA parameter is a favorable alternative for the presence of the position dependence as described in Ref [24] The LA parameter is found for the sum of the initial part of the pulses The integration range is determined by the mean-time value of the pulses The meantime and LA parameters are defined as, +r +r (vt t)/ tmean = −l vt , (7) −l tmean LA = vt , −l (8) where vt is the measured voltage signal at time t subtracting its base level The time scale of the triggered signals is redefined to zero at the time when the signal rises at 10% of the pulse height l and r indicate the time length of the signal ACCEPTED MANUSCRIPT 10 e+e− annihilation, 208 Tl 511 keV 228 Ac 911 keV 40 K 1461 keV 10 10 CR IP T 10 Tl 583 keV 208 Tl 2615 keV AN US Counts / keV 208 1000 2000 Energy (keVee) 3000 ED M Figure 3: An energy spectrum of the heat channel measured with an external 232 Th source Most of the peaks resulted from the gamma-rays of the source, except the 511- and 1461-keV peaks The five peak positions marked with arrows are used for the energy calibration of β/γ signals toward left and right directions from the redefined trigger time, respectively, used to calculate the mean-time as described in Ref [24] AC CE PT 3.2 Energy calibration The energy spectrum shown in Fig was obtained with a 232 Th source at 10 mK The energy scale of the spectrum is determined using the LA parameter as the signal amplitude of the heat channel Five gamma-ray peaks, indicated by arrows, are chosen for the calibration points of the electron-induced β/γ events The spectrum shows some other peaks that are likely coming from neighboring gamma lines with a few keV apart, and are not added in the calibration to avoid ambiguity Energy calibration of the α signals is separately made with alpha-induced peaks originating from internal alpha decay events inside the crystal Alphainduced signals can be clearly selected based on their pulse-shapes and light/heat ratios, as described in the following subsections CR IP T ACCEPTED MANUSCRIPT AN US 10 PT M ED FWHM (keV) 15 1000 2000 Energy (keVee ) 10 mK 20 mK 30 mK 40 mK 3000 AC CE Figure 5: Energy resolution of the phonon sensor for gamma-ray peaks measured at different temperatures 12 ACCEPTED MANUSCRIPT AC CE PT ED M AN US CR IP T readout system largely dominates over the thermodynamic fluctuation noise in the present measurement environment It was expected that the energy resolution of the detector does not depend on the amount of energy deposited into its absorber, but is rather related to the noise level of a measurement condition In other words, the energy resolution of a linear thermal detector should be close to the baseline resolution independent of the measured energy However, our measurement indicates that the measured resolutions for the full absorption of gamma-rays become worse as the energy increases This effect is more dominant at 10 mK, for which the baseline resolution is better than those at higher temperatures We interpret the energy-dependent resolution results from a few origins, such as the position dependence of the signal shape and the imperfect drift correction of the signal amplitude over time The phonon sensor in this design is sensitive to thermal and athermal phonons in the crystal [25] Athermal phonons are initially generated in the crystal They have a finite life-time before down-converting to a thermal phonon distribution or being absorbed in the gold phonon collector These athermal phonons are responsible for the initial part of the phonon-measured heat signals The shape of the heat signals is related to the event location relative to the phonon collector in the crystal The LA parameter takes some position dependency into account for the signal amplitude [24], but the correction is not yet complete This degrades the energy resolution with respect to the signal amplitude The phonon signals exhibited a small amount of amplitude drift over the time of measurement This is mostly because of instability of the temperature regulation of the mixing chamber where the detector assembly was attached First, most of the apparent drift was corrected by fixing a linear anti-correlation between the signal amplitude and the DC level of the pre-triggered signals The DC level corresponds to the base temperature Further drift adjustment was applied by setting up a characteristic function for 2615-keV gamma events with a long time constant about 4-5 hours Although a significant portion of the drift was corrected, the drift correction cannot be perfect Signal amplitude instability and imperfect drift correction may broaden the peak resolutions with respect to their energy In future studies, improved drift corrections could be made using known heat pulses applied to the absorber using a heater film evaporated on the crystal surface On the other hand, the scintillation process is one of the sources that may affect the energy resolution in phonon detection of the absorber crystal It leads to an integer number of photons emitting out of a scintillating crystal, with some uncertainty in their number The scintillation efficiency of a CaMoO4 crystal is found to be about 6% at K [31] and may become greater at millikelvin temper13 AN US CR IP T ACCEPTED MANUSCRIPT ED M Figure 6: A scatter plot of the energy and mean-time parameters at 10 mK The α signals are distributed in the lower band, and the β/γ signals are in the upper band At 10 mK, the nonlinearity of the temperature-increase causes the energy dependence of the mean-time parameter Some pile-up events appear in between the distributions of α and β events AC CE PT atures However, the Poission statistics of the number of photons not provide sufficient uncertainties to explain the resolutions in phonon measurement of the CaMoO4 crystal In short, scintillation provides a small portion of the energy broadening of the heat channel in the present experiment with a CaMoO4 crystal The energy resolutions of the 511-keV peaks are worse than those expected based on the trend of the other energies measured at all temperatures In the present above-ground experiment, the majority of the 511-keV gamma-ray signals mostly come from positron annihilations in the surrounding materials induced by pair productions by cosmic muons [32] This is a clear evidence that the 511 keV gamma-rays measured in our detector encounter the Doppler broadening effect in the annihilation procedure [33, 34] 3.4 Pulse shape discrimination The phenomenon that heat signals of α- and β/γ-induced events have different pulse shapes has been reported in low-temperature thermal detectors using a 14 ACCEPTED MANUSCRIPT AC CE PT ED M AN US CR IP T scintillating crystal absorber [14, 24] In this present detector with a 40 Ca100 MoO4 crystal absorber, pulse shape discrimination (PSD) is also clearly observed Fig shows a scatter plot of the electron-equivalent energy and mean-time parameters measured by the phonon sensor Most of peaks in Fig are from alpha decays in the CaMoO4 crystal The internal background of this crystal was previously studied in Ref [23] α events distributed in several groups with their energies larger than 4000 keV appear in smaller mean-time values than β/γ events that are scattered in the major band distributed over the entire energy region Pile-up events populate in the intermediate region between two bands The number of the intermediate events is reduced with a pile-up rejection cut parameter, and can be minimized in a low-background environment at an underground laboratory The mean-time values measured at 10 mK show energy-dependent characteristics However, the slope is less dominant at higher operating temperatures, and becomes unnoticeable at 40 mK This effect possibly originates from the nonlinear behavior of the detector response to the amount of energy input A similar tendency was reported for the 10 mK measurement with TeO2 crystals, where the decay time of phonon signals showed a positive slope with respect to the energy [35] The amount of temperature change (∆T ) of those detectors due to the energy input is no longer small compared with the temperature (T ) in the extreme cases The total heat capacity of our detector times the temperature (Ctot T ) is about 50 MeV at 10 mK, whereas it is about 2.4 GeV at 40 mK It is meaningful to compare the shape of the α and β/γ signals during their rise and decay parts The signals of the most frequent alpha events (i.e., 5.4 MeV signals from internal 210 Po decay) are averaged, and the β/γ signals with the same amplitude as the signals are selected The α signal rises and decays faster than the β/γ signal as shown in Fig This shape difference results in the PSD for α and β/γ signals using the mean-time parameters Consequently, the rise part of the signal should also provide similar PSD capability.The energy of the direct muon signals is related to the length of the track in the crystal Muons passing through near the edge of the oval cylinder crystal are responsible for the muon events in the energy region of the electron band in Fig The muon track distribution and position dependence of the signals may result in a non-Gaussian distribution of the PSD parameter for the muon events The rise-time and mean-time distributions are shown for α and β/γ events around 5.4 MeV of alpha energy at 10-40 mK in Fig Here, the rise-time is defined as the time interval between 10% and 90% positions of the pulse maximum Both the rise-time and mean-time values decrease at higher temperatures 15 ACCEPTED MANUSCRIPT A parameter to indicate the discrimination power (DP) is defined as µβ/γ − µα σ2β/γ + σ2α (9) , CR IP T DP ≡ ED M AN US assuming that each distribution follows a Gaussian distribution with mean µ and standard deviation (SD) σ The dimensionless DP has an effective unit of σeff of the distributions, i.e., (σ2β/γ +σ2α )1/2 Higher DP is favored for better discrimination between α and β/γ events This requires large separation of the means ∆µ = µα − µβ/γ and small σβ/γ and σα values Different levels of DP in the same data set can be found for the mean-time and rise-time parameters independently As shown in Fig 8, ∆µ of the rise-time parameter decreases as temperature increases The DP of the rise-time parameter was 20 and 10 at 10 and 40 mK, respectively However, it is shown that the mean-time values not change much by temperature, and ∆µ of the mean-time parameter is similar at all of the temperatures Similar DP values of the mean-time parameter are found within 18-20 at 10-40 mK The DP values under different parameter conditions are listed in Table All values indicate high DP values greater than At higher temperatures, the DP of the mean-time parameter is not degraded much by the temperature This implies that high quality PSD can be realized over a wide temperature range, and wide selection of the operating temperature can be made by considering the event rate, refrigerator performance and other non-stationary noise conditions PT 3.5 Light signals In addition to heat signals measured using the phonon sensor, scintillation light was measured by a photon sensor The major purpose of the light/heat simultaneous measurement is to make an additional separation method for α and AC CE Table 1: Measured values of DP and energy resolution of the heat channel The subscripts MT, RT and L/H denote mean-time, rise-time, and light/heat ratio respectively The FWHM energy resolutions at 2.6 MeV are shown in keV units T DPRT DPMT DPL/H ∆E 10 mK 20 mK 30 mK 40 mK 20.1 ± 0.4 16.0 ± 0.4 14.9 ± 0.4 9.6 ± 0.4 19.0 ± 0.5 20.4 ± 0.8 18.4 ± 0.5 17.6 ± 0.6 8.6 ± 0.4 9.6 ± 0.4 9.2 ± 0.4 10.9 ± 0.6 8.7 ± 0.5 9.8 ± 0.4 8.7 ± 0.4 11 ± 0.5 16 ACCEPTED MANUSCRIPT AC CE PT ED M AN US CR IP T β/γ events The quenching process in a scintillating crystal generally yields lower scintillation efficiency for the α-induced events than the β/γ-induced ones It results in smaller light/heat ratios of their signal amplitudes for α-induced events Fig shows a scatter plot of the relative signal amplitudes measured using the phonon and photon sensors The α and β/γ events are distributed in the lower and upper bands, respectively Using Eq 9, the DP of this measurement was found to be 9.6 [36] Unlike the mean-time parameter, the light/heat ratios not have energy dependent behavior even at the lowest temperature In principle, the pulse shape parameters (rise-time and mean-time) and the light/heat ratio are correlated α events have faster rise-times and smaller light/heat ratios, whereas β/γ events have slower rise-times and larger light/heat ratios However, the PSD parameters and the light/heat ratio react differently to pile-up signals in the case that two pulses randomly appear whitin a short time comparable to or less than the signal rise-time For instance, α-α pile-up signals coming whitin a short time difference can be counted as a single event with a rise-time and meantime out of their narrow distributions toward those for β/γ events The light/heat ratio, however, stays in the distribution of α events Likewise, two β/γ events in a similar condition can be regarded as a single β/γ event in the usual light/heat distribution of β/γ events, although their rise-time and mean-time parameters can be out of the normal distribution of β/γ events Another type of information obtained from the light detector is pulse shape differences in the light signals measured by the photon sensor Similarly with pulse shape difference in heat signals, α-induced scintillation light signals have faster rise-times than those of β/γ [36] Both signals are much slower than signals from X-rays directly absorbed in the light detector, which have an about 0.2-ms rise-time This behavior indicates that the scintillation process has a finite lifetime, with its own values for α and β/γ events The relation between scintillation life-time and pulse shape of heat signals will be studied in future work The light signal properties suggest that photon sensor operation together with a phonon sensor provides additional information for each event occurring in a crystal absorber In spite of the doubling of the number of measurement channels, the use of a light sensor has a significant advantage for background reduction 3.6 Rejection efficiency for random coincidence signals In an experiment to search for the 0νββ decay of 100 Mo using the detection scheme of low-temperature thermal calorimeters based on phonon (heat) measurement, random coinciding of two 2νββ decay events can be one of the major background sources [16, 37] Because of the relatively short half-life of 100 Mo 17 ACCEPTED MANUSCRIPT AC CE PT ED M AN US CR IP T 2νββ decay and slow signal property of heat measurement, any two events appearing during a short time can be regarded as a single event that may appear in its energy near the Q-value of 2νββ decay An efficient way to reduce such random coincidence events is to increase the timing resolution of the phonon and/or photon sensors The response time (i.e., rise-time) of the heat signals measuring excess phonons caused by particle absorption in an absorber crystal by using a temperature sensor is mainly determined by the sensor technology and the operating temperature When using a scintillating crystal as an absorber, phonon generation in the scintillation process may play an important role in event-dependent pulse shapes, together with the acoustic properties of the absorber crystal, heat transfer between the absorber and the sensor, and thermal response time of the sensor technology The present detector with an MMC-based phonon sensor and a CaMoO4 absorber has rise-times of 2.5 and 0.83 ms for 2615-keV gamma events measured at 10 and 40 mK respectively Using the time resolution of the present phonon sensor, the rejection efficiency for random coincidence signals was investigated First, two pulses with the sum of their energy being MeV were generated with selected values for the amplitude ratio and time delay Each signal was scaled using a template signal that is the averaged signal of 2615-keV gamma events measured at each considered temperature and added within a certain time delay to make a pile-up signal Noise signals previously measured at the same condition with a random trigger were added to the noise-free pile-up signal The rise-time parameters were found for a set of about 1000 coincidence signals which were generated with the measured noise signals for an amplitude ratio and time delay This procedure was repeated for different values of amplitude ratios and time delays at different temperatures The rejection efficiency shown in Fig 10 was determined by the rise-time distribution of the pile-up events, considering a 95% signal-selection line for single-electron events 50% rejection efficiency was found for a time difference of approximately 120 and 60 µs between two events with the same amplitude (i.e., 5:5 in Fig 10) at 10 and 40 mK, respectively The dispersion (SD) of the rise-time distribution of the measured 2615-keV gamma events was 2.2 µs, which is 2.8 times greater than that of the signals generated with the measured noise for the 10-mK data set, while 2.5 and 1.6 µs were found for the rise-time dispersions of measured signals and generated signals, respectively, at 40 mK Using this relation, the rise-time dispersions of the pile-up signals were 2.8 and 1.6 times broadened for the 10 and 40-mK sets, receptively, to calculate the rejection efficiency shown in Fig 10 A Monte-Carlo (MC) simulation suggests that 1.2×10−4 counts/kg/keV/year 18 ACCEPTED MANUSCRIPT AN US CR IP T (ckky) is expected in 3034±10 keV as the rate of coincidence signals of two 2νββ decays within a 0.5-ms time difference for an AMoRE phase-1 detector composed of 35 310-g 40 Ca100 MoO4 [21] Moreover, an upper limit of 1.1×10−4 ckky is expected for a single 2νββ decay randomly coincident with other background sources in the ROI within the short time delay Considering the present rise-time analysis, the random coincidence rates can be reduced by a significant amount Later, a full MC simulation will be performed with the rejection efficiency found using this type of pulse shape analysis Nevertheless, this simplified analysis highlights the importance of the time resolution of phonon sensors, and estimates rejection efficiency for random coincidence signals Using light signals can improve discrimination power because photon detector has faster detector response than the phonon detector Measured light signals in this measurement have much slower rise-time compare to detector response [36], which may be due to longer scintillation decay time of CaMoO4 crystal at operation temperatures [20] Improving light detector performance or using large and fast light output Mo-containing crystals will increase the rejecting power for the pile-up events M Conclusions AC CE PT ED Given detector mass and measurement time, the maximum sensitivity to probe a rare event such as 0νββ decay is obtained under the zero-background condition, where the number of expected backgrounds in ROI is less than one Minimizing internal and external backgrounds is essential to achieve such extreme measurement conditions In addition, the detector ought to provide high energy resolution for narrow ROI and to increase the accuracy of energy measurement Active background rejection capabilities are highly recommended to reach the detection condition In 0νββ search cases using cryogenic scintillating crystals containing enriched 100 Mo, the timing resolution is another important parameter for realizing the zero-background condition According to our recent MC study, the upper limit of the total background rate for the AMoRE phase-I detector was 1.2×10−3 ckky in the energy region of 3034±10 keV [21] Realistic numbers of internal and external source rates were used in the simulation The 20 keV ROI used in the simulation is greater than times σ of the worst energy resolution listed in Table The values of the DP from the PSD parameters and light/heat ratios satisfy the requirements used in the simulation 19 ACCEPTED MANUSCRIPT PT ED M AN US CR IP T In the present experimental study, simultaneous heat and light measurements were carried out at various temperatures The phonon-scintillation detector showed weak temperature dependence in energy resolution and discrimination power with the mean-time parameter and the light/heat ratio Although the discrimination power with the rise-time parameter at 40 mK is half of that at 10 mK, the timing resolution is significantly increased for better rejection efficiency for random coincidence signals With the MMC-based detection method, operation temperature can be tuned as an additional method to improve the detector performance during the operation stage In summary, this report demonstrated the performance of the detector described with respect to the energy and timing resolutions and event discrimination power Currently, five detector modules with a total mass of about 1.5 kg have been constructed in a similar method They are installed in a low-background measurement setup as a pilot phase of the AMoRE project at Y2L Although the pilot experiment does not aim to reach the best published limit of the 0νββ search, it will conduct a preliminary measurement before large-scale experiments are built As a next generation 0νββ search, AMoRE phase-II is scheduled to be built with X100 MoO4 crystals containing about 100-kg 100 Mo in 2020 where X corresponds to a composing element of molybdate crystals such as Li2 , 40 Ca, Zn, Pb, etc The phase-II detector requires further reduction of internal and external background sources Even if it satisfies the sources requirements, 2νββ signals are unavoidable, and their random coincidences may become the major backgrounds in the ROI We expect the timing resolution of the detector technology with MMCbased sensors to play an important role in reducing this signal-rise-time-dependent background CE Acknowledgements AC We are grateful to AMoRE collaboration for helpful discussions This research was funded by Grant no IBS-R016-G1 and partly supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF2013K2A5A3000039) References [1] M C Gonzalez-Garcia, et al., Physics Reports 460 (1) (2008) 1–129 [2] G L Fogli, et al., Physical Review D 86 (1) (2012) 013012 20 ACCEPTED MANUSCRIPT [3] S R Elliott, et al., Reviews of Modern Physics 87 (1) (2015) 137 [4] J D Vergados, et al., Reports on Progress in Physics 75 (10) (2012) 106301 CR IP T [5] H Bhang, et al., J Phys Conf Ser 375 (4) (2012) 042023 [6] S J Lee, et al., Astropart Phys 34 (9) (2011) 732 – 737 [7] V Alenkov, et al., arXiv:1512.05957 [8] S Rahaman, et al., Phys Lett B 662 (2) (2008) 111 – 116 [9] J Barea, et al., Physical review letters 109 (4) (2012) 042501 AN US [10] J.-P Porst, et al., J Low Temp Phys 176 (5-6) (2014) 617–623 [11] M Rodrigues, et al., Applied Radiation and Isotopes 109 (2016) 570–575 [12] P Ranitzsch, et al., Nucl Instr and Meth A 652 (1) (2011) 299–301 [13] W S Yoon, et al., Nucl Instr and Meth A 784 (2015) 143–146 M [14] C Arnaboldi, et al., Astropart Phys 34 (11) (2011) 797 – 804 [15] J W Beeman, et al., The European Physical Journal C 72 (9) (2012) 1–6 ED [16] J W Beeman, et al., Physics Letters B 710 (2) (2012) 318–323 [17] O Barinova, et al., Nucl Instr and Meth A 613 (1) (2010) 54–57 PT [18] E Armengaud, et al., arXiv:1601.04989 CE [19] X Zhang, et al., Astroparticle Physics 79 (2016) 31–40 [20] X Zhang, et al., Applied Physics Letters 106 (24) (2015) 241904 AC [21] A Luqman, et al., arXiv:1601.01249 [22] J Y Lee, et al., IEEE Trans Nucl Sci 63 (2) (2016) 543–547 [23] J H So, et al., IEEE Trans Nucl Sci 59 (5) (2012) 2214–2218 [24] G B Kim, et al., Advances in High Energy Physics 2015 (2015) 817530 [25] G B Kim, et al., J Low Temp Phys 176 (5-6) (2014) 637–643 21 ACCEPTED MANUSCRIPT [26] H J Lee, et al., Nucl Instr and Meth A 784 (2015) 508–512 [27] Y H Kim, et al., Nucl Instr and Mech A 520 (1) (2004) 208–211 CR IP T [28] D McCammon, Thermal equilibrium calorimeters–an introduction, in: Cryogenic particle detection, Springer, 2005, pp 1–34 [29] Y N Yuryev, et al., Nucl Instr and Meth A 635 (1) (2011) 82 – 85 [30] L Gironi, Nucl Instr and Meth A 617 (1) (2010) 478–481 [31] V B Mikhailik, et al., Phys Status Solidi B 247 (7) (2010) 1583–1599 AN US [32] J Puzovic, et al., Nucl Instr and Mech A 480 (2) (2002) 565–570 [33] P J Schultz, et al., Reviews of Modern Physics 60 (3) (1988) 701 [34] R L Coldwell, et al., Journal of Radioanalytical and Nuclear Chemistry 307 (3) (2016) 2509–2512 [35] M Vignati, Journal of Applied Physics 108 (8) (2010) 084903 M [36] G B Kim, et al., IEEE Trans Nucl Sci 63 (2) (2016) 539–542 AC CE PT ED [37] D M Chernyak, et al., The European Physical Journal C 72 (4) (2012) 1–6 22 α events β events AN US 0.5 −6 0.96 −4 −2 Time (ms) M 0.98 ED Normalized signal (a.u.) 1.02 CR IP T ACCEPTED MANUSCRIPT PT −2 Time (ms) AC CE Figure 7: Pulse shape comparison of the averaged α and β/γ pulses The normalized pulses are aligned at their pulse maximum The rise and decay times are faster for α signals than for β/γ signals 23 ACCEPTED MANUSCRIPT (a) CR IP T 10 mK Counts 20 mK AN US 30 mK 40 mK (b) 2.5 ED 10 mK 1.5 Rise-time (ms) M 0.5 PT 30 mK AC CE Counts 20 mK 40 mK 9.2 9.4 9.6 Mean-time (ms) 9.8 10 Figure 8: Histograms of rise-time (a) and mean-time (b) parameters of α and β/γ events in 5200 keV < E < 5600 keV region The left- and right-side peaks correspond to α- and muon-induced events, respectively All of the histograms are linear in y-axes, with the limit re-sized for their maximum counts in the same relative scale 24 PT ED M AN US CR IP T ACCEPTED MANUSCRIPT AC CE Figure 9: A scatter plot of energy (heat) and light-heat ratio measured at 10 mK α-induced events have smaller light-heat ratio values because of the quenching effect 25 CR IP T ACCEPTED MANUSCRIPT AN US 0.5 10 mK 0.5 CE 1:9 2:8 3:7 4:6 5:5 6:4 7:3 8:2 9:1 40 mK PT 0 M ED Rejection efficiency 100 200 300 Time differences (µs) 400 AC Figure 10: Rejection efficiencies for various time differences and amplitude ratios of pile-up signals 26 ...ACCEPTED MANUSCRIPT Novel measurement method of heat and light detection for neutrinoless double beta decay CR IP T G.B Kima,b , J.H Choia,b , H.S.Joa , C.S... major purpose of the light /heat simultaneous measurement is to make an additional separation method for α and AC CE Table 1: Measured values of DP and energy resolution of the heat channel The... search for the 0νββ decay of 100 Mo using the detection scheme of low-temperature thermal calorimeters based on phonon (heat) measurement, random coinciding of two 2νββ decay events can be one of