dataesr/scientific-paragraphs-categorization huggingface dataset:
While DM experiments are mostly located deep underground, CEνNS experiments usually take data above ground. Additionally, prototype measurements for both of these rare event searches are often performed in above ground or shallow underground facilities. The energy scales measured, as well as the type of energy deposition, provide another important distinction between experiments. Depending on the type of signal (i. e. heat, charge, light or a combination of any of these), type of calibration and capability for event-by-event particle discrimination, an energy deposition may be measured in units of total energy, nuclear recoil equivalent energy, or electron equivalent energy. As nuclear recoil signals measured via charge or light are quenched with respect to electron recoils, this can have an impact on the interpretation of and comparability between results of different measurements.
CRESST-III Section editor: Christian Strandhagen (christian. strandhagen@uni-tuebingen. de) The results shown here pertain to the module Det-A operated in the first data taking period of CRESST-III (from 05/2016 until 02/2018). The experimental setup at Laboratori Nazionali del Gran Sasso (LNGS), the CRESST-III detector concept, the data acquisition and analysis of this module are described in much detail in  [28]. Detector concept and setup CRESST detectors are operated in a shielded cryostat located in hall A of the LNGS underground laboratory. The rock provides a water-equivalent overburden of 3600 m. In addition to a layered passive shielding consisting of polyethylene, lead and copper, the setup is surrounded by plastic scintillator panels acting as a muon veto. With the exception of a small hole on top accommodating the neck of the cryostat, this covers the entire part where the detectors are hosted (98.
To have an in-situ measurement of the nuclear recoil bands another calibration with a neutron source is performed in each run. The pulse shape of the neutron induced nuclear recoil events is the same as for electron/gamma events, so all cuts should affect both event Energy spectrum from Det-A In the workshop, data from the module Det-A operated in the first data taking period of CRESST-III were presented. The module is based on a CaWO 4 crystal with a mass of 23. 6 g and achieved a baseline energy resolution of σ = 4. 6 eV  [28]. With this the offline trigger threshold was set to a value corresponding to an energy of 30. 1 eV for nuclear recoils using the method outlined in  [31]. The exposure before cuts used for the DM analysis with Det-A amounts to 5. 594 kg•day. The average survival probability for signal events (neglecting the energy dependence introduced by the trigger efficiency) is ∼65 %.
The data of this module in the energy range from 30. 1 eV up to 16 keV are published at  [34]. Fig. 2  shows the energy spectrum of all events in the DM data set of Det-A from  [28]. At energies below 200 eV one can observe a sharp rise of the event rate. The average pulse shape of these events can not be distinguished from particle-induced events at higher energies. Due to the low light output at these energies it is impossible to tell if these events are caused by nuclear recoils or by electron/gamma events. According to the noise model a total of 3. 6 events from noise triggers are expected, which is much less than what is observed. A similar event population is observed in all other detectors operated in the same run which had a sufficiently low energy threshold. However, the rate and spectral shape of the excess contributions is not compatible between these different detectors which disfavours a common origin of these events (like e.
Data acquisition and processing The data acquisition system and readout electronics are described in detail in  [38]. The data from the phonon and ionization channels are digitized at a frequency of 100 kHz, filtered, averaged, and continuously stored on disk with a digitization rate matching the Ge-NTD modulation frequency. Events are identified off-line using optimal filters based on the measured noise PSDs and the pulse shape of the heat signal. The events are searched for and selected iteratively using a decreasing energy ordering rule. At each iteration, the data within a given time window of width ±∆T is excluded from further pulse searches. The value of ∆T depends on the typical rate in the detector: 2 s for the data recorded in the underground laboratory, and 1 s for the above-ground laboratory data.
The procedure also measures the systematic shift in energy that appears when the signal amplitude approaches that of typical noise fluctuations, see  [4]  for a more detailed discussion of the processing pipeline. For a reliable bin-to-bin comparison with the other energy spectra in the EXCESS database, the selected ranges are restricted to those where the shift between the true and reconstructed energies are smaller than the energy bins. Event populations with distinctive pulse shapes (such as interactions occurring within the Ge-NTD sensor, by pulses injected through the clamps or glitches in the digitization) were removed using cuts based on the χ 2 obtained using different pulse shape hypotheses  [4, 5].
63 eV ee , or 0. 54 electronhole pairs. The resolution at 160 eV ee (M-shell) is 8 eV ee , consistent with an expected Fano factor of 0. 15. Seven days of data were recorded at 78V, while the temperature was kept at 20. 7 mK. 89h of data were selected for the stability of the baseline resolution. It was split in a blind sample of 58h, sandwiched between two non-blind intervals used to optimise the analysis procedure and cuts. The heat resolution in the blind sample is 1. 58 eV ee (0. 53 electron-hole pair). Three days after the search, the detector was exposed again to a strong AmBe source for 15 h, in order to confirm the stability of the detector response and to provide a sample of 858 reference K-shell events for the pulse simulation. A fraction of 19% of that sample exhibits a degraded charge collection.
The current DAQ operates in a triggerless mode and is thus not limited by any artificial trigger thresholds, although it comes at the expense of much more demanding resource requirements for data storage and the analysis pipeline. Figure  6:  (left) MINER: The spectrum obtained from a 4mm thick sapphire detector with the 55 calibration lines, (right) The low energy excess. These events were obtained using a triggerless DAQ followed by software trigger for pulses.
g. in  [32] ). In this way, energy reconstruction could be performed beyond the linear range (up to 12 keV), which is necessary for calibration with the 55 Fe source. The energy resolution found with the optimum filter method is 3. 84 ± 0. 16 eV. The trigger threshold of the detector was set to 19. 7 eV. The final energy spectrum of the 5. 31 hour data acquisition was derived using several event selection criteria. In the first step, periods of unstable detector temperature were manually identified using saturated pulses and removed. This reduced the live time of the detector to 3. 26 hours. Two energy-independent cuts were used against artifacts and mis-reconstructed events: a cut on pulse decay time removes heater pulses and mis-reconstructed saturated pulses, and a cut on the baseline slope removes SQUID resets and pile-up events.
Energy spectrum from the 1g-prototype The final observed energy spectrum (Fig. 8 ) contains the calibration lines at 5. 9 keV and 6. 5 keV, a flat background (attributed to environmental gamma radiation) of around 6 • 10 5 count /keV /kg /day and a sharp rise in event rate below ∼ 200 eV energy of currently unknown origin. Subsequent to the first experimental run in February 2017, similar detectors were operated, proving out the holding and cryogenic veto concept of NUCLEUS  [47]. "Prototype Run 2" featured a different TES design with a better energy resolution, a new silicon holder and calibration as well as background data-sets. The low-energy rise is present in the background dataset and therefore unrelated to the calibration source. "Prototype Run 4" operated for the first time the "inner cryogenic veto" of NUCLEUS: flexible silicon wafers equipped with TES and holding the target cube.
Data acquisition and processing The data were acquired with a sampling frequency of 1. 25 MHz (1. 51 MHz) for Run1 (Run2). The Run1 data were triggered with a shaped pulse-sum of the two QET channels through a shaping amplifier. The Run2 data were taken continuously and triggered offline with a matched filter trigger. For both runs the amplitude of each event was calculated with an optimum filter. The data were calibrated with a room-temperature laser with a wavelength of 650 nm for Run1 and 635 nm for Run2. The light signal was directed to the detector's center with an optical fiber. The fiber was pointed to the back side of the detector (shining onto the aluminum electrode) in Run1 and to the TES sensor in Run2. During the laser calibration, the detectors are illuminated by bursts of photons with an average photon number between 0.
5 and 4. Single electron-hole pairs, corresponding to individual photons, are used to calibrate the detector and evaluate non-linearity at higher energies. A baseline resolution of 14 eV  [49]  and 2. 7 eV  [51]  was achieved respectively during Run1 and Run2, where the energy resolution is expressed in total phonon energy and is independent of the applied voltage. Live-time selections and data quality cuts were applied to these data. During Run1 data, 100 200 300 400 500 600 Total phonon energy (eV) Events/(s•g•n eh ) Figure  10 : Energy spectra acquired during SuperCDMS-HVeV Run1 (R1) and Run2 (R2). An additional point is added above each electron-hole pair peak to highlight the event rate contained in a 3σ window around the peak (corresponding to the counts in the peak). Each point has a 3σ uncertainty on the number of counts.
153 hours to read out the active area). The data from each such cycle comprises an "image," and 22 such images were included in the blinded dataset, in addition to 7 commissioning images that were used to develop the analysis. The total blinded exposure (before cuts) was 19. 93 g-day for the 1 e -and 2 e -analyses, and 27. 82 g-day for the 3 e -and 4 e -analyses. Analysis cuts were applied to reject regions of each image that contained large amounts of charge from high-energy events and regions where excess charge could be expected (at the locations of known CCD defects, near high-energy events, in regions with an excess of other events). The 1 e -and 2 e -analyses searched for single-pixel events; the 3 e -and 4 e -analyses searched for contiguous clusters of nonempty pixels. The effective exposure for each analysis was corrected for the efficiency of the cuts and the probability that a DM event generating the given amount of charge would diffuse into a configuration accepted by the analysis (a single pixel for 2 e -, a contiguous cluster of pixels for 3 e -and 4 e -).
Data acquisition and processing From the commissioning runs, 156 hours of data were taken in 135 mbar of CH 4 (0. 114 kg), 2030 V applied on the ACHINOS, fixed trigger conditions, and a sampling frequency of 1. 04 MHz. The results discussed in this work represent South hemisphere data for only 21 hours from the whole dataset, for a total exposure of 0. 0156 kg • days. A λ = 213 nm pulsed laser  [90]  was shined into the detector through a fiber feedthrough to monitor the stability of the gain and drift during physics runs by extracting photoelectrons from the S140 internal surface. Additional daily one hour low-intensity laser calibrations were performed to study the single electron response of the detector. At the end of the physics runs, eleven hours of data with 37 Ar were taken under the same operating conditions to calibrate the fiducial volume associated with each ACHINOS channel and the attachment rate of primary electrons.
Acknowledgements The  SuperCDMS CPD  project has been supported through the  National Science Foundation  -Grants No. 1809730  and No. 1707704 , the  U. S. Department of Energy (DOE) ,  Fermilab   URA Visiting Scholar Grant  No. 15-S-33 ,  NSERC Canada , the  Canada First Excellence Research Fund , the  Arthur B. McDonald Institute (Canada) ,  Michael M. Garland , the  Department of Atomic Energy Government of India (DAE)  and the  Deutsche Forschungsgemeinschaft (DFG, German Research Foundation )-Project No. 420484612. Fermilab  is operated by  Fermi Research Alliance, LLC , under Contract No. DE-AC02-37407CH11359  with the  US Department of Energy. Pacific Northwest National Laboratory  (PNNL) is operated by  Battelle Memorial Institute  for the DOE under Contract No. DE-AC05-76RL01830. SLAC is operated under Contract No.
DEAC02-76SF00515  with the  United States Department of Energy. The  SENSEI  project is grateful for the support of the  Heising-Simons Foundation  under Grant No. 79921. RE also acknowledges support from  DoE Grant   DE-SC0017938  and  Simons Investigator in Physics Award 623940. It was supported by  Fermilab  under  DOE  Contract No. DE-AC02-07CH11359. The work of TV and EE is supported by the  I-CORE Program of the Planning Budgeting Committee  and the  Israel Science Foundation  (grant No. 1937/12 ). TV is further supported by the  European Research Council (ERC)  under the  EU Horizon 2020 Programme  (ERC-CoG-2015 -Proposal n. 682676 LDMThExp), and a grant from The  Ambrose Monell Foundation , given by the  Institute for Advanced Study. The work of  SU  is supported in part by the  Zuckerman STEM Leadership Program.
IB is grateful for the support of the Alexander Zaks Scholarship, The Buchmann Scholarship, and the  Azrieli Foundation. TTY is supported in part by  NSF   CAREER grant   PHY-1944826. DB was supported through the  U. S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center. The MINER work was supported by the  DOE  Grant Nos DE-SC0018981 for multiple detector R&D efforts for MINER and  SuperCDMS ,  DE-SC0017859  for the Hybrid detector development for MINER, DE-SC0020097 for the cryogenic inner active veto development, and  DE-SC0021051  for the partial support to procure the Bluefors fridge. We acknowledge the yearly operations funding provided by the  Mitchell Institute. We would like to acknowledge the support of  DAE-India  through the project  Research in Basic Sciences -Dark Matter  and  SERB-DST-India  through the J.
C. Bose Fellowship. The  EDELWEISS  project is supported in part by the  French Agence Nationale pour la Recherche (ANR)  and the  LabEx Lyon Institute of Origins  ( ANR-10-LABX-0066 ) of the  Université de Lyon  within the program " Investissements d'Avenir"  ( ANR-11-IDEX-00007 ), by the  P2IO LabEx  ( ANR-10-LABX-0038 ) in the framework " Investissements d'Avenir"  ( ANR-11-IDEX-0003-01 ), and the  Russian Foundation for Basic Research  (grant No. 18-02-00159 ). It has received funding from the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Skłodowska-Curie Grant  Agreement No. 838537. The NUCLEUS experiment is funded by the  CEA , the  INFN , the  ÖAW  and partially supported by the  MPI für Physik , by the  DFG  through the  SFB1258  and the  Excellence Cluster ORIGINS , and by the  European Commission  through the  ERC-StG2018-804228  " NU-CLEUS ".
The  RICOCHET  project has received funding from the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation program  under Grant Agreement  ERC-StG-CENNS 803079 , the  French National Research Agency (ANR)  within the project  ANR-20-CE31-0006 , the  LabEx Lyon Institute of Origins  ( ANR-10-LABX-0066 ) of the  Université de Lyon. A portion of the work carried out at  MIT  was supported by  DOE QuantISED  award  DE-SC0020181  and the  Heising-Simons Foundation. A portion of this work carried out at  Northwestern University  was supported in part under  NSF  Grant  PHY-2013203. This work is also partly supported by the  Ministry of science and higher education of the Russian Federation  (the contract No. 075-15-2020-778 ). The NEWS-G experiment acknowledges the help of the technical staff of the  Laboratoire Souterrain de Modane.
This work was undertaken, in part, thanks to funding from the  Canada Research Chairs program , as well as from the  French National Research Agency  (No. ANR15-CE31-0008 ). This project has received support from the  European Union 's  Horizon 2020 research and innovation programme  under grant agreements No. 841261  ( DarkSphere ) and No. 895168  (neutronSPHERE), and from the  UK Research and Innovation -Science and Technology Facilities Council  through grants No. ST/S000860/1 ,  ST/V006339/1 , and  ST/W005611/1. This work has received support from the  Arthur B. McDonald Canadian Astroparticle Physics Research Institute. The  CRESST  project is partly funded by the  DFG  through the  SFB1258  and the Origins Cluster, by the  BMBF  projects  05A17WO4  and  05A17VTA , by the  Austrian Science Fund FWF  projects  I3299-N36 ,  I5420-N  and  W1252-N27.
Acknowledgements We thank  Ahmadullah Zahed  and  Debapriyo Chowdhury  for discussions. SDC is supported by a  Kadanoff fellowship  at the  University of Chicago , and in part by  NSF  Grant No. PHY2014195. KG is supported by  ANR Tremplin-ERC  project  FunBooTS. KG thanks  ICTS, Bangalore  for hospitality during the intial stage of this work. AS acknowledges partial support from a  SPARC  grant  P315  from  MHRD, Govt of India.
Age-Ranked Storage and the SAS Function There are two functions that are somewhat more elaborate than the simple age distributions: the age-ranked storage S T and the StorAge Selection (SAS) functions ω. They are defined here and they will be used later in the formulation of the water age balance (Section 3. 2. 2 and Figure  4 ). 16 ) using the transport column analogy. An educational video that further describes the water age balance is available in  Harman (2022)  and can be accessed online at https://www. youtube. com/watch?v=WBYy_iDPRv0 (October 2022). The age-ranked storage S T (T, t) is defined  (Harman, 2015)  as the cumulative storage age distribution multiplied by the storage: 𝑆𝑆𝑇𝑇 (𝑇𝑇 𝑇 𝑇𝑇) = 𝑆𝑆(𝑇𝑇)𝑃𝑃𝑆𝑆 (𝑇𝑇 𝑇 𝑇𝑇) (6) Thus, S T (T, t) can be seen as an un-normalized cumulative distribution whose maximum is S(t) rather than 1.
A number of similar reformulations and their potential uses are discussed in  Harman (2019a) , but only S T will be further discussed here. The age-ranked storage quantifies the mass of water with age equal to or less than T at time t and it has units of volume. The terminology "ranked" stresses that the water storage volumes are classified according to their age. As it will be shown in Section 3. 2, this ranking is a convenient way to tag stored water parcels. Many recent advances in TTD approaches have come from better understanding the relationship between the distribution of ages in storage p S (T, t) and ages in an outflow p Q (T, t). SAS functions (see also Section 3. 2. 3) were originally defined by  Botter et al. (2011)  as: 𝜔𝜔𝑄𝑄(𝑇𝑇 𝑇 𝑇𝑇) = 𝑝𝑝𝑄𝑄(𝑇𝑇 𝑇 𝑇𝑇)∕𝑝𝑝𝑆𝑆 (𝑇𝑇 𝑇 𝑇𝑇) (7) When this ratio is equal to 1 for all T, the outflow age distribution is the same as the age distribution in storage (i.
e. , the uniform sampling case). Values greater than (or less than) 1 for a given age T mean that water of that age is over-represented (or under-represented) in the outflow relative to its presence in storage. Starting from this initial definition, useful transformed versions of the SAS function have been developed (see Section 3. 2. 2 and  Harman, 2015). The integral form of the SAS function is usually indicated as Ω Q (T, t). The terminology "storage selection" should not induce a reader to think that outflows are expected to actively select water based on its age. The term selection was simply born in analogy to statistical sampling because it highlights the link between the pool of available waters (i. e. , the water storage) and the subsample of that pool that is released to stream or evapotranspiration.
This implies that outflowing water can only be a subsample of the existing stored water and for example, there cannot be any storage of age 10 days if no rain fell 10 days ago, and thus no streamflow can be 10 days old. The introduction of ω had fundamental implications in transport hydrology because, by providing closure to the water age balance, it enabled consistency between transit times and mass conservation. After decoupling the problem of flow and transport (Equations 11 and 12) and introducing the SAS functions (Equation  7 ), the water age balance equation after  Botter et al. (2011)  reads: p Q (T, t) = ω Q (T, t) p S ( 𝜕𝜕 (𝑆𝑆(𝑡𝑡)𝑝𝑝𝑠𝑠(𝑇𝑇 𝑇 𝑡𝑡)) 𝜕𝜕𝑡𝑡 = 𝐽𝐽 (𝑡𝑡)𝛿𝛿(𝑇𝑇 ) -𝑄𝑄(𝑡𝑡)𝜔𝜔𝑄𝑄(𝑇𝑇 𝑇 𝑡𝑡)𝑝𝑝𝑆𝑆 (𝑇𝑇 𝑇 𝑡𝑡) -𝐸𝐸𝑇𝑇 (𝑡𝑡)𝜔𝜔𝐸𝐸𝑇𝑇 (𝑇𝑇 𝑇 𝑡𝑡)𝑝𝑝𝑆𝑆 (𝑇𝑇 𝑇 𝑡𝑡) - 𝜕𝜕 (𝑆𝑆(𝑡𝑡)𝑝𝑝𝑠𝑠(𝑇𝑇 𝑇 𝑡𝑡)) 𝜕𝜕𝑇𝑇 ( 13 ) Equation 13 is equivalent to the population balance (Equation  10 ), but age distributions now appear explicitly and the SAS function is used to describe how the current water storage, which comprises a distribution of past precipitation inputs, contributes to current discharge or evaporation.
As mentioned above, Equations 11 and 12 allow decoupling flow from transport, but the price to pay is a nonlinear constraint enforcing that an outflow must be equal to the sum of all the stored parcels that contribute to it per unit time: 𝐴𝐴 𝐴𝐴(𝑡𝑡) = ∫ ∞ 0 𝑞𝑞(𝑇𝑇 𝑇 𝑡𝑡)𝑑𝑑𝑇𝑇 = ∫ ∞ 0 𝐴𝐴(𝑡𝑡)𝜔𝜔𝐴𝐴(𝑇𝑇 𝑇 𝑡𝑡)𝑝𝑝𝑆𝑆 (𝑇𝑇 𝑇 𝑡𝑡)𝑑𝑑𝑇𝑇. This translates into the constraint: ∫ ∞ 0 𝜔𝜔𝑄𝑄(𝑇𝑇 𝑇 𝑇𝑇)𝑝𝑝𝑆𝑆 (𝑇𝑇 𝑇 𝑇𝑇)𝑑𝑑𝑇𝑇 = 1 (14) A convenient way to deal with this constraint is reasoning in terms of a different variable, as proposed by van der Velde et al. (  2012 ), who introduced a transformed SAS function (termed STorage Outflow Probability STOP function at the time), and by  Harman (2015) , who reformulated the problem in terms of "rank storage" rather than absolute age. In both cases, the transformed problem is based on a mapping from age to the cumulative storage age distribution: 𝑇𝑇 ↦𝑆𝑆𝑇𝑇 (𝑇𝑇 𝑇 𝑇𝑇) = 𝑆𝑆(𝑇𝑇)𝑃𝑃𝑆𝑆 (𝑇𝑇 𝑇 𝑇𝑇) ( 15 ) This transformation is explained in more detail in  Benettin, Rinaldo, et al.
Harman, 2015, Figure  1 ). By expressing the SAS functions in terms of rank storage (or normalized-rank storage, as done by van der Velde et al. , 2012), Equation  14 is automatically verified whenever the SAS function ω(S T , t) is a pdf. After integrating Equation 13 over age, we obtain the evolution of the rank storage over time and age  (Harman, 2015 , Equation  3 ): 𝜕𝜕𝜕𝜕𝑇𝑇 (𝑇𝑇 𝑇 𝑇𝑇) 𝜕𝜕𝑇𝑇 = 𝐽𝐽 (𝑇𝑇) -𝑄𝑄(𝑇𝑇)Ω𝑄𝑄 (𝜕𝜕𝑇𝑇 𝑇 𝑇𝑇) -𝐸𝐸𝑇𝑇 (𝑇𝑇)Ω𝐸𝐸𝑇𝑇 (𝜕𝜕𝑇𝑇 𝑇 𝑇𝑇) - 𝜕𝜕𝜕𝜕𝑇𝑇 (𝑇𝑇 𝑇 𝑇𝑇) 𝜕𝜕𝑇𝑇 ( 16 ) with initial condition   (   = 0) =  0 and boundary condition S T (T = 0, t) = 0. The symbol Ω indicates the cumulative SAS function. Once again, the age balance Equation 16 is a statement of mass conservation over time and age, which can be visualized in Figure  4 : the rank storage (i. e. , the storage volume younger than age T ) changes over time because new storage with age 0 is introduced through precipitation, storage of different ages is released to evapotranspiration and streamflow, and all storage volumes get older with time.
To help visualize how the water age balance evolves over time, we have created an educational video available in  Harman (2022)  and accessible online at https://www. youtube. com/watch?v=WBYy_iDPRv0 (October 2022). The age balance equation, being a reformulation of mass conservation, is not a "model" by itself, but solving this equation requires a model for the SAS functions. As SAS functions need to satisfy the properties of a probability distribution, it makes sense to model them as pdfs (e. g. , a gamma distribution, see Section 3. 2. 3), with one or more parameters that need to be assigned or calibrated. When the SAS parameters are set for both Ω Q (S T , t) and Ω ET (S T , t), and hydrologic fluxes (J, Q, ET) are given, the mathematical problem framed in Equation 16 can be solved. A numerical implementation is usually required except for special cases of uniform sampling and perfect piston flow (see.