CsI(Tl) Pulse Shape Discrimination with the Belle II Electromagnetic Calorimeter as a Novel Method to Improve Particle Identification at Electron-Positron Colliders
S. Longo, J.M. Roney, C. Cecchi, S. Cunliffe, T. Ferber, H. Hayashii, C. Hearty, A. Hershenhorn, A. Kuzmin, E. Manoni, F. Meier, K. Miyabayashi, I. Nakamura, M. Remnev, A. Sibidanov, Y. Unno, Y. Usov, V. Zhulanov
aa r X i v : . [ phy s i c s . i n s - d e t ] S e p CsI(Tl) Pulse Shape Discrimination with the Belle IIElectromagnetic Calorimeter as a Novel Method toImprove Particle Identification at Electron-PositronColliders
S. Longo a,1, ∗ , J.M. Roney a,e , C. Cecchi j,k , S. Cunliffe b , T. Ferber b ,H. Hayashii c , C. Hearty d,e , A. Hershenhorn d , A. Kuzmin f,g , E. Manoni k ,F. Meier m , K. Miyabayashi c , I. Nakamura i,h , M. Remnev f,g , A. Sibidanov a ,Y. Unno l , Y. Usov f,g , V. Zhulanov f,g a University of Victoria, Victoria, British Columbia, V8W 3P6, Canada b Deutsches Elektronen–Synchrotron, 22607 Hamburg, Germany c Nara Women’s University, Nara 630-8506, Japan d University of British Columbia, Vancouver, British Columbia, V6T 1Z1, Canada e Institute of Particle Physics (Canada), Victoria, British Columbia V8W 2Y2, Canada f Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russian Federation g Novosibirsk State University, Novosibirsk 630090, Russian Federation h The Graduate University for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan i High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan j Dipartimento di Fisica, Universit`a di Perugia, I-06123 Perugia, Italy k INFN Sezione di Perugia, I-06123 Perugia, Italy l Department of Physics and Institute of Natural Sciences, Hanyang University, Seoul04763, South Korea m Duke University, Durham, North Carolina 27708, U.S.A.
Abstract
This paper describes the implementation and performance of CsI(Tl) pulseshape discrimination for the Belle II electromagnetic calorimeter, represent-ing the first application of CsI(Tl) pulse shape discrimination for particleidentification at an electron-positron collider. The pulse shape characteriza-tion algorithms applied by the Belle II calorimeter are described. Controlsamples of γ , µ + , π ± , K ± and p/ ¯ p are used to demonstrate the significant ∗ Corresponding author
Email address: [email protected] (S. Longo) Present Address: Deutsches Elektronen–Synchrotron, 22607 Hamburg, Germany
Preprint submitted to NIM A September 8, 2020 nsight into the secondary particle composition of calorimeter clusters thatis provided by CsI(Tl) pulse shape discrimination. Comparisons with sim-ulation are presented and provide further validation for newly developedCsI(Tl) scintillation response simulation techniques, which when incorpo-rated with GEANT4 simulations allow the particle dependent scintillationresponse of CsI(Tl) to be modelled. Comparisons between data and simula-tion also demonstrate that pulse shape discrimination can be a new tool toidentify sources of improvement in the simulation of hadronic interactions inmaterials. The K L efficiency and photon-as-hadron fake-rate of a multivari-ate classifier that is trained to use pulse shape discrimination is presentedand comparisons are made to a shower-shape based approach. CsI(Tl) pulseshape discrimination is shown to reduce the photon-as-hadron fake-rate byover a factor of 3 at photon energies of 0.2 GeV and over a factor 10 atphoton energies of 1 GeV. Keywords:
Belle II, Calorimeters, Pulse Shape Discrimination, Thalliumdoped Cesium Iodide, Particle Identification, GEANT4
1. Introduction
The Belle II experiment at the SuperKEKB asymmetric electron-positroncollider plans to integrate a 50 ab − dataset while operating at and near theΥ(4 S ) resonance, corresponding to a centre-of-mass energy of 10 .
58 GeV.With this unprecedented dataset, Belle II will search for physics beyond theStandard Model through precision flavour sector measurements and searchesfor rare/forbidden processes as well as darks sectors [1, 2]. Complimentary tothe improved statistical precision to be achieved at Belle II, advancements innew experimental techniques can also further enhance Belle II sensitivities tonew physics and potentially allow for new measurements. This paper presentsthe performance of a new method for calorimeter-based particle identifica-tion in high energy physics through the novel application of pulse shape dis-crimination (PSD) with thallium-doped cesium iodide (CsI(Tl)) scintillatorcrystals. The results presented demonstrate that with pulse shape discrimi-nation direct insight into the secondary particle composition of calorimeterclusters is gained, providing a means for highly effective discrimination be-tween electromagnetic and hadronic showers in the Belle II calorimeter. Thisinformation is shown to be independent of that from other particle identifi-cation observables in Belle II, including current calorimeter-based quantities,2eading to improvements in K L vs. photon identification. The results pre-sented represent the first application of this experimental technique at a e + e − collider experiment and opens the way to improve many Belle II measure-ments where hadronic shower identification is crucial, such as in the flag shipmeasurement of sin 2 φ using B → J/ψK L [1].The scintillation response of CsI(Tl) is empirically well known to dependon the ionization dE / d x of the particle that is depositing energy in the crys-tal [3]. Highly ionizing particles, such as stopping protons or alpha particles,are observed to produce CsI(Tl) scintillation emission with a faster decaytime relative to the CsI(Tl) scintillation emission produced from energy de-posits by photons or low dE / d x particles [3, 4, 5, 6]. This phenomenon hasbeen widely exploited in the energy regime of <
10 MeV to discriminatebetween interactions caused by electrons, protons and alpha particles [3, 6],as well as in nuclear physics for low energy nuclei identification [5, 7, 8, 9].Recent studies have demonstrated the significant potential for PSD to im-prove hadronic shower identification at electron-positron collider experiments[4, 10, 11, 12]. Although several past and present detectors operating at highenergy e + e − colliders have employed CsI(Tl) calorimeters, such as Belle [13],BaBar [14, 15] and BESIII [16], applying CsI(Tl) PSD to improve particleidentification has yet to be attempted at a high energy e + e − collider experi-ment.This paper presents the implementation and performance of CsI(Tl) pulseshape discrimination with the Belle II calorimeter using collision data col-lected during the summer 2018 commissioning of the Belle II experiment.The data used in this analysis corresponds to an integrated luminosity of0 . − collected at the Υ(4 S ) resonance [17].The Belle II detector has a cylindrical geometry and is constructed from ofa collection of sub-detectors that together perform as a spectrometer operat-ing in a 1.5 T magnetic field. The innermost sub-detector is a vertex detectorbeginning at a radius of 14 mm from the interaction point and consists of twolayers of pixel detectors followed by four layers of double-sided silicon stripdetectors. During the summer 2018 commissioning of the Belle II experi-ment only one octant of the vertex detector was installed. Extending froma radius of 160 mm to 1100 mm is the central drift chamber, which appliesa 50% He, 50% C H gas mixture to perform charged particle detection,and identification through dE/d x measurements. After the drift chamberis a charged particle identification system consisting of a Cherenkov-basedtime-of-propagation detector in the barrel region and an aerogel ring imaging3herenkov detector in the forward region. The electromagnetic calorimeteris constructed from CsI(Tl) scintillator crystals and includes a barrel regionbeginning at a radius of 1250 mm, in addition to forward and backward end-caps. The outermost sub-detector is the K L -muon detector system. Theendcaps and the initial layers of the barrel region of the K L -muon detectorare constructed from alternating layers of iron plates and scintillating stripdetectors. The outer barrel layers substitute the scintillating strip detectorswith resistive-plate chambers. Additional details of the Belle II detector canbe found in reference [18].This paper is organized as follows: Section 2 describes the experimen-tal details concerning the implementation of CsI(Tl) PSD with the Belle IIelectromagnetic calorimeter. In Section 3 the pulse shapes of crystals incalorimeter clusters produced by control samples of γ , µ + , π ± , K ± and p/ ¯ p selected from Belle II data and simulation are studied. This survey demon-strates that by analysing the scintillation pulse shapes of the CsI(Tl) crystalsin a calorimeter cluster, the types of secondary particles produced in the clus-ter can be identified. In Section 4 the performance of a multivariate classifier,which is trained to use CsI(Tl) PSD to separate K L and photons, is mea-sured and compared with a shower-shape based approach to neutral particleidentification. Section 5 presents the conclusions of this study and discussesareas for further development of this new experimental technique.
2. Pulse Shape Discrimination with the Belle II Calorimeter
In this section the reconstruction and simulation methods implementedto apply pulse shape discrimination with the Belle II calorimeter are de-scribed. The relevant features of the Belle II calorimeter signal chain that al-low for CsI(Tl) waveforms to be digitized and recorded for offline pulse shapeanalysis are outlined. The waveform shape characterization techniques arethen described and the methods applied to simulate the ionization-dependentCsI(Tl) response are discussed.The Belle II calorimeter re-uses the calorimeter of Belle, but with up-graded electronics following the initial pre-amplification stage. The calorime-ter is constructed from 8736 CsI(Tl) scintillator crystals that have a trape-zoidal geometry with front face area of ∼ . × . , rear face area of ∼ × and nominal length of 30 cm. Each crystal is equipped with twoHamamatsu S2744-08 photodiodes, which have a surface area of 10 ×
20 mm and are glued to the rear crystal face [18]. Two pre-amplifiers, one for each4hotodiode, are also mounted on the rear of the crystal to integrate the signalemitted by each photodiode [18].Following the initial pre-amplification stage, the two signals are summedthen processed by a CR-(RC) shaping amplifier with shaping time of 0 . µ s [19]. The signal is then digitized into 31 samples with 18-bit precisionand at a sample frequency of 1.7669 MHz (sample time of 0.56594 µ s).During data-taking the digitized waveform is processed online with Field-Programmable-Gate-Array’s (FPGA’s) to measure the magnitude and timeof the energy deposit in the crystal. At present, the waveform analysis by theFPGA’s is limited to computing only the energy and time of the waveform.As this does not explicitly contain information that characterizes the wave-form shape, which is required for PSD, an upgrade of the FPGA firmwarewas implemented such that if the energy measurement by the FPGA ex-ceeds 30 MeV then the 31 waveform data points are stored offline. Althoughcrystals with energy deposits below 30 MeV are expected to contain PSDinformation, the 30 MeV energy threshold is applied due to the bandwidthlimitations of the Belle II data acquisition system, which is unable to recordthe waveforms of all 8736 CsI(Tl) channels for every event. Due to energydeposits from beam backgrounds produced by SuperKEKB, the number ofcrystals per event which are above a given energy threshold grows rapidly asthe threshold decreases below 30 MeV. To maximize the PSD performance,the 30 MeV value for this threshold was determined to be the minimal valuethat the data acquisition system could sustain given the beam backgroundslevels experienced during operation [20].To characterize the waveform pulse shape the techniques developed in ref-erence [4] are applied. The study in reference [4] demonstrated that energydeposits by highly ionizing particles produce a CsI(Tl) scintillation com-ponent measured to have a decay time of 630 ±
10 ns. This scintillationcomponent is referred to as the hadron component as it is only produced byhighly ionizing energy deposits and thus not present in scintillation emissionfrom electromagnetic showers or energy deposits from low dE / d x particles,such as minimum ionizing particles [4]. The shape of the CsI(Tl) waveformis characterized by the crystal hadron intensity defined as the fraction ofscintillation emission emitted in the hadron component relative to the totalscintillation emission.To measure the magnitude of the total and hadron component scintilla-tion emission, the waveforms recorded offline are fit to the model defined in5quation 1. G ( t ) = L Photon R Photon ( t − t ) + L Hadron R Hadron ( t − t ) (1)In equation 1, G ( t ) is the CsI(Tl) waveform. t is time. t is the time the incident particle’s energy is deposited. R Photon is the photon template, which is defined as the shape of the signalat the output of the full signal chain of a Belle II crystal channel associatedwith the CsI(Tl) scintillation produced in an electromagnetic shower. R Hadron is the hadron template, which is defined as the shape of the signalat the output of the full signal chain of a Belle II crystal channel associatedwith the additional CsI(Tl) scintillation component produced whenhadronic interactions take place. L Photon is the photon scintillation component light output yield. L Hadron is the hadron scintillation component light output yield.From the quantities measured by the model described in equation 1, thecrystal energy, E crystalTotal , and crystal hadron intensity are computed using equa-tions 2 and 3, respectively.E crystalTotal = L Photon + L Hadron (2)Hadron Intensity = L Hadron L Photon + L Hadron (3)From these definitions, electromagnetic shower energy deposits are ex-pected to have hadron intensity of zero, whereas energy deposits from highlyionizing particles, are expected to have hadron intensity greater than zero.The exact value of the hadron intensity will depend on the magnitude of6nergy deposited at an ionization dE / d x that is above the threshold requiredto produce hadron scintillation component emission.Two examples of typical waveforms recorded during summer 2018 Belle IIcommissioning runs are shown in Figure 1. Figure 1a shows a typical wave-form with a photon-like pulse shape and Figure 1b shows a typical waveformwith hadron-like pulse shape. Comparing these two waveforms, it is observedthat hadron-like pulse shapes have a suppressed tail relative to the photon-like pulse shapes, which is well modelled by the hadron template. µ Time ( A m p li t ude ( a r b ) DataTotal FitPhoton ComponentHadron Component
Cell ID: 2721 (brl)= 2698 MeV
Total
E = 0.1 MeV
Hadron
EHadron Intensity = 0.000= 27.0 (NDF=27) χ − − D a t a - F i t Belle II (a) µ Time ( A m p li t ude ( a r b ) DataTotal FitPhoton ComponentHadron Component
Cell ID: 5598 (brl)= 667 MeV
Total
E = 115.5 MeV
Hadron
EHadron Intensity = 0.173= 28.1 (NDF=27) χ − − D a t a - F i t Belle II (b)
Figure 1: Typical Belle II CsI(Tl) waveforms from data with fit to Photon+Hadron tem-plates overlaid. a) Waveform with photon-like pulse shape, as expected from an electro-magnetic shower. b) Waveform with hadron-like pulse shape, as expected from a hadronicshower.
To simulate particle interactions in the Belle II detector, Monte Carlo(MC) simulations using GEANT4 particle interactions in matter simulationlibraries are applied [21]. The GEANT4 physics list used is the
FTFP_BERT .By default, GEANT4 does not include simulations of the ionization dE / d x dependent CsI(Tl) scintillation response. To simulate the CsI(Tl) scintilla-tion response to highly ionizing particles we apply the simulation methodsdescribed in reference [4]. These methods compute the magnitude of thehadron scintillation component emission and Birk’s scintillation efficiency[22] using the instantaneous dE / d x of the primary and secondary particlesthat contribute to the total energy deposited in the CsI(Tl) crystal. Simu-lated waveforms are constructed by iterating over all discrete energy depositsin the crystal volume and accumulating a template sum, weighted by thecorresponding scintillation light output contributions from photon compo-nent scintillation emission and hadron component scintillation emission. Tomodel the detector noise conditions, noise waveforms recorded from events7hat are randomly triggered during data-taking runs are added to the sim-ulated waveform. After pulse construction, the simulated pulse is fit usingthe same methods as described above for data.
3. CsI(Tl) Pulse Shapes of Crystals in Clusters from a Selection ofParticle Control Samples
This section presents a survey of the scintillation pulse shapes observedin crystals from calorimeter clusters produced by control samples of γ , µ + , π ± , K ± and p/ ¯ p selected from Belle II commissioning data. These controlsamples are presented to demonstrate the variety of pulse shape signatures,which arise due to the different material interactions initiated by differenttypes of particles, and the ability to accurately simulate them.Demonstrated in reference [4], energy deposits by highly ionizing particlesgenerate hadron scintillation component emission in CsI(Tl), which is differ-entiated from scintillation produced by low dE / d x energy deposits due toits relatively fast scintillation time. The CsI(Tl) scintillation pulse shape isthus determined by the fraction of energy deposited at an ionization dE / d x that is significant enough to produce the hadronic scintillation componentemission. This direct dependence allows the CsI(Tl) pulse shape to be usedto identify the types of secondary particles that contributed to the energydeposit in the crystal. As a result the pulse shapes of the crystals in thecluster will depend on the primary particle type.The main features of each control sample are summarized as: • γ - CsI(Tl) pulse shapes of energy deposits from electromagnetic show-ers. • µ ± - CsI(Tl) pulse shapes of energy deposits from minimum ionizingparticles. • π ± - CsI(Tl) pulse shapes of crystals in hadronic showers. • K ± - Due to strangeness conservation in strong interactions, hadronicinteractions of K + in the momentum regime studied are suppressed rel-ative to K − [23]. This effect is observed with CsI(Tl) PSD, illustratingthat CsI(Tl) PSD can measure the hadronic activity in a cluster. • p/ ¯ p - In the momentum regime studied p frequently will ionize andstop in the calorimeter. During this process the p becomes highly8onizing, demonstrating the scenario when the primary particle candirectly produce hadron scintillation light output. The pulse shapedistribution is shown to be distinct from a ¯ p , which annihilates in theCsI(Tl). How PSD can be used to improve the GEANT4 simulation of¯ p interactions is also discussed.Selections for each control sample are described the respective section below.A momentum dependent efficiency correction is applied to simulation to ac-count for inefficiencies in data due to event triggering and reconstructioninefficiencies. After the momentum dependent efficiency correction, the mo-mentum distributions in data and simulation are in agreement thus allowingthe calorimeter quantities to be compared [20]. Only clusters in the barrelregion of the calorimeter are studied. A sample of electromagnetic showers produced by photons with lab mo-mentum magnitude, p lab , in the range 0.5 < p lab ≤ e + e − → µ + µ − ( γ ) events. This selection requires the event to have twowell reconstructed oppositely charged tracks in addition to a photon. Bhabhaevents are rejected by requiring the calorimeter cluster energy of each trackto be consistent with an ionization cluster. The mass of the µ + µ − γ system isrequired to be consistent with the total centre-of-mass energy of SuperKEKB.In addition, the magnitude and direction of the photon momentum vectoris required to be consistent with the recoil momentum of the µ + µ − system.Backgrounds from e + e − → π + π − ( γ ) and e + e − → K + K − ( γ ) are suppressedby vetoing events where the µ + µ − invariant mass is consistent with a ρ or φ [20].In this momentum range a photon is likely to interact in the CsI(Tl)calorimeter by generating an electromagnetic shower, consisting of only sec-ondary electrons, positrons and photons. Due to the absence of highly ioniz-ing particles in the electromagnetic shower, the hadron component intensityvalues of the crystals in the photon clusters are expected to be distributedclose to zero, independent of the photon energy and the crystal energy.Shown in Figure 2 is the crystal hadron intensity vs. crystal energy distri-bution for the crystals in the selected photon clusters. Observed in this figure,the crystal hadron intensity values are distributed near zero in data and sim-ulation, as expected. The hadron intensity fluctuations about zero present inthese distributions arise because a small hadron component contribution can9rtificially be added during the multi-component fit to compensate for noisepresent in the waveform. As observed in the data and simulation, this fittingeffect results in the hadron intensity to sometimes have small negative valuesdespite the true hadron intensity always being greater or equal to zero. C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 1768Number of Crystal Entries: 3581 2018
Belle II
Dataphotons (a) C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 1767Number of Crystal Entries: 3441 2018
Belle II
Simulationphotons (b)
Figure 2: Crystal hadron intensity vs crystal energy distributions for crystals in calorimeterclusters produced by 0.5 < p lab ≤ e + e − → µ + µ − ( γ ), a)data b) simulation. A sample of calorimeter clusters produced by muons with momentummagnitude in the range 1 < p lab ≤ e + e − → µ + µ − ( γ ) events [20]. At this momentum scale, the dominant interactionfor muons in CsI(Tl) is ionization. If the muon has sufficient transversemomentum, frequently it will traverse the entire 30 cm depth of the CsI(Tl)calorimeter, resulting in a ∼
200 MeV total energy deposit from ionization.This energy deposit will be concentrated a compact region of 1-2 crystals.Figure 3 shows the crystal hadron intensity vs. crystal energy distributionfor crystals in the sample of calorimeter clusters produced by the selectedmuons. The abundance of crystals with total energy of ∼
200 MeV in thesedistributions originates from calorimeter clusters where the muon trajectoryconstrained the muon ionization energy deposit to be contained mostly ina single crystal. The sample of crystals with energies below ∼
200 MeVare caused by the clusters where the muon trajectory traverses over multiplecrystals, thus the energy deposition is divided into those crystals. The crystalenergy deposits above 250 MeV are typically from electromagnetic showers10enerated by energetic delta rays emitted during the muon ionization. Thedistributions in Figure 3 demonstrate that independent of the crystal energythe hadron intensity values of the crystals are distributed near zero, similarto the crystals in the photon control sample. This observation is consistentwith the measurements presented in reference [4], further demonstrating theionization dE / d x of the muons in this sample is too low to produce significantamounts of hadron scintillation component emission. The pulse shapes ofcrystals in clusters from µ − were observed to display the same characteristicsas the crystals from µ + clusters shown in Figure 3 [20]. C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 10024Number of Crystal Entries: 11956 2018
Belle II
Data + µ (a) C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 9859Number of Crystal Entries: 11540 2018
Belle II
Simulation + µ (b) Figure 3: Crystal hadron intensity vs crystal energy distributions for crystals in calorimeterclusters produced by 1 < p lab ≤ e + e − → µ + µ − ( γ ), a) datab) simulation. A sample of charged pions in the momentum range 1 < p lab ≤ K S → π + π − decays. This control sample provided a cleansample of charged pions by selecting tracks that formed a displaced vertexand with invariant mass consistent with the K S mass. In addition, the labmomentum vector of the displaced vertex was required to be co-linear withthe vector connecting the interaction point to the vertex location [20]. In thismomentum range, a charged pion has about a 50% probability to undergoa nuclear interaction while traversing 30 cm of CsI(Tl) [24]. This results intwo distinct types of calorimeter clusters, as illustrated by Figure 4 showingthe calorimeter cluster energy distribution for the selected pion sample. Thepeak in the distributions at ∼
200 MeV corresponds to calorimeter clusters11here the pion did not hadronically interact in the CsI(Tl). In this case thepion leaves an ionization cluster in the calorimeter, similar to that of muonsdiscussed in the previous section. The remaining clusters in this distributionprimarily correspond to clusters where the pion generated a hadronic shower.For CsI(Tl), the scintillation response to highly ionizing particles is knownto be non-linear due to the Birk’s scintillation efficiency as well as due tochanges in the scintillation pulse shape [4, 25]. In Figure 4 two versions ofsimulation are overlaid to illustrate the impact that including the full CsI(Tl)scintillation response in simulation has on the simulated pion cluster energydistributions. In Figure 4 the simulation labelled
No Birks and PS uses de-fault GEANT4 simulations, which do not include modelling of the ionizationdE / d x dependent changes in the CsI(Tl) scintillation response. The simula-tion labelled w Birks and PS , where “PS” stands for Pulse Shape simulations,adds to the GEANT4 simulation the Birk’s scintillation efficiency [22] andpulse shape simulation techniques developed in reference [4], which allow theionization dE / d x dependent CsI(Tl) scintillation response to be modelled.Comparing the data to the two versions of simulation, it is observed that in-cluding the full CsI(Tl) scintillation response results in improved agreementbetween data and simulation. When the full CsI(Tl) scintillation responseis included in the simulation, a general trend observed is that the simulatedcluster energies increase. This can occur from the presence of energy depositsby secondary protons produced in the pion hadronic showers. In the Birk’sscintillation efficiency parametrization that is applied in the simulation, theCsI(Tl) scintillation efficiency is greater than one for an intermediate dE / d x range, as supported by data reported in references [4, 25, 26, 27, 28]. Thisresults in the electron-equivalent light yield for the energy deposit from astopping proton with kinetic energy above several MeV to be larger thanthe energy deposited. This causes the measured cluster energy, which isproportional to the scintillation yield, to increase in the simulation.The pulse shapes of crystals in pion ionization clusters were observedto have hadron intensity values distribution near zero similar to the muonsshown previously. This is attributed to the pion ionization dE / d x being toolow to produce hadronic scintillation component emission during pion ioniza-tion. When the pion initiates a nuclear interaction however, the secondaryhadrons generated in the cluster can produce significant amounts of hadronscintillation component emission. This is illustrated by Figure 5 showing thecrystal hadron intensity vs. crystal energy distribution for crystals in the 1-3GeV/c π + clusters with cluster energy outside the energy range of 150-25012 Cluster Energy (GeV) E n t r i e s DataMC (w Birks and PS)MC (No Birks and PS)
Belle II - π (a) Cluster Energy (GeV) E n t r i e s DataMC (w Birks and PS)MC (No Birks and PS)
Belle II + π (b) Figure 4: Cluster energy distributions for charged pions a) π − b) π + in the momentumrange 1 < p lab ≤ K S → π + π − decays. The simulation labelled NoBirks and PS uses default GEANT4 simulations, which do not include modelling of theionization dE / d x dependent changes in the CsI(Tl) scintillation response. The simulationlabelled w Birks and PS adds to the GEANT4 simulation the Birk’s scintillation efficiencyand pulse shape simulation techniques developed in reference [4], allowing the ionizationdE / d x dependent CsI(Tl) scintillation response to be modelled. MeV. This cluster energy veto removes ionization clusters, which are formedby a pion ionizing through the depth of the calorimeter without hadronicallyinteracting, ensuring the sample is primarily composed of clusters from pionhadronic showers. In this figure an abundance of crystals with large hadronintensity values, ranging up to 0.6, is observed in data and simulation. Thisis very distinct from the photon and muon distributions discussed previouslywhere only photon-like pulse shapes were observed and demonstrates thepotential for particle identification with pulse shape discrimination.The distributions shown in Figure 5 display several features, which areobserved to be present in the data and simulation. These features arisedue to specific material interactions resulting in crystal energy deposits byspecific compositions of secondary particles. In the region of crystal energybelow 150 MeV and hadron intensity near zero, these energy deposits aremainly from the primary pion, or a secondary charged pion emitted from thepion nuclear interaction, ionizing through a ∼
10 cm CsI(Tl) crystal segmentbefore escaping the crystal volume, without initiating a nuclear interaction.The population of crystals with energies above ∼
300 MeV and hadron in-tensity near zero however are unlikely to originate from this scenario dueto the CsI(Tl) crystal dimensions limiting the total crystal energy deposit13 C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 9267Number of Crystal Entries: 23702 2018
Belle II
Data + π (a) C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 8925Number of Crystal Entries: 21821 2018
Belle II
Simulation + π (b) Number of Clusters: 9267Number of Crystal Entries: 23702 C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − − C r ys t a l H ad r on I n t en s i t y (c) Figure 5: Crystal hadron intensity vs crystal energy distributions for crystals in calorimeterclusters produced by π + in the momentum range 1 < p lab ≤ K S → π + π − decays, a) data b) simulation c) zoom of data shown in Figure 5a withreduced binning allowing for the presence of the single proton band in the data to be seenin detail. from only pion ionization. By investigating the GEANT4 simulation truth iswas confirmed that the crystals with energy above ∼
300 MeV and hadronintensity near zero primarily originate from clusters where a secondary π was emitted from the charged pion hadronic interaction. The π rapidly de-cays to two photons leaving a large energy deposit from the electromagneticshower, which has a photon-like pulse shape.In Figure 5 a band structure is observed in the data and simulation inthe region of crystal energies below 200 MeV and hadron intensity up to0.2. A zoom of this feature in the data is shown in Figure 5a. This feature isknown as the single proton band [4] as crystals will have a pulse shape on thisband when the crystal energy deposit is from a single proton ionizing then14topping in the crystal volume. The protons producing these crystal energydeposits are emitted as secondary particles from the pion inelastic interac-tion. As the proton kinetic energy approaches zero, the ionization dE / d x ofthe proton reaches large values and significant amounts of hadron scintilla-tion component emission are produced, resulting in a hadron-like pulse shape.In Figure 5 the single proton band is better resolved in simulation relativeto the data. The resolution degradation observed in the data is attributedto crystal-by-crystal variations in the hadronic scintillation response, whichare not included in the simulation. As these distributions integrate informa-tion from crystals across the entire barrel section of the Belle II calorimeter,the accumulation of variations in hadron response, which could arise due tonon-simulated factors such as differences in thallium concentration, radia-tion damage and diode spectral response, are expected to smear the datadistribution. The observation of the single proton band in data in Figure5 demonstrates that crystal-by-crystal variations in the hadron scintillationresponse due to these factors however cannot be large, and that the hadronand photon templates are well calibrated across the calorimeter.An additional feature observed in Figure 5 is the scatter of crystals withenergy above ∼
200 MeV and hadron intensity above 0 .
02. Crystals in thispulse shape range are referred to as multi-hadron pulse shapes because theenergy deposits that generate these crystals are from numerous low energyhadrons (protons, neutrons, deuterons, tritons, alphas) emitted from thenucleus de-excitation, which follows the pion hadronic interaction [4]. Thesignificant spread in crystal energy and hadron intensity values is a resultof the large variation in the energy, type and multiplicity of the secondaryparticles emitted from this interaction.
A charged kaon control sample in the lab momentum range of 0.3-0.5GeV/c was selected using dE / d x information measured by the Belle II centraldrift chamber [20]. The strangeness of kaons provides an interesting controlsample to illustrate how the CsI(Tl) pulse shapes can give a measure of thehadronic activity in a calorimeter cluster. This is because in the momentumrange 0.3-0.5 GeV/c strangeness conservation restricts the hadronic materialinteractions of K + relative to K − . For example, a K − nuclear interaction inthis momentum range can produce a variety of hyperon final states such as π Λ, π ± Σ ∓ and π Σ , which are unavailable to the K + [23].15 C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 17972Number of Crystal Entries: 30487 2018
Belle II
Data + K (a) C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 18083Number of Crystal Entries: 31151 2018
Belle II
Simulation + K (b) C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 17168Number of Crystal Entries: 29803 2018
Belle II
Data - K (c) C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 17179Number of Crystal Entries: 31561 2018
Belle II
Simulation - K (d) Figure 6: Crystal hadron intensity vs crystal energy distributions for crystals in calorimeterclusters produced by charged kaons in the momentum range 0.3 < p lab ≤ . K + data b) K + simulation c) K − data d) K − simulation. This asymmetry can be visualized in Figure 6 showing the crystal hadronintensity vs. crystal energy for crystals in calorimeter clusters produced bycharged kaons in the momentum range 0 . < p lab < . K − results in a significant presence of crystals with largehadron scintillation emission. The abundance of crystals with hadron pulseshapes in the K − sample originate from secondary hadrons, such as protons,emitted in the decays of secondary hyperons, which are produced by the K − hadronic interactions. The charge-conjugate interactions however, aresuppressed for the K + resulting in very few crystals with significant hadronintensity values to be present in the K + sample. The small sample of crystalsin the K + distributions with hadron-like pulse shapes are found, using sim-16lation truth, to mainly originate from hadronic interactions initiated by asecondary pion, which was emitted from the K + decaying in the calorimeter.The K + vs. K − asymmetry observed in the CsI(Tl) pulse shapes was foundto be maximal at low momentum. As the kaon momenta exceeds 1 GeV/c,the energy is sufficient for numerous K + hadronic interactions to be abovethreshold, resulting in the pulse shape distributions to become more chargesymmetric and appear similar to the charged pion distributions shown inSections 3.3 [20]. A proton and anti-proton control sample in the lab momentum range of0.3-1 GeV/c was selected using dE / d x information measured by the Belle IIcentral drift chamber [20]. Protons and anti-protons in this momentum rangegenerate unique CsI(Tl) pulse shape signatures. Proton’s are unlike the par-ticles in the previous samples studied because in this case the primary trackcan directly produce hadron scintillation component emission. This is dueto the significant mass of protons relative to pions and kaons resulting in theionization dE / d x of protons at the equivalent momenta to be significantlyhigher.In Figure 7 the crystal hadron intensity vs. crystal energy distributionsare shown for crystals from calorimeter clusters produced by protons with p lab in the range 0.3-1 GeV/c. In p distributions shown in Figure 7 two bandsare observed both in data and simulation. The double band structure wasalso displayed in the proton testbeam studies in reference [4] and arises fromthe possibility of the primary proton ionizing across multiple crystals. If the p ionizes initially through a crystal at a momentum large enough such at theionization dE / d x of the p is not yet significant enough to produce hadronscintillation light output, then this results in the energy deposit to have aphoton-like pulse shape and would correspond to the crystals in the lowerband. After escaping the initial crystal volume, the proton will then enteran adjacent crystal where it then is likely to deposit its remaining kineticenergy. When this occurs the proton becomes highly ionizing and produceshadron light output, resulting in the energy deposit in the adjacent crystalto have a pulse shape residing on the single proton band.Comparing the p and ¯ p distributions, a charge asymmetry due to ¯ p an-nihilation is clearly observed in the pulse shape distributions. The ¯ p distri-butions display similar features to the pions studied in Section 3.3. This is17 C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 10443Number of Crystal Entries: 14656 2018
Belle II
Datap (a) C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 10349Number of Crystal Entries: 14653 2018
Belle II
Simulationp (b) C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 4806Number of Crystal Entries: 17776 2018
Belle II
Datap (c) C r ys t a l E n t r i e s pe r B i n Crystal Total Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 4729Number of Crystal Entries: 45715 2018
Belle II
Simulationp (d)
Figure 7: Crystal hadron intensity vs crystal energy distributions for crystals in calorimeterclusters produced by protons in the momentum range p lab . − p data b) p simulation c) ¯ p data d) ¯ p simulation. expected as anti-proton annihilation typically results in the emission of nu-merous charged pions [29]. The pions emitted are then likely to ionize acrossmultiple crystal widths. This accounts for the significant presence of crystalswith energy below 0.2 GeV and photon-like pulse shapes, which are observedin the ¯ p data and simulation. A scatter of crystals in the multi-hadron pulseshape region (crystal energy > . p sample. These energy deposits originate from nu-merous hadrons emitted from nuclear de-excitations. Comparing the ¯ p dataand simulation, it is observed that the hadron intensity values of the crystalsin the multi-hadron pulse shape region are on average lower in simulationrelative to data. In addition, the average number of crystals per cluster insimulation for ¯ p is over twice that of data. This is interesting because for18he higher momentum pions discussed in Sections 3.3, reasonable agreementin data and simulation was observed for these quantities. This suggests thatthe GEANT4 modelling of the secondary particle emission for ¯ p annihilationcan be improved. Further investigation into this discrepancy is beyond thescope of this work however, this result demonstrates how pulse shape dis-crimination can be used as a tool to evaluate and improve the simulationmodelling of hadronic interactions.
4. Particle Identification with Pulse Shape Discrimination
The results presented in Section 3 illustrate that the scintillation pulseshapes of the crystals in a calorimeter cluster are determined by the types ofsecondary particles produced in the cluster. Furthermore, as the compositionof secondary particles is dependent on the material interaction, and by exten-sion, the type of primary particle, this allows the scintillation pulse shapesof the crystals in a calorimeter cluster to be used to improve particle iden-tification. In this section we demonstrate that through CsI(Tl) pulse shapediscrimination, significant improvements in K L vs. photon identification areachieved over current techniques, which are restricted to characterizationusing only the spatial distribution of energy in the cluster. A single calorimeter cluster can typically have multiple waveforms associ-ated with it, one for each crystal in the cluster with energy above 30 MeV. Tocondense the information contained in the multiple waveforms into a singlequantity that characterizes the cluster, a multivariate classifier was trainedto use the crystal level information to classify the cluster as an electromag-netic or hadronic shower. For each crystal in the cluster that has a waveformrecorded offline and where the offline fit to the waveform has a good χ , thecrystal level quantities listed below are used as classifier inputs. • Crystal energy computed by multi-template offline fit. • Crystal hadron intensity computed by multi-template offline fit. • Crystal offline fit type. In addition to the Photon+Hadron templatefit described Section 2, fit hypotheses for a Photon+Hadron+out-of-time photon and Photon+Diode-crossing are also implemented and areattempted if the Photon+Hadron template fit results in a poor χ .19he Photon+Hadron+out-of-time photon fit models waveforms with anadditional energy deposit that is shifted in time relative to the time ofthe primary energy deposit and the Photon+Diode-crossing fit modelsthe scenario where energy is directly deposited in the PIN diodes. • Crystal energy computed by a photon template fit done online inFPGA. • Location of crystal centre relative to the cluster centre. • Crystal weight computed by clustering algorithm to measure associa-tion of crystal to the cluster on a scale of 0 − K L and anti-neutrons. The classifier was trained such that the classifier output responseto photons is 1.0 while the response to K L and anti-neutrons is 0.0. K L To evaluate the classifier performance, control samples of photons and K L ’s were selected from Belle II data. The photon control sample was se-lected using e + e − → µ + µ − ( γ ) events, which allowed a clean sample of pho-tons in the momentum range 0 . − K L ’s was kinematically selected using the process e + e − → φ ( γ ) → K S K L ( γ ). For this selection, a K S → π + π − is required to be reconstructedin addition to two neutral calorimeter clusters. One cluster is required tohave energy above 4 GeV in the centre-of-mass frame and is identified as theinitial state radiation (ISR) photon. By applying energy conservation, themagnitude of the momentum of the K L candidate is computed. The momen-tum direction of the K L is defined by the location of the second calorimetercluster. To further constrain the event to be consistent with the process e + e − → φ ( γ ) → K S K L ( γ ), we require the invariant mass of the K S and K L to be consistent with the φ mass. From this selection a sample of K L inmomenta range 2-4.5 GeV/c was selected.In Figure 8 the classifier response is shown for the selected control samplesof photons and K L ’s with data and simulation overlaid. In Figure 8a theclassifier response to K L ’s is observed to be peaking in data and simulationnear 0.0, indicating that the classifier is correctly classifying the significantfraction of K L ’s as hadronic showers. Conversely, in Figure 8b the classifier20esponse to photons is observed to be peaking near 1.0 in data and simulation,indicating that a significant fraction of the photons are correctly classifiedas electromagnetic showers with significant likelihood. The peaking natureof the distributions in Figure 8 demonstrate the high degree of separationthat can be achieved by applying pulse shape discrimination for hadronic vs.electromagnetic shower identification.In Figure 8a a small sample of K L candidates are observed to have classi-fier response above 0.8. By studying truth information of the simulation, the K L in this region correspond to mis-identified K L from background processessuch as e + e − → K ¯ K π ( γ ) or K ¯ K η ( γ ). In these events the K S → π + π − and the radiated photon satisfied the selection requirements and one of thephotons from the decay of the the π or η is mis-identified as a K L by thekinematic selection applied. This known photon background is removed fromthe K L selected from the ISR sample when computing the efficiency measure-ments completed in Section 4.4 by excluding K L candidates in this samplewith classifier output above 0.8. The bias introduced by this cut on the K L efficiency is shown in Section 4.4 to be minimal relative to the statistical errorof the measurement. This is demonstrated by the measurements presentedin Section 4.4 Figure 11a as K L efficiency measured for this sample is shownto be in agreement with independent K L samples selected from particle gunand B ¯ B events, which do not impose this cut. PSD Classifier Output E n t r i e s Phase 2 Data) γ ( K Kssother
Belle II L0 K (a) PSD Classifier Output E n t r i e s Phase 2 Data) γ ( - µ + µ ) γ ( - π + π ) γ ( - K + K Belle II photons (b)
Figure 8: Classifier response to control samples of a) K L ’s and b) photon’s. To further understand the behaviour of the classifier and confirm that theclassifier response is driven by the pulse shape information, a sample of K L B ¯ B simulation. This K L selection applied truth infor-mation to select calorimeter clusters, which are produced from K L emittedfrom a B decay chain in the event. The K L ’s selected in this sample alsospan a wide momentum range down to 0.2 GeV/c, allowing for the classi-fier performance in this momentum region to be measured in the followingsection.For the K L from B ¯ B sample, the distribution of the classifier responsewas similar to the K L sample shown in Figure 8a such that the distributionwas peaking near 0.0. With this sample however we show that the classifierresponse is driven by the input pulse shape information. This is demon-strated by Figure 9 showing the distribution of the crystal hadron intensityvs. crystal energy for the crystals in the K L from B ¯ B clusters, divided intosamples using the output of the classifier. By scanning from Figure 9a toFigure 9d the types of pulse shapes that are present in K L clusters classifiedas hadron-like to photon-like can be visualized.Comparing Figure 9a to Figure 9d, it is observed that clusters classifiedas less hadron-like correspond to clusters that contain crystals with pulseshapes that are less hadron-like. From Figure 9a it is shown that if the clustercontains a crystal with a pulse shape in the multi-hadron region, then thecluster will be classified as hadronic with significant likelihood, contributingto the peaking structure near 0.0 in Figure 8a. This is in contrast to K L clusters mis-classified as photon-like. As shown by Figure 9d, the K L clustersclassified as photon-like are observed to contain only crystals with photon-likepulse shapes. This demonstrates that these clusters are mis-classified becausethe pulse shapes of the crystals in the clusters are photon-like and thus interms of pulse shape discrimination, the cluster appears as an electromagneticshower. To present the performance of the classifier a threshold of < . K L efficiency and photon-as-hadron fake-rate are then measured as afunction of cluster energy and particle momentum. This approach is ad-vantageous because, although for photons the cluster energy is equal to thephoton momentum, for K L the cluster energy is only loosely correlated withthe K L momentum due to energy leakage from the invisible component ofthe hadronic shower. In addition the relative components of the K L interac-tion cross section will vary as a function of the K L momentum and thus the22 C r ys t a l E n t r i e s pe r B i n Crystal Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 77010Number of Crystal Entries: 155640
Belle II
Simulation L0 KPSD Classifier < 0.02 (a) C r ys t a l E n t r i e s pe r B i n Crystal Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 17843Number of Crystal Entries: 33568
Belle II
Simulation L0 K PSD Classifier < 0.2 ≤ (b) C r ys t a l E n t r i e s pe r B i n Crystal Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 12316Number of Crystal Entries: 21794
Belle II
Simulation L0 K PSD Classifier < 0.9 ≤ (c) C r ys t a l E n t r i e s pe r B i n Crystal Energy (GeV) − C r ys t a l H ad r on I n t en s i t y Number of Clusters: 676Number of Crystal Entries: 1543
Belle II
Simulation L0 K 0.9 ≥ PSD Classifier (d)
Figure 9: Crystal hadron intensity vs. crystal energy distribution for crystals in clustersfrom K L from the B ¯ B sample, divided into four samples of classifier response. classifier performance should be studied as a function of the cluster energyand particle momentum.Figure 10 presents measurements of the K L efficiency and photon-as-hadron fake-rate as a function of cluster energy for the selected control sam-ples of photons and K L ’s. Focusing on the photon-as-hadron fake-rate shownin Figure 10, a dependence on the cluster energy is observed. Above 1 GeVthe photon-as-hadron fake-rate is measured to be below 2% in data andsimulation. As the photon momentum drops below 0.5 GeV/c the photon-as-hadron fake rate increases in data and simulation to a maximum of 25% at0.1 GeV/c. This energy dependence is driven by two factors. The first is dueto the 30 MeV waveform readout threshold causing lower energy photons tohave less crystals with pulse shape information available. The second factoris due to the degradation of the hadron intensity resolution at lower crystal23 Cluster Energy (GeV) E ff i c i en cy , P ho t on F a k e -r a t e K ) γ ( K from K Data: K ) γ ( - µ + µ from γ Data: ) γ ( K from K MC: K ) γ ( - µ + µ from γ MC: B from B MC: K PSD classifier 2018
Belle II
Figure 10: Measurement of the K L efficiency and photon-as-hadron fake-rate for the PSDclassifier as a function of cluster energy for several control samples of K L , and photons.Errors bars correspond to statistical errors. energies, which arises from the decrease in the signal-to-noise ratio of thewaveforms. This effect was observed previously in Section 3.1 Figure 2 bythe broadening of the hadron intensity values with decreasing crystal energy.This degradation in resolution increases the difficulty to definitively classifya crystal energy deposit as hadronic or electromagnetic.In Figure 10 multiple K L efficiency measurements are overlaid. Thesemeasurements are complementary as together they span the full K L momen-tum range of interest for the Belle II experiment. Beginning by studying the K L from ISR sample, it is observed that at cluster energies below 1 GeVthe K L efficiency is measured to be above 80% in data and simulation. Atcluster energies above 1 GeV, the K L efficiency in data is observed to be2 σ below the value in simulation. Note the error bars in Figure 11 corre-spond to statistical errors. With a larger data sample the significance of thisdifference in data and simulation can be verified. If confirmed, a potentialsource of this discrepancy could be from the modelling of the K L hadronicinteractions in CsI(Tl) by GEANT4. If the simulated cross section for K L interactions that produce final states with π ’s is over estimated then thiscould result in such a discrepancy. This is because in these interactions thefull π energy is typically absorbed in the form of an electromagnetic shower24nd thus if a π is produced the resulting cluster will likely be on the higherend of the cluster energy spectrum. In addition the significant electromag-netic shower component of the hadronic shower would result in the clusterto appear more photon-like in to the pulse shape classifier. This effect wasverified through simulation truth information to be the cause of the drop inefficiency at larger clusters energies, which is observed in Figure 10 for the K L from B ¯ B sample. To demonstrate the improvement in particle identification that can beachieved with pulse shape discrimination, this section compares the PSDclassifier performance to two shower-shape approaches to K L vs photon iden-tification.The shower-shape variable E E is defined as the ratio of the energy inthe centre cluster crystal to the total energy of the 3 × E values larger thanhadronic showers, where the energy in the cluster is more widely distributed.We note that although E E is one of several shower-shapes and likely alonedoes not exploit the full shower-shape potential, it has been selected for usein independent optimization studies for photon selection at Belle II for π reconstruction [31]. This allows it to provide a reference to the performanceof the typical shower-shape variables currently applied.A second shower-shape approach that we compare to is an independentlytrained shower-shape based classifier referred to as the Zernike classifier. TheZernike classifier is a Boosted Decision Tree trained to use the spatial distri-bution of the cluster energy to perform photon vs. K L identification. Theinputs to the Zernike classifier are the first eleven Zernike moments of thecluster computed from the energy of the cluster crystals, in addition to thefirst eleven Zernike moments of the larger connected region of clusters thatthe local cluster might belong to. Each of these moments corresponds toa cluster energy centroid-like quantity computed by applying the Zernikepolynomials [32] as weights. Unlike the PSD classifier and the variable E E ,the input information to the Zernike classifier extends beyond the primarycluster as the second eleven inputs to the Zernike classifier incorporate in-formation from all clusters in close spatial proximity to the main cluster.For K L identification, this boosts performance from the use of split-off infor-mation, however, this in turn limits performance of the Zernike classifier in25ituations where the photon is not well isolated.To compare the performance of the PSD classifier to the shower-shapeapproaches, Figure 11 shows the K L efficiency and corresponding photon-as-hadron fake-rate measured as a function of particle momentum for the PSDclassifier (Figure 11a), the E E variable (Figure 11b) and for the Zernikeclassifier (Figure 11c) at threshold’s which set the corresponding K L effi-ciency above 3 GeV/c to be equal to the PSD classifier efficiency. For themeasurements in Figure 11, the Zernike classifier and E E thresholds areset such that the same K L efficiency as the PSD classifier is achieved. Bysetting the K L efficiency equal between the three methods, the performanceof the methods is compared using the corresponding photon-as-hadron fake-rate, where a lower photon-as-hadron fake-rate indicates better performance.In Figure 11 the momentum of the K L from e + e − → K S K L ( γ ) sample iscomputed using the measured K S and γ momentum, and applying energyconservation. The momentum of the K L from the B ¯ B sample and the par-ticle gun sample corresponds to the generated momentum of the simulated K L .In Figure 11b the photon-as-hadron fake-rate for the E E shower-shapevariable is observed to be approximately constant as a function of the photonenergy with a value of about 55%. Compared to the PSD classifier, whichat 1 GeV/c achieves a photon-as-hadron fake-rate below 2% and a photon-as-hadron fake-rate of 15% at 0.2 GeV/c, the significant improvement in K L vs. photon separation that can be achieved by applying CsI(Tl) pulse shapediscrimination is demonstrated.In Figure 11c the Zernike classifier is shown have a photon-as-hadron fake-rate of 23% at 1 GeV/c, increasing to a fake-rate of 50% at 0.2 GeV/c. Theimprovement of the Zernike classifier over the E E shower-shape variabledemonstrates that incorporating information beyond the primary cluster canimprove the K L vs. photon identification performance. The PSD classifier isobserved to achieved improved performance over the Zernike classifier, reduc-ing the photo-as-hadron fake-rate by a factor of 3 at lower photon energiesand a factor of 10 at photon energies above 1 GeV. Recall that the Zernikeclassifier uses information not just from the primary cluster but also fromany clusters in close proximity to the primary cluster in order to improve the K L efficiency. Further investigating the Zernike classifier behaviour in thephoton sample we find that, even in the low multiplicity e + e − → µ + µ − ( γ )events, a limiting factor of the photon-as-hadron fake-rate for the Zernikeclassifier is due to the photon isolation from the muons in the event. Due to26 Lab Momentum (GeV/c) E ff i c i en cy , P ho t on F a k e -r a t e K ) γ ( K from K Data: K ) γ ( - µ + µ from γ Data: ) γ ( K from K MC: K ) γ ( - µ + µ from γ MC: B from B MC: K particle gun K PSD classifier 2018
Belle II (a)
Lab Momentum (GeV/c) E ff i c i en cy , P ho t on F a k e -r a t e K ) γ ( K from K Data: K ) γ ( - µ + µ from γ Data: ) γ ( K from K MC: K ) γ ( - µ + µ from γ MC: B from B MC: K particle gun K shower-shape E E 2018
Belle II (b)
Lab Momentum (GeV/c) E ff i c i en cy , P ho t on F a k e -r a t e K ) γ ( K from K Data: K ) γ ( - µ + µ from γ Data: ) γ ( K from K MC: K ) γ ( - µ + µ from γ MC: B from B MC: K particle gun K Zernike classifier 2018
Belle II (c)
Figure 11: Measurement of the K L efficiency and photon-as-hadron fake-rate for the a)PSD classifier b) E E shower-shape c) Zernike classifier as a function of particle mo-mentum for several control samples of K L , and photon’s. The Zernike classifier is anindependent classifier, which uses only shower shape information. The threshold for theE E shower-shape and Zernike classifier is set such that the same K L efficiency as thePSD classifier is achieved; this allows the comparison of the performance of the classifiersto be made using the photon-as-hadron fake-rate. Errors bars correspond to statisticalerrors. the PSD classifier only using information from the primary cluster, and thatPSD is directly sensitive to the secondary particle composition of the clus-ter whereas shower-shape approaches can only have indirect inference, PSDapproaches are much less sensitive to cluster isolation effects. This also indi-cates an area for future studies can be to investigate the application of PSDtechniques in specialized cases where shower-shape approaches are known tobe limited, such as clusters from merged photons resulting in the shape ofthe electromagnetic shower to appear hadron-like.27 . Summary and Conclusions This paper presents the first application of CsI(Tl) pulse shape discrimi-nation at an electron-positron collider. The results demonstrate that CsI(Tl)pulse shape discrimination provides a new and effective method for improving K L vs. photon separation at the Belle II experiment.The upgrade of the Belle II calorimeter readout with waveform digitiza-tion having 18-bit precision and a 1.7669 MHz sampling frequency enabledthe implementation of pulse shape discrimination. A multi-template fit isapplied to characterize the waveform shape by measuring the fraction ofscintillation emission emitted by the hadron scintillation component. Distri-butions of the scintillation pulse shape of crystals from calorimeter clustersproduced by control samples of γ , µ + , π ± , K ± and p/ ¯ p illustrated how thescintillation pulse shape can identify the secondary particle composition ofthe calorimeter cluster. Comparisons between data and simulation providedfurther validation of the CsI(Tl) scintillation response simulation techniquesdeveloped in reference [4] and now are applied at Belle II. These studiesdemonstrate the potential application of pulse shape discrimination as a newtool to identify areas of improving the simulation modelling of hadronic in-teractions in materials.The K L efficiency and photon-as-hadron fake-rate of a multivariate clas-sifier trained to use pulse shape discrimination to classify calorimeter clustersas hadronic or electromagnetic showers was evaluated using control samplesof photons and K L ’s selected from Belle II commissioning data. Pulse shapediscrimination was shown to be responsible for the classifier performance,which was measured to achieve a K L efficiency above 80% with a corre-sponding photon-as-hadron fake-rate of 15% at cluster energies of 0.2 GeVand below 2% at cluster energies of 1 GeV. This corresponds to a significantimprovement in photon vs. K L identification over a standard shower-shapeapproach, which for comparison was measured to have a photon-as-hadronfake-rate of 55% in order to achieve the same K L efficiency. Comparisons toa shower-shape based classifier also demonstrated that PSD can reduce thephoton-as-hadron fake-rate by a factor of 3 at photon energies of 0.2 GeVand a factor 10 at photon energies of 1 GeV.To improve performance there are several areas for potential upgrades inthe future. A limitation of the present performance was shown to be due tothe 30 MeV waveform readout threshold restricting the amount of pulse shapeinformation available for lower energy clusters. Implementation of waveform28hape characterization at the FPGA level could remove this limitation inthe future. In addition, although this study focused on K L vs. photonidentification, the results presented show clear potential for the application ofpulse shape discrimination to improve charged particle identification, as wellas, motivating studies to explore the potential for neutron vs. K L separationusing pulse shape discrimination.The improvements in the areas of neutral particle identification achievedwith the application of CsI(Tl) pulse shape discrimination at Belle II encour-ages other calorimeters constructed from pulse shape discrimination capablescintillators such as NaI(Tl) [10], CsI(Na)[33], pure CsI [34], PbWO (doped)[35], BaF [33] to consider implementing this technique. In addition calorime-ter designs for future experiments should consider extending design criteriato include pulse shape discrimination. Acknowledgements
We thank the SuperKEKB group for the excellent operation of theaccelerator; the KEK cryogenics group for the efficient operation of thesolenoid; and the KEK computer group for on-site computing support.This work was supported by the following funding sources: Science Com-mittee of the Republic of Armenia Grant No. 18T-1C180; AustralianResearch Council and research grant Nos. DP180102629, DP170102389,DP170102204, DP150103061, FT130100303, and FT130100018; AustrianFederal Ministry of Education, Science and Research, and Austrian Sci-ence Fund No. P 31361-N36; Natural Sciences and Engineering ResearchCouncil of Canada, Compute Canada and CANARIE; Chinese Academy ofSciences and research grant No. QYZDJ-SSW-SLH011, National NaturalScience Foundation of China and research grant Nos. 11521505, 11575017,11675166, 11761141009, 11705209, and 11975076, LiaoNing RevitalizationTalents Program under contract No. XLYC1807135, Shanghai Municipal Sci-ence and Technology Committee under contract No. 19ZR1403000, Shang-hai Pujiang Program under Grant No. 18PJ1401000, and the CAS Cen-ter for Excellence in Particle Physics (CCEPP); the Ministry of Education,Youth and Sports of the Czech Republic under Contract No. LTT17020and Charles University grants SVV 260448 and GAUK 404316; EuropeanResearch Council, 7th Framework PIEF-GA-2013-622527, Horizon 2020Marie Sklodowska-Curie grant agreement No. 700525 ‘NIOBE,’ and Hori-zon 2020 Marie Sklodowska-Curie RISE project JENNIFER2 grant agree-29ent No. 822070 (European grants); L’Institut National de PhysiqueNucl´eaire et de Physique des Particules (IN2P3) du CNRS (France); BMBF,DFG, HGF, MPG, AvH Foundation, and Deutsche Forschungsgemeinschaft(DFG) under Germany’s Excellence Strategy – EXC2121 “Quantum Uni-verse”’ – 390833306 (Germany); Department of Atomic Energy and Depart-ment of Science and Technology (India); Israel Science Foundation grantNo. 2476/17 and United States-Israel Binational Science Foundation grantNo. 2016113; Istituto Nazionale di Fisica Nucleare and the research grantsBELLE2; Japan Society for the Promotion of Science, Grant-in-Aid for Sci-entific Research grant Nos. 16H03968, 16H03993, 16H06492, 16K05323,17H01133, 17H05405, 18K03621, 18H03710, 18H05226, 19H00682, 26220706,and 26400255, the National Institute of Informatics, and Science Informa-tion NETwork 5 (SINET5), and the Ministry of Education, Culture, Sports,Science, and Technology (MEXT) of Japan; National Research Founda-tion (NRF) of Korea Grant Nos. 2016R1D1A1B01010135, 2016R1D1A1B-02012900, 2018R1A2B3003643, 2018R1A6A1A06024970, 2018R1D1A1B-07047294, 2019K1A3A7A09033840, and 2019R1I1A3A01058933, RadiationScience Research Institute, Foreign Large-size Research Facility Applica-tion Supporting project, the Global Science Experimental Data Hub Centerof the Korea Institute of Science and Technology Information and KRE-ONET/GLORIAD; Universiti Malaya RU grant, Akademi Sains Malaysiaand Ministry of Education Malaysia; Frontiers of Science Program con-tracts FOINS-296, CB-221329, CB-236394, CB-254409, and CB-180023, andSEP-CINVESTAV research grant 237 (Mexico); the Polish Ministry of Sci-ence and Higher Education and the National Science Center; the Min-istry of Science and Higher Education of the Russian Federation, Agree-ment 14.W03.31.0026; University of Tabuk research grants S-1440-0321,S-0256-1438, and S-0280-1439 (Saudi Arabia); Slovenian Research Agencyand research grant Nos. J1-9124 and P1-0135; Agencia Estatal de Inves-tigacion, Spain grant Nos. FPA2014-55613-P and FPA2017-84445-P, andCIDEGENT/2018/020 of Generalitat Valenciana; Ministry of Science andTechnology and research grant Nos. MOST106-2112-M-002-005-MY3 andMOST107-2119-M-002-035-MY3, and the Ministry of Education (Taiwan);Thailand Center of Excellence in Physics; TUBITAK ULAKBIM (Turkey);Ministry of Education and Science of Ukraine; the US National Science Foun-dation and research grant Nos. PHY-1807007 and PHY-1913789, and theUS Department of Energy and research grant Nos. DE-AC06-76RLO1830,DE-SC0007983, DE-SC0009824, DE-SC0009973, DE-SC0010073, DE-30C0010118, DE-SC0010504, DE-SC0011784, DE-SC0012704; and the Na-tional Foundation for Science and Technology Development (NAFOSTED)of Vietnam under contract No 103.99-2018.45.
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