Charged particle identification with the liquid xenon calorimeter of the CMD-3 detector
V.L. Ivanov, G.V. Fedotovich, R.R. Akhmetshin, A.N. Amirkhanov, A.V. Anisenkov, V.M. Aulchenko, N.S. Bashtovoy, A.E. Bondar, A.V. Bragin, S.I.Eidelman, D.A. Epifanov, L.B. Epshteyn, A.L. Erofeev, S.E. Gayazov, A.A. Grebenuk, S.S. Gribanov, D.N. Grigoriev, F.V. Ignatov, S.V. Karpov, V.F. Kazanin, A.A. Korobov, A.N. Kozyrev, E.A. Kozyrev, P.P. Krokovny, A.E. Kuzmenko, A.S. Kuzmin, I.B. Logashenko, P.A. Lukin, K.Yu. Mikhailov, V.S. Okhapkin, Yu.N. Pestov, A.S. Popov, G.P. Razuvaev, A.A. Ruban, N.M. Ryskulov, A.E. Ryzhenenkov, A.V. Semenov, V.E. Shebalin, D.N. Shemyakin, B.A. Shwartz, E.P. Solodov, V.M. Titov, A.A. Talyshev, S.S. Tolmachev, A.I. Vorobiov, Yu.V. Yudin
CCHARGED PARTICLE IDENTIFICATIONWITH THE LIQUID XENONCALORIMETER OF THE CMD-3DETECTOR
V.L. Ivanov a,b,1 , G.V. Fedotovich a,b , R.R. Akhmetshin a,b ,A.N. Amirkhanov a,b , A.V. Anisenkov a,b , V.M. Aulchenko a,b ,N.S. Bashtovoy a , A.E. Bondar a,b , A.V. Bragin a , S.I. Eidelman a,b,c ,D.A. Epifanov a,b , L.B. Epshteyn a,b,d , A.L. Erofeev a,b ,S.E. Gayazov a,b , A.A. Grebenuk a,b , S.S. Gribanov a,b ,D.N. Grigoriev a,b,d , F.V. Ignatov a,b , S.V. Karpov a ,V.F. Kazanin a,b , A.A. Korobov a,b , A.N. Kozyrev a,d ,E.A. Kozyrev a,b , P.P. Krokovny a,b , A.E. Kuzmenko a,b ,A.S. Kuzmin a,b , I.B. Logashenko a,b , P.A. Lukin a,b ,K.Yu. Mikhailov a , V.S. Okhapkin a , Yu.N. Pestov a , A.S. Popov a,b ,G.P. Razuvaev a,b , A.A. Ruban a , N.M. Ryskulov a ,A.E. Ryzhenenkov a,b , A.V. Semenov a,b , V.E. Shebalin a,b,e ,D.N. Shemyakin a,b , B.A. Shwartz a,b , E.P. Solodov a,b , V.M. Titov a ,A.A. Talyshev a,b , S.S. Tolmachev a , A.I. Vorobiov a , Yu.V. Yudin a,b a Budker Institute of Nuclear Physics, SB RAS, Novosibirsk, 630090, Russia b Novosibirsk State University, Novosibirsk, 630090, Russia c Lebedev Physical Institute RAS, Moscow, 119333, Russia d Novosibirsk State Technical University, Novosibirsk, 630092, Russia e University of Hawaii, Honolulu, Hawaii 96822, USA
Abstract
The paper describes a method of the charged particle identification, de-veloped for the CMD-3 detector, installed at the VEPP-2000 e + e − collider.The method is based on the application of the boosted decision trees classi-fiers, trained for the optimal separation of electrons, muons, pions and kaonsin the momentum range from 100 to 1200 MeV /c . The input variables for Corresponding author: [email protected]
Preprint submitted to Elsevier August 20, 2020 a r X i v : . [ phy s i c s . i n s - d e t ] A ug he classifiers are linear combinations of the energy depositions of chargedparticles in 12 layers of the liquid xenon calorimeter of the CMD-3. Theevent samples for training of the classifiers are taken from the simulation.Various issues of the detector response tuning in simulation and calibrationof the calorimeter strip channels are considered. Application of the methodis illustrated by the examples of separation of the e + e − ( γ ) and π + π − ( γ ) finalstates and of selection of the K + K − final state at high energies.
1. Introduction
The VEPP-2000 e + e − collider [1, 2, 3, 4] at the Budker Institute of Nu-clear Physics (Novosibirsk, Russia) covers the center-of-mass (c.m.) energy( E c . m . ) range from 0.32 to 2.01 GeV and uses a technique of round beams toreach an instantaneous luminosity of 10 cm − s − at E c . m . = 2 . e + e − annihilation intohadrons, which provides, for instance, a necessary input for the theoreticalcalculation of the hadronic contribution to the muon anomalous magneticmoment ( g − µ and the running fine structure constant [6, 7, 8, 9].The precise measurement of any hadronic cross section requires selectionof a clean sample of signal events. The latter often requires the effectiveprocedure of particle identification (PID), i.e. separation of electrons, muons,pions, kaons etc . In particular in the CMD-3: • e ± identification can be performed on the base of the total energy de-position in the calorimeter [10]; • identification of muons can be carried out with the muon veto system; • identification of antineutrons can be done with the time-of-flight sys-tem [11]; 2 separation of charged kaons and pions at the momenta less than 550 MeV/ c is performed using specific energy losses of particles in the drift chamber( dE/dx DC ) [12].In this paper we describe a new technique of the charged PID based on themultiple measurements of the energy depositions of a particle in the layersof liquid xenon (LXe) calorimeter of the CMD-3 [13]. The LXe-based PIDmethod is developed mainly for the task of K ± /π ± separation at momentalarger than 550 MeV/ c , where the dE/dx DC -based PID is inefficient. Forthe hadronic final states like K + K − , K + K − π , K + K − π , K S K ± π ∓ theLXe-based PID turns out to be an efficient tool for background suppressionat high c.m. energies.
2. The liquid xenon calorimeter of the CMD-3 detector
The CMD-3 detector layout is shown in Fig. 1. The major trackingsystem is the cylindrical drift chamber (DC) [12], installed inside a thin(0.085 X ) superconducting solenoid with 1.3 T magnetic field. Amplitudeinformation from the DC signal wires is used to measure z -coordinates oftracks and ionization losses of charged particles. The endcap calorimeter ismade of BGO crystals 13.4 X thick [10]. The barrel calorimeter consistsof the inner LXe-based (5.4 X ) ionization and outer CsI-based (8.1 X )scintillation calorimeters [14]. The total amount of material in front of thebarrel calorimeter is 0.35X .The LXe calorimeter consists of a set of ionization chambers with sevencylindrical cathodes and eight anodes with a 10.2 mm gap between them, seeFig. 2. The electrodes are made of copper-plated G-10. The typical electricfield in the gap is 1.1 kV/cm. The conductive surfaces of the anode electrodesare divided into rectangular pads, electrically connected by the wire goingthrough the cathode layers. These 264 sets of pads form the towers orientedto the interaction point and are used to measure the energy deposition of theparticles. 3 x y z Figure 1: The CMD-3 detector layout: 1 — beam pipe, 2 — drift chamber, 3 — BGO end-cap calorimeter, 4 — Z-chamber (ZC), 5 — superconducting solenoid, 6 — LXe calorime-ter, 7 — time-of-flight system (TOF), 8 — CsI calorimeter, 9 — yoke. z and ϕ coordinatesof the clusters.A current induced on the strip during the ionization flow is integrated for4.5 µ s, where the integration time corresponds to the maximum drift timeof electrons in the gap. The strip channels are used for the measurementsof the photon conversion point coordinates and the dE/dx of the particle ineach of the 14 layers. Due to the gaps between the strips the cathodes aresemitransparent, i.e. the ionization in one layer of the anode-cathode-anodedouble layer induces the charge on the strips of both sides of the cathode.This allows one to measure the coordinates of the point of photon conversionon the base of ionization that happened in one anode-cathode gap only. Figure 2: Structure of LXe calorimeter elec-trodes. Figure 3: Anode-cathode-anode doublelayer of the LXe calorimeter and the stripstructure of the cathode.
3. The idea of the PID procedure
5n what follows we denote by dE/dx
LXe the energy deposition produced bya particle in each LXe layer, normalized to the expected path length d LXe of theparticle in the layer, estimated via the DC-track extrapolation. dE/dx
LXe is the single designation for the minimum ionizing and nuclear interactingparticles as well as for the electromagnetic showers. The distributions of dE/dx
LXe in 14 LXe layers depending on the particle momentum for thesimulated single e ± and µ ± , π ± and K ± are shown in Figs. 4 and 5, respec-tively. One should note the following features of dE/dx LXe : • In Figs. 4 and 5 a certain momentum threshold p thr is seen for eachparticle type that corresponds to a minimum energy necessary to passthrough the material in front of the LXe. Below this threshold onlythe products of the particle decay or nuclear interaction can reach thecalorimeter. For kaons p K thr is about 300 MeV/ c for the normal incident; • The dE/dx
LXe spectra and the values of p thr depend on d LXe . Thisdependence is caused by the dependences of the shower developmentrate, the nuclear interaction probability, the particle deceleration rate etc. on d LXe . Figure 4: dE/dx
LXe in all LXe layers vs.particle momentum for e ± (gray) and µ ± (black) in simulation. Figure 5: dE/dx LXe in all LXe layers vs.particle momentum for K ± (gray) and π ± (black) in simulation. dE/dx LXe in theLXe-layers for different particle types. Namely, for each track in the DCreaching LXe, we calculate six values of the responses of the boosted deci-sion trees (BDT) classifiers provided by the TMVA package [15], trained foroptimal separation of particular pairs of particle types in certain ranges ofthe momentum p and d LXe , i.e. in the ∆ p i × ∆ d LXe , j cell. In what followswe denote these six values as BDT( e ± , µ ± ), BDT( e ± , π ± ), BDT( e ± , K ± ),BDT( µ ± , π ± ), BDT( µ ± , K ± ), BDT( π ± , K ± ).For training of each classifier we use samples of ∼ simulated eventswith single e ± , µ ± , π ± , K ± , having the momentum and d LXe uniformly dis-tributed in the ∆ p i × ∆ d LXe , j cell. In total, we have 55 ∆ p i cells of 20 MeV/ c width in the momentum range from 100 to 1200 MeV/ c and eight ∆ d LXe , j cells (from 1.0 to 1.5 cm at large momenta). Thus, there is 2 × × × dE/dx LXe values in LXe layers described later in Section 5.Since this PID method is based on the precise measurement of the energydeposition for different type of particles we need in the accurate energy cali-bration of the strip channels of the LXe calorimeter. Issues of the calibrationof strip channels and the detector response tuning in MC are considered inthe next sections.
4. Calibration of LXe calorimeter strip channels
In what follows we call cluster the group of the neighboring triggeredstrips (on one side of the cathode) with at least one strip having an amplitudeabove the cluster reconstruction threshold . This threshold is set to 1.5 MeV(in terms of the calibrated amplitude), which corresponds to the minimumamplitude induced by the minimum ionizing particles (MIPs) on the stripand is well above the level of electronics noise which energy equivalent is ∼ . c . There are three stages of thecalibration:1. Equalization of the strip amplitudes normalized to the particle pathlength, within each of seven cathodes separately;2. Equalization of the cluster amplitudes normalized to the particle pathlength in all seven cathodes by bringing them to a common average;3. Calculation of the MeV to ADC channel [16] transition coefficient.The calibrated strip amplitude is calculated as A calib = A raw K / ( K K ),where K ... are the calibration coefficients of the corresponding stages, A raw isthe raw amplitude with the pedestal subtracted. To achieve the convergenceof the K ... the calibration is carried out iteratively: reconstruction of eventsat the current iteration is performed with the application of the calibrationcoefficients calculated at the previous iteration. To obtain the calibrationprecision of about 1%, three iterations are sufficient. The K and K arenot calculated at the first iteration, since it does not make sense to clusterizenon-equalized strips. The equalization of the strip amplitudes is performed by fitting the spec-tra of amplitudes of the main strips in the clusters, i.e. of the strips withthe maximum amplitude, see Fig. 6. These amplitudes are normalized to theparticle’s path length to suppress the dependence on the inclination of thetrack in the anode-cathode gap. Let us denote by A maxmain strip the position ofthe maximum of the normalized strip amplitude spectrum obtained from theGaussian fit (Fig. 6). The K for a given strip is calculated as the ratio K = A maxmain strip /A maxmain strip , (1)where A maxmain strip is the average maximum position for the strips on both sidesof the given cathode. 8imulation of cosmic muons reveals the residual angular dependence ofthe K , MC manifested as the systematic ±
1% modulation of the K , MC fordifferent strips, see Fig. 7. The same modulation is seen in the differencebetween the K coefficients, calculated in the experiment on the base of eventswith cosmic muons ( K , cosmic ) and using muons from the process e + e − → µ + µ − ( K , µ + µ − ). Since muons from the process e + e − → µ + µ − have the uniformazimuthal angle distribution, there is no azimuthal modulation in K , µ + µ − .To account for observed modulation the experimental K is multiplied bythe approximated angular dependence of the K , MC (Fig. 7).Figure 8 shows the K trends for the first and second calibration iterationsin the runs of 2020 year. / ndf χ ± ± ±
50 100 150 200 250 300 350 400 450 5000102030405060 / ndf χ ± ± ± N u m be r o f e v en t s main strip amplitude, channels Figure 6: Typical amplitude spectrum of thecluster main strip and its Gaussian approx-imation near the maximum. The amplitudeis normalized to the particle path length. / ndf 2 χ ± ± ± ± ± − p5 0.0003799 ± − p6 0.8815 ± − p7 2.828 ± − p8 1.414 ± ±
43 p10 0 ± ± Strip number K Figure 7: K , MC dependence on the stripnumber for simulated cosmic muons (blackmarkers) and its approximation (blackcurve). The K , cosmic − K , µ + µ − differencein the experiment as a function of the stripnumber is shown by the gray markers. At the second stage we equalize the average cluster amplitudes normalizedto the particle’s path length, dE/dx l clust , l = 1 ...
7, between cathodes. Theaverage is calculated near the maximum of spectra in the limits containing ∼
90% of events. The calibration coefficients K l bringing the dE/dx l clust oneach cathode to the common interlayer average are calculated as9 l = dE/dx l clust7 (cid:80) l =1 dE/dx l clust / . (2)The same equalization procedure is performed for simulation. Figure 9shows the K l trends for different cathodes at the second calibration iterationin the 2020 runs. Run number K Figure 8: The typical K trend for one stripat the first (black) and second (gray) cali-bration iterations in the 2020 runs. The graybands show the statistical uncertainties. Run number l K Layer
Figure 9: The K l trends for different cath-odes at the second calibration iteration inthe 2020 runs, see color/double layer corre-spondence in the legend. c hannel transition coefficient We calculate the MeV/channel transition coefficient K via the relation K = (cid:80) l =1 dE/dx l, MCclust7 (cid:80) l =1 dE/dx l, dataclust · K , MC [MeV / channel] , (3)where K , MC is the transition coefficient tabulated in the MC. Figure 10shows the K trends for the second and third calibration iterations in the2020 runs. 10 Run number , M C / K K Figure 10: The K /K , MC trends at the second (gray) and third (black) calibration iter-ations in the 2020 runs.
5. Detector response tuning in simulation
Figure 11 shows dE/dx
LXe of the cosmic muons measured in the innermostdouble layer by the upper strips ( dE/dx up ) vs. that measured by the lowerstrips ( dE/dx low ). The events in the pair of inclined bands correspond to thecases, when the large ionization in one anode-cathode gap induces the largeamplitude on the strips on the opposite side due to the cathode transparency.This cross-layer induction, compared with the normal interlayer induction,occurs with some suppression factor, which depends on the position of theionization in the gap. The average of this factor over all possible ionizationpositions is called the transparency coefficient T l , l = 1 ...
7. The T l dependson the geometry of the cathode, namely on the widths of the strips and thegaps and on the thickness of dielectric. Initially we fix the T l values to the apriori value of 0.17 for all double layers.The transparency mixes up the real energy depositions dE/dx reallow , up intothe amplitudes measured by the lower and upper strips dE/dx measlow , up : (cid:20) dE/dx measup dE/dx measlow (cid:21) = 11 + T l (cid:20) T l T l (cid:21) · (cid:20) dE/dx realup dE/dx reallow (cid:21) . (4)11hese relations should be understood as correct on average, or as thedefinitions of dE/dx reallow , up . For convenience in what follows we operate withthe half sum and the half difference of the dE/dx reallow , up : (cid:20) dE/dx summ dE/dx diff (cid:21) = 12(1 − T l ) (cid:20) − (cid:21) · (cid:20) − T l − T l (cid:21) · (cid:20) dE/dx measup dE/dx measlow (cid:21) . (5)We use dE/dx summ and dE/dx diff in six inner double layers as the inputvariables of the BDT classifiers, described in Section 3. The outer seventhdouble layer suffers from the incomplete xenon fill and is not used in PID.The data/MC comparison of the dE/dx summ spectra for cosmic muons revealsthe relative broadening of the experimental spectra, see Fig. 12 (in whatfollows the simulated histograms are normalized to the number of events inthe experimental one unless otherwise stated). The alleged reason of thebroadening is the complicated cathode structure, not taken into account inthe MC, where the cathode is supposed to be just a solid plane. To accountfor this broadening, we add in simulation the random Gaussian noise to theamplitudes induced on the strips on both sides of the cathode. The widthof the Gaussian noise is taken the same for all double layers, its energyequivalent is ∼ . dE/dx diff vs. dE/dx summ forthe cosmic muons in the innermost double layer in the experiment. Thevertical lines show the slices of the distribution, inside which we performthe data/MC comparison of the dE/dx diff spectra. For example, such acomparison for the third double layer is shown in Fig. 14. Since the positionof the peaks in Fig. 14 is mainly controlled by the T l , the discrepancy betweenthe data/MC peak positions means that the a priori taken T l values arewrong. We tune the T l values to achieve the coincidence of the peaks andthus obtain the true transparency coefficients T = 0 . T = 0 . T = 0 . T = 0 . T = 0 . T = 0 . T = 0 .
33 with about 5% uncertainty.Apart from the shift of the peak positions we observe the relative broad-ening of the experimental dE/dx diff spectra, presumably related to the vari-12 igure 11: dE/dx
LXe for cosmic muons mea-sured in the innermost double layer by theupper strips vs. that measured by the lowerstrips in the experiment. h_summ_cosmics_after_tuning
Entries 429315Mean 4.086Std Dev 0.6413 N u m be r o f e v en t s , MeV/cm summ dE/dx Figure 12: The dE/dx summ spectra in theinnermost double layer for cosmic muons inthe experiment (markers) and MC before(open histogram) and after (gray histogram)tuning.Figure 13: The dE/dx diff vs. dE/dx summ distribution for the cosmic muons in the in-nermost double layer in the experiment. The slicing on the dE/dx summ is also shown. T l . To account for thisbroadening, we add the anticorrelated Gaussian noise to the amplitudes, in-duced on the upper and lower strips in simulation. This means that the samerandom value is added to the amplitude of the upper strips and subtractedfrom the amplitude of the lower strips. This additional anticorrelated noisesimulates the effect of the redistribution of the charge between upper andlower strips due to the T l variations. The variance of the additional noiseis tuned individually in all double layers, the noise energy equivalents are ∼ . − .
12 MeV depending on the layer. After the applied corrections weobserve a good data/MC agreement in the dE/dx diff spectra, see Fig. 14.
Another kind of the data/MC discrepancy is observed in the dE/dx summ spectra for the electromagnetic (e.m.) showers, produced in the calorimeterby electrons and positrons from the process e + e − → e + e − , see Fig. 15. Theadditional noises used for tuning of the MIPs in simulation show no seriouseffect on the large amplitudes of the e.m. showers. The actual reasons of theobserved discrepancy remain unclear, but many possible sources were stud-ied, including the imprecise description of the dead material in front of thecalorimeter, the influence of the electronegative admixtures in LXe, the inac-curate value of LXe density etc. Fortunatelly, the discrepancy can be mostlyeliminated by the simple linear transformation of the simulated amplitudes dE/dx meas , corr = a · dE/dx meas − b , where a = 1 .
055 is the “additional calibra-tion” coefficient for the showers and b = 0 . e ± momenta and angles.
6. Spectra of classifier response and signal/background separationpower
In this section we perform the data/MC comparison of the resulting BDTresponse spectra for different types of particles. Figures 16–21 provide a14 − − − − N u m be r o f e v en t s − − − − − N u m be r o f e v en t s − − − − − N u m be r o f e v en t s − − − − − , MeV/cm diff dE/dx N u m be r o f e v en t s − − − − − − − − − − − − − − − − − − − − , MeV/cm diff dE/dx − − − − − − − − − − − − − − − − − − − − , MeV/cm diff dE/dx − − − − − N u m be r o f e v en t s − − − − − N u m be r o f e v en t s − − − − − N u m be r o f e v en t s − − − − − N u m be r o f e v en t s , MeV/cm diff dE/dx − − − − − − − − − − − − − − − − − − − − , MeV/cm diff dE/dx − − − − − − − − − − − − − − − − − − − − , MeV/cm diff dE/dx Figure 14: The dE/dx diff spectra for the cosmic muons in the third double layer in allslices in the experiment (markers) and MC (gray histogram) before (upper figure) andafter (lower figure) T l tuning and addition of the anticorrelated noise. h_summ_cosmics_after_tuning_0 Entries 87210Mean 17.22Std Dev 11.23 N u m be r o f e v en t s , MeV/cm summ dE/dx
20 40 60 80 100 1200200040006000800010000120001400016000 h_summ_cosmics_after_tuning_2
Entries 87210Mean 43.01Std Dev 19.57 N u m be r o f e v en t s , MeV/cm summ dE/dx
20 40 60 80 100 120020004000600080001000012000140001600018000 h_summ_cosmics_after_tuning_4
Entries 87210Mean 46.95Std Dev 18.6 N u m be r o f e v en t s , MeV/cm summ dE/dx Figure 15: The dE/dx summ spectra in the first (left), third (middle) and fifth (right)double layers for e ± from the process e + e − → e + e − in the experiment (markers), MC before(open histogram) and after (gray histogram) linear transformation. The beam energy is987.5 MeV. general view of the potential effectiveness of all six types of classifiers asa function of particle momentum according to simulation. The “comb” inthe BDT spectra at low momentum corresponds to the cases when all inputvariables of the classifiers are zero. It is seen, that µ/π separation (Fig. 19) isnot effective at all, whereas separation of e ± from µ ± , π ± and K ± (Figs. 16–18) is effective starting from some threshold momentum. Figure 16: The BDT( e − , µ − ) vs. particlemomentum for simulated e − (black) and µ − (gray), uniformly distributed in d LXe . Figure 17: The BDT( e − , π − ) vs. particlemomentum for simulated e − (black) and π − (gray), uniformly distributed in d LXe . We select e ± from e + e − → e + e − events using the following criteria: 1) thereare exactly two DC-tracks with the opposite charges; 2) the | ρ | and | z | of the16 igure 18: The BDT( e − , K − ) vs. particlemomentum for the simulated e − (black) and K − (gray), uniformly distributed in d LXe . Figure 19: The BDT( µ − , π − ) vs. particlemomentum for simulated µ − (black) and π − (gray), uniformly distributed in d LXe .Figure 20: The BDT( µ − , K − ) vs. parti-cle momentum for simulated µ − (black) and K − (gray), uniformly distributed in d LXe . Figure 21: The BDT( π − , K − ) vs. parti-cle momentum for simulated π − (black) and K − (gray), uniformly distributed in d LXe . π − . | θ + θ − π | < .
15 radand || ϕ − ϕ | − π | < .
15 rad; 5) the energy deposition of each particle in thebarrel calorimeter (LXe and CsI) is larger than the half beam energy ( E beam ).Data/MC comparison for the BDT( e ± , µ ± ), BDT( e ± , π ± ) and BDT( e ± , K ± )spectra for the selected e ± at the low (280 MeV) and high (987.5 MeV) beamenergies is shown in Fig. 22. Agreement is good in all cases. − − − − − − h_tot_bdt_e_mu_0Entries 87372Mean 0.2386 − Std Dev 0.1012 N u m be r o f e v en t s BDT(e , ) µ ± ± − − − − − h_tot_bdt_e_pi_0 Entries 87372Mean 0.009766 − Std Dev 0.06699 N u m be r o f e v en t s BDT(e , ) π ±± − − h_tot_bdt_e_k_0 Entries 87372Mean 0.007714Std Dev 0.08469 N u m be r o f e v en t s BDT(e ,K ) ±± − − − − − N u m be r o f e v en t s BDT(e , ) µ ± ± − − − BDT(e , ) N u m be r o f e v en t s π ± ± − − − N u m be r o f e v en t s BDT(e ,K ) ± ±
Figure 22: The BDT( e ± , µ ± ) (left), BDT( e ± , π ± ) (middle) and BDT( e ± , K ± ) (right)spectra for the e ± selected from e + e − → e + e − events in the experiment (markers) and MC(gray histrogram) at E beam = 280 MeV (top figures) and E beam = 987 . We select a sample of µ ± from events with cosmic muons using the follow-ing criteria: 1) there is only one DC-track; 2) the track momentum is in therange from 100 to 1200 MeV/ c ; 3) track is not central: the minimal distancefrom the track to the beam axis is in the range from 3 to 15 cm; 4) the energydeposition of the particle in the calorimeter is less than 400 MeV. Reasonabledata/MC agreement for the BDT( e ± , µ ± ), BDT( µ ± , π ± ) and BDT( µ ± , K ± )spectra can be seen in Fig. 23. 18 N u m be r o f e v en t s BDT(e, ) µ − − − N u m be r o f e v en t s BDT( ) µ, π − − − N u m be r o f e v en t s BDT( ,K) µ Figure 23: The BDT( e ± , µ ± ) (left), BDT( µ ± , π ± ) (middle) and BDT( µ ± , K ± ) (right)spectra for the cosmic µ ± in the experiment (markers) and MC (gray histrogram). Themuon momentum is in the range from 100 to 1200 MeV/c. The clean π ± sample with well-predicted angular-momentum distribu-tions can be obtained by selection of e + e − → φ (1020) → π + π − π events. To dothis, we search for events with exactly two DC-tracks with opposite chargesand momenta larger than 100 MeV/c. Then, there should be not less thantwo photons with energies larger than 40 MeV. Sorting over all the pairsof such photons, we perform the 4C-kinematic fit for two tracks and thephoton pair assuming energy-momentum conservation and choose the pairgiving the smallest χ . If the invariant mass of the photon pair m γ satisfiesthe | m γ − m π | <
40 MeV / c condition, we consider the π + π − π event asreconstructed.First of all, since simulation of nuclear interactions of pions is not perfect,we check the data/MC agreement in the dE/dx summ and dE/dx diff spectra forselected π ± , see Fig. 24. The agreement is good for all pion momenta. Then,Fig. 25 shows good data/MC agreement for the BDT( e ± , π ± ), BDT( µ ± , π ± )and BDT( π ± , K ± ) spectra. The agreement is good for both pion charges.The efficiency of e − rejection vs. the efficiency of π − selection (ROC-curve)for the BDT( e − , π − ) at different pion momenta is shown in Fig. 26. The clean K ± sample can be selected from the four-track e + e − → K + K − π + π − events. We select these events on the base of ∼
60 pb − of integrated lumi-nosity collected in the 2019 runs and use data from all energy points above19
10 15 20 25 3010 h_summ_0_0Entries 24084Mean 5.049Std Dev 3.621 N u m be r o f e v en t s , MeV/cm summ dE/dx h_summ_0_2Entries 24084Mean 5.231Std Dev 3.729 N u m be r o f e v en t s , MeV/cm summ dE/dx h_summ_0_4Entries 24084Mean 5.326Std Dev 3.801 N u m be r o f e v en t s , MeV/cm summ dE/dx − − − h_diff_0_0 Entries 22775Mean 0.01591Std Dev 2.458 N u m be r o f e v en t s , MeV/cm diff dE/dx − − − h_diff_0_2 Entries 20917Mean 0.01414Std Dev 2.803 N u m be r o f e v en t s , MeV/cm diff dE/dx − − − h_diff_0_4 Entries 18797Mean 0.0419Std Dev 2.85 N u m be r o f e v en t s , MeV/cm diff dE/dx Figure 24: The dE/dx summ (top figures) and dE/dx diff (bottom figures) in the 1st (left),3rd (middle) and 5th (right) double layers for the π ± selected from e + e − → π + π − π events in the experiment (markers) and simulation (gray histogram). The c.m. energy is1019 MeV ( φ (1020) meson peak). − h_bdt_e_pi_0Entries 24084Mean 0.2684Std Dev 0.1147 N u m be r o f e v en t s BDT(e , ) π ± ± − h_bdt_mu_pi_0Entries 24084Mean 0.1872Std Dev 0.2244 N u m be r o f e v en t s BDT( , ) µ π ±± − − − − h_bdt_pi_k_0Entries 24084Mean 0.1227 − Std Dev 0.1043 N u m be r o f e v en t s BDT( ,K ) ± ± π Figure 25: The BDT( e ± , π ± ) (left), BDT( µ ± , π ± ) (middle) and BDT( π ± , K ± ) (right)spectra for the π ± selected from e + e − → π + π − π events in the experiment (markers) andMC (gray histrogram). The c.m. energy is 1019 MeV ( φ (1020) meson peak). .65 0.7 0.75 0.8 0.85 0.9 0.95 10.50.60.70.80.91 ROC for pi/e separation200 MeV/c300 MeV/c400 MeV/c1000 MeV/c selection r e j e c t i on − e − π Figure 26: The ROC-curves for the BDT( e − , π − ) classifier for different particle momenta(see legend) according to simulation. the reaction threshold. The event selection procedure involves the kinematicenergy-momentum selections along with the cuts on the value of the like-lihood function, based on the dE/dx DC of tracks, as described in [17, 18].However, a large part of selected kaons has the momenta lower than the p Ktrh ∼
300 MeV/c, and for such momenta only the products of kaon decayor nuclear interaction can reach the LXe.Similarly to the case of pions, we check the accuracy of simulation of thenuclear interactions of kaons by the data/MC comparison for the dE/dx summ and dE/dx diff spectra for selected K ± , see Fig. 27. The agreement is reason-able for all kaon momenta. The data/MC comparison for the BDT( e ± , K ± ),BDT( µ ± , K ± ) and BDT( π ± , K ± ) spectra is shown in Fig. 28. The simu-lated BDT( π ± , K ± ) spectrum seems somewhat distorted for K ± with lowmomenta (lower left picture in Fig. 28), presumably due to the inacurracyin the simulation of nuclear interactions. However, the distortion mostlydisappears at large kaon momenta, see lower right picture in Fig. 28.The LXe-based π/K separation is of special importance in the studiesof the hadronic processes with K ± , and it should be compared with theseparation based on dE/dx DC . Figure 29 shows the distributions of the dE/dx DC vs. momentum for the simulated K ± and π ± . The ROC-curves21or both types of classification at different particle momenta are shown inFig. 30. At the momenta below 400 MeV/c the LXe-based classifier has poorefficiency. At the largest momenta its efficiency gradually reduces due to thedecrease of the difference between kaon and pion ionization losses, see Fig. 5.Hovewer, the LXe-based π/K separation remains effective at the momenta650–900 MeV/c, where the dE/dx DC -based separation does not work.
10 20 30 40 50 60 7010 h_summ_0_0Entries 681230Mean 14.79Std Dev 13.11 N u m be r o f e v en t s , MeV/cm summ dE/dx
10 20 30 40 50 60 7010 h_summ_0_2Entries 681230Mean 12.2Std Dev 12.08 N u m be r o f e v en t s , MeV/cm summ dE/dx
10 20 30 40 50 60 7010 h_summ_0_4Entries 681230Mean 10.13Std Dev 11.05 N u m be r o f e v en t s , MeV/cm summ dE/dx − − − h_diff_0_0 Entries 589084Mean 0.2411 − Std Dev 9.292 N u m be r o f e v en t s , MeV/cm diff dE/dx − − − h_diff_0_2 Entries 466597Mean 0.2094 − Std Dev 9.659 N u m be r o f e v en t s , MeV/cm diff dE/dx − − − h_diff_0_4 Entries 349629Mean 0.1812 − Std Dev 9.264 N u m be r o f e v en t s , MeV/cm diff dE/dx Figure 27: The dE/dx summ (top figures) and dE/dx diff (bottom figures) in the 1st (left),3rd (middle) and 5th (right) double layers for the K ± selected from e + e − → K + K − π + π − events in the experiment (markers) and simulation (gray histogram). The data from allexperimental runs of 2019 are used.
7. Examples of the application of the LXe-based PID e + e − ( γ ) and π + π − ( γ ) final states at E beam < MeV
The developed PID procedure can be used for the important task of thepion form factor | F π | measurement [19]. To calculate the | F π | at the given E c . m . point one needs to determine the number of events of the π + π − ( γ )final state, N π + π − . The major background sources for π + π − ( γ ) are the22 .2 − − h_bdt_e_k_0_1 Entries 525543Mean 0.2Std Dev 0.1002 N u m be r o f e v en t s ))/2 + ,K + )+BDT(e − ,K − (BDT(e − − h_bdt_e_k_0_1 Entries 155508Mean 0.2959Std Dev 0.1254 N u m be r o f e v en t s ))/2 + ,K + )+BDT(e − ,K − (BDT(e − h_bdt_mu_k_0_1Entries 525543Mean 0.2826Std Dev 0.1498 N u m be r o f e v en t s ))/2 + )+BDT( ,K − (BDT( ,K − µ + µ − h_bdt_mu_k_0_1Entries 155508Mean 0.4468Std Dev 0.1533 N u m be r o f e v en t s ))/2 + )+BDT( ,K − (BDT( ,K − µ + µ − − h_bdt_pi_k_0_1 Entries 525543Mean 0.1179Std Dev 0.131 N u m be r o f e v en t s ))/2 + )+BDT( ,K − (BDT( ,K − π + π − − h_bdt_pi_k_0_1 Entries 155508Mean 0.218Std Dev 0.1551 N u m be r o f e v en t s ))/2 + )+BDT( ,K − (BDT( ,K − π + π Figure 28: The BDT( e ± , K ± ) (top), BDT( µ ± , K ± ) (middle) and BDT( π ± , K ± ) (bottom)spectra for the K ± and π ± selected from e + e − → K + K − π + π − events in the experiment(filled circles for K ± and empty circles for π ± ) and simulation (gray histogram for K ± and open histogram for π ± ). The left figures are drawn for particles with momenta lowerthan 400 MeV, the right – larger than 400 MeV. The data from all experimental runs of2019 are used. igure 29: dE/dx DC as a function of particle momentum for simulated K ± (gray) and π ± (black). e + e − ( γ ), µ + µ − ( γ ) final states and cosmic muons. The effective separationof the π + π − ( γ ) and µ + µ − ( γ ) final states at the CMD-3 is a difficult taskat the energies E beam >
350 MeV. However, since the cross sections of the e + e − → e + e − ( γ ) and e + e − → µ + µ − ( γ ) processes are precisely calculated inthe frame of QED, the number of events N µ + µ − can be calculated once thenumber of events N e + e − is known. In turn, determination of the N e + e − be-comes possible with the application of the effective separation of the e + e − ( γ )and π + π − ( γ ) final states. Currently at CMD-3 we use two independentapproaches for the e + e − ( γ ) and π + π − ( γ ) separation: 1) using the particlemomenta; 2) using the full energy depositions of particles in the calorimeter.The LXe-based PID provides us another method of e + e − ( γ ) and π + π − ( γ )separation.As an example we consider the e + e − ( γ ) and π + π − ( γ ) separation at theenergies E beam <
500 MeV in the experimental runs of 2018. We selectevents having exactly two oppositely charged tracks, satisfying the followingconditions: 1) the momenta of tracks are larger than 100 MeV /c ; 2) the | ρ | and | z | of the track point of the closest approach to the beam axis shouldbe less than 0.6 and 12 cm, respectively; 3) the polar angles of tracks shouldbe in the range from 1.0 to π − . .4 0.5 0.6 0.7 0.8 0.9 100.20.40.60.81 DC, p=400 MeV/cLXe, p=400 MeV/c selection − K r e j e c t i on − π DC, p=500 MeV/cLXe, p=500 MeV/c selection − K r e j e c t i on − π DC, p=600 MeV/cLXe, p=600 MeV/c selection − K r e j e c t i on − π DC, p=700 MeV/cLXe, p=700 MeV/cLXe, p=800 MeV/cLXe, p=900 MeV/c selection − K r e j e c t i on − π Figure 30: The ROC-curves for the BDT( π − , K − ) classifier and dE/dx DC -based π − /K − separation for different particle momenta according to simulation. The classifier types andparticle momenta are shown in the legends.
00 150 200 250 300 350 400 450110 h_p_PipPim Entries 130352Mean 241.5Std Dev 9.084 data − π + π MC − e + MC e − µ + µ MC ± µ MC cosmic N u m be r o f e v en t s p, MeV/c Figure 31: The momentum spectra of the particles selected at E beam = 280 MeV inthe experiment (markers), simulation of π + π − ( γ ) (gray histogram), e + e − ( γ ) (horizontalhatching), µ + µ − ( γ ) (vertical hatching) and cosmic muons (open histograsm). The blackline shows the total MC of the signal and background processes. | θ + θ − π | < .
25 rad and || ϕ − ϕ | − π | < .
15 rad.Figure 31 shows the momentum spectrum for the particles, selected inthe experiment and simulation at E beam = 280 MeV. The contribution of thecollinear final states is estimated according to the known cross sections ofthe processes and luminosity, while the contribution of the cosmic muons isestimated using the events with the momenta larger than 1 . · E beam . Fur-ther, Fig. 32 shows the distribution of the average BDT( e, π ) response fortwo tracks, i.e. (BDT( e − , π − ) + BDT( e + , π + )) /
2, for E beam = 280 MeV (lefttail of the ρ (770)) and 380 MeV (near the peak of ρ (770)). It is seen that the(BDT( e − , π − ) + BDT( e + , π + )) / e + e − ( γ ) and π + π − ( γ ) separation, see corresponding ROC-curves in Fig. 33.At E beam = 380 MeV the classifier allows to select 99.5% of π + π − ( γ ) eventsby the 98% rejection of the e + e − ( γ ) background.26 .2 − − h_bdt_e_pi_PipPimEntries 65176Mean 0.2677Std Dev 0.08411 dataMC sig+bkg − π + π MC − e + MC e − µ + µ MC ± µ MC cosmic N u m be r o f e v en t s ))/2 + ,K + )+BDT(e − ,K − (BDT(e − − h_bdt_e_pi_PipPimEntries 66344Mean 0.2826Std Dev 0.07684 dataMC sig+bkg − π + π MC − e + MC e − µ + µ MC ± µ MC cosmic N u m be r o f e v en t s ))/2 + ,K + )+BDT(e − ,K − (BDT(e Figure 32: The distribution of the (BDT( e − , π − ) + BDT( e + , π + )) / E beam =280 MeV, right — E beam = 380 MeV) in the experiment (markers), simulation of π + π − ( γ )(gray histogram), e + e − ( γ ) (horizontal hatching), µ + µ − ( γ ) (vertical hatching) and cosmicmuons (dashed line). The open histogram shows the total MC of the signal and backgroundprocesses. pi + /pi e + ROC for BDT e=280 MeV ebeam
E =340 MeV ebeam
E =380 MeV ebeam
E =450 MeV ebeam E r e j e c t i on − e + e selection − π + π Figure 33: ROC-curves for separation of the e + e − ( γ ) and π + π − ( γ ) final states using(BDT( e − , π − ) + BDT( e + , π + )) / E beam (see legend) according to simulation. .2. Selection of the K + K − final state at high energies Another application of the LXe-based PID is the task of the selection ofthe K + K − final state at high energies. As an example, we perform suchselection on the base of 2.2 pb − of data collected at E c . m . = 1 .
975 GeVin the 2019 runs. To select the two-track collinear events, we apply theselections listed earlier in Section 7.1. The main background sources are the e + e − ( γ ), µ + µ − ( γ ), π + π − ( γ ) final states and the events with cosmic muons,their contributions in simulation are estimated in a way described earlier inSection 7.1. The background suppression is done by the cuts, imposed onthe values of the average BDT responses (BDT( e − , K − ) + BDT( e + , K + )) / µ − , K − ) + BDT( µ + , K + )) / µ − , K − ) + BDT( µ + , K + )) / ∼
5% ofsignal events and also provides significant suppression of the e + e − → π + π − ( γ )process. Since the cross section of the latter is relatively low at E c . m . ∼ π + π − events are kinematically separated from K + K − , we do not imposeany cuts on BDT( π ± , K ± ). − − dataMC sig+bkg − K + MC K − e + MC e N u m be r o f e v en t s ))/2 + ,K + )+BDT(e − ,K − (BDT(e cut Figure 34: The (BDT( e − , K − ) +BDT( e + , K + )) / K + K − ( γ )(gray histogram), e + e − ( γ ) (hatched his-togram). The open histogram shows thetotal MC of the signal and backgroundprocesses. − dataMC sig+bkg − K + MC K − π + π MC MC muons N u m be r o f e v en t s ))/2 + )+BDT( ,K − (BDT( ,K − µ + µ cut Figure 35: The (BDT( µ − , K − ) +BDT( µ + , K + )) / K + K − ( γ )(gray histogram), µ + µ − ( γ ) and cosmicmuons (hatched histogram), π + π − ( γ )(dotted line). The open histogram showsthe total MC of the signal and backgroundprocesses. E , defined as∆ E = (cid:112) (cid:126)p c + m K + c + (cid:112) (cid:126)p − c + m K − c + | (cid:126)p + + (cid:126)p − | c E beam − , (6)where (cid:126)p ± are the particle momenta. The additional term | (cid:126)p + + (cid:126)p − | , cor-responding to the total momentum of two tracks, allows to get rid of thesuperimposition of the signal peak with the e + e − ( γ ) radiative tail. Figure 36shows the ∆ E spectra before and after the application of cuts on BDT. Itis seen that after the background suppression the signal/background separa-tion in the ∆ E spectrum becomes possible. To perform the separation, weapproximate the experimental ∆ E spectra using the sum of three Gaussiansto approximate the peaking background and the linear function to approxi-mate the contribution of cosmic muons. The shape of the signal peak is fixedfrom the approximation of the simulated ∆ E spectra for the e + e − → K + K − process, except for the shift of the signal peak as a whole and its additionalbroadening, which are added as the floating parameters. Thus, we obtain548 ±
27 of signal events at E c . m . = 1 .
975 GeV (Fig. 36, right).It should be noted that for the c.m. energies larger than 1.5 GeV usageof the LXe-based PID is the only way to measure the e + e − → K + K − processcross section at CMD-3.
8. Conclusions
The procedure of the charged PID using the LXe calorimeter of theCMD-3 detector was developed. The procedure uses the energy depositions,measured in 12 layers of the LXe calorimeter, as the input for the set ofboosted decision trees classifiers, trained for the separation of the electrons,muons, pions and kaons in the momentum range from 100 to 1200 MeV /c .Since the event samples for the classifier training are taken from the MC,special attention was paid to the tuning of the simulated detector response.29 .2 − − −
10 110 dataMC sig+bkg − K + MC K N u m be r o f e v en t s E ∆ − − dataMC sig+bkg − K + MC K N u m be r o f e v en t s E ∆ Figure 36: The ∆ E spectra before (left) and after (right) background suppression in theexperiment (markers) and MC of the K + K − ( γ ) (gray histogram). The open histogramshows the total MC of the signal and background processes. The solid curve on the rightpicture shows the fit of the distribution in the experiment, dotted curve — the backgroundpart of the fit. From the experimental side the procedure of the calibration of strip channelsof LXe calorimeter with the precision of about 1% was developed. Theseefforts resulted in good data/MC agreement for the classifier responses forall particle types. Finally, the application of the method was demonstratedby the examples of separation of the e + e − ( γ ) and π + π − ( γ ) final states at E beam <
500 MeV and of the selection of the K + K − final state at highenergies.
9. Acknowledgments
We thank the VEPP-2000 personnel for excellent machine operation. Partof work related to the method of the selection of e + e − → K + K − π + π − processevents mentioned in the Section 6.4 is partially supported by the grant of theRussian Foundation for Basic Research 20-02-00496 A 2020. REFERENCES [1] V.V. Danilov et al., Proceedings EPAC96, Barcelona, p.1593 (1996).[2] I.A. Koop, Nucl. Phys. B (Proc. Suppl.) 181-182, 371 (2008).303] P.Yu. Shatunov et al., Phys. Part. Nucl. Lett. 13, 995 (2016).[4] D. Shwartz et al., PoS ICHEP2016, 054 (2016).[5] B.I. Khazin et al. (CMD-3 Collaboration), Nucl. Phys. B (Proc. Suppl.)181-182, 376 (2008).[6] F. Jegerlehner, Springer Tracks Mod. Phys. 274, 1 (2017).[7] M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, Eur. Phys. J. C 77,827 (2017).[8] A. Keshavarzi, D. Nomura, T. Teubner, Phys. Rev. D 97, 114025 (2018).[9] K. Hagiwara et al., J. Phys. G 38, 085003 (2011).[10] D. Epifanov (CMD-3 Collaboration), J. Phys. Conf. Ser. 293, 012009(2011).[11] A. Amirkhanov et al., Nucl. Instrum. Meth. A936, 598 (2019).[12] F. Grancagnolo et al., Nucl. Instr. Meth. A623, 114 (2010).[13] A.V. Anisyonkov et al., Nucl. Instr. Meth. A598, 266 (2009).[14] V.E. Shebalin et al., JINST 9 (10), C10013 (2014).[15] H. Voss, A. Hcker, J. Stelzer, F. Tegenfeldt, PoS(ACAT) 040.[16] K.I. Kakhuta and Yu.V. Yudin, Nucl. Instr. and Meth. A , 342 (2009).[17] D.N. Shemyakin et al. (CMD-3 Collaboration), Phys.Lett. B 756, 153(2016).[18] R.R. Akhmetshin et al. (CMD-3 Collaboration), Phys. Lett. B 794, 64(2019).[19] F.V. Ignatov et al. (CMD-3 Collaboration), EPJ Web Conf.218