A study of muon-electron elastic scattering in a test beam
Giovanni Abbiendi, Giovanni Ballerini, Dipanwita Banerjee, Johannes Bernhard, Matteo Bonanomi, Claudia Brizzolari, Luca G. Foggetta, Mateusz Goncerz, Fedor V. Ignatov, Marco Incagli, Marcin Kucharczyk, Umberto Marconi, Valerio Mascagna, Clara Matteuzzi, Riccardo Pilato, Dinko Pocanic, Michela Prest, Antonio Principe, Federico Ronchetti, Mattia Soldani, Roberto Tenchini, Erik Vallazza, Graziano Venanzoni, Mariusz Witek, Milosz Zdybal
PPrepared for submission to JINST
A study of muon-electron elastic scattering in a test beam
Giovanni Abbiendi, 𝑎 Giovanni Ballerini, 𝑏,𝑐
Dipanwita Banerjee, 𝑑 Johannes Bernhard, 𝑑 Matteo Bonanomi, 𝑐,𝑒, 𝑓
Claudia Brizzolari, 𝑐,𝑒
Luca G. Foggetta, 𝑔 Mateusz Goncerz, 𝑘 Fedor V.Ignatov, 𝑙 Marco Incagli, 𝑗 Marcin Kucharczyk, 𝑘 Umberto Marconi, 𝑎 Valerio Mascagna, 𝑏,𝑐
Clara Matteuzzi, 𝑒 Riccardo Pilato, 𝑗 Dinko Pocanic, 𝑚 Michela Prest, 𝑏,𝑐
Antonio Principe, 𝑎 Federico Ronchetti, 𝑏,𝑐
Mattia Soldani, ℎ,𝑖
Roberto Tenchini, 𝑗 Erik Vallazza, 𝑐 GrazianoVenanzoni, 𝑗 Mariusz Witek, 𝑘 Milosz Zdybal 𝑘 𝑎 INFN Sezione di Bologna,Via Irnerio , Bologna, Italy 𝑏 Università degli Studi dell’Insubria,Via Valleggio 11, Como, Italy 𝑐 INFN Sezione di Milano Bicocca,Piazza della Scienza 3, Milano, Italy 𝑑 CERNEsplanade des Particules, Geneva, Switzerland 𝑒 Università degli Studi di Milano Bicocca,Piazza della Scienza 3, Milano, Italy 𝑓 Laboratoire Leprince-Ringuet, CNRS/IN2P3,Ecole Polytechnique, Palaiseau, France 𝑔 INFN Laboratori Nazionali di Frascati,Via Fermi 54, Frascati, Italy ℎ Università degli Studi di Ferrara,Via Saragat 1, Ferrara, Italy 𝑖 INFN Sezione di Ferrara,Via Saragat 1, Ferrara, Italy 𝑗 INFN Sezione di Pisa,Largo Bruno Pontecorvo 3, Pisa, Italy 𝑘 Institute of Nuclear Physics PAN,Ul. Radzikowskiego 152,Krakow, Poland 𝑙 Budker Institute of Nuclear Physics,SB RAS, 11 Acad. Lavrentieva Pr.,Novosibirsk, Russia 𝑚 University of Virginia,Charlottesville, VA, USA a r X i v : . [ h e p - e x ] F e b bstract: In 2018, a test run with muons in the North Area at CERN was performed, runningparasitically downstream of the COMPASS spectrometer. The aim of the test was to investigate theelastic interactions of muons on atomic electrons, in an experimental configuration similar to theone proposed by the project MUonE, which plans to perform a very precise measurement of thedifferential cross-section of the elastic interactions.COMPASS was taking data with a 190 GeV 𝜋 beam, stopped in a tungsten beam dump: themuons from these 𝜋 decays passed through a setup including a graphite target followed by 10 planesof Si tracker and a BGO crystal electromagnetic calorimeter placed at the end of the tracker. Theelastic scattering events were analysed, and compared to expectations from MonteCarlo simulation.Keywords: Particle tracking detectors (Solid-state detectors), Pattern recognition, cluster finding,calibration and fitting methods, Performance of High Energy Physics Detectors, Simulation methodsand programs ontents Recently a new experiment, MUonE, has been proposed with the aim of measuring the running ofthe effective electromagnetic coupling at low momentum transfer in the space-like region ( 𝛼 (q ),q < 0) to provide an independent determination of the leading hadronic contribution to the (g-2) 𝜇 of the muon [1]. Such a measurement relies on the precise determination of the measured anglesof the outgoing particles emerging from the elastic scattering 𝜇 + 𝑒 → 𝜇 + 𝑒 of high-energy muons(160 GeV) impinging on atomic electrons of a light material (beryllium or carbon) target [2].In 2018, a test run was performed at CERN, with a setup located behind the COMPASSspectrometer in the North Area [3], in order to set guidelines for the proposed configurationfor MUonE. The detector consisted of an 8 mm graphite target followed by a Si tracker and anelectromagnetic calorimeter. Despite the fact that the Si tracker used in this test had a worse spatialresolution than the MUonE final apparatus [2], much interesting information was obtained fromthis test. The 2018 test run was performed in EHN2, downstream of the COMPASS spectrometer, andexploited the ∼
187 GeV / 𝑐 positive muons that result from the decay of pions in the beam usedby COMPASS. The remaining hadrons being stopped in a 1 . . ∼
400 m upstream of COMPASS[3, 4]. The latter configuration was occasionally used for the COMPASS calibrations [2]. At thelocation of the test setup, the muon beam has a width of several tens of centimetres. Within the ≈ ×
10 cm tracking system acceptance, the divergence along the horizontal (vertical) directionis ∼ . . he tracker The core of the apparatus was the silicon microstrip-based tracking system developedby the INSULAb group [5]. Each of the 16 tracking planes consisted of a 9 . × . × .
041 cm single-side sensor with 384 channels, manufactured by Hamamatsu on high resistivity substrates forthe AGILE experiment [6]. The strips have a 121 𝜇 m pitch and, given the fact that the floating stripscheme is used, a 242 𝜇 m readout pitch. Each sensor is read out by three 128-channel, low-noise,analog-digital ASICs – TA1 or TAA1 by IDEAS. The readout of the differential analog output ismultiplexed with a 2 . ∼ 𝜇 m. yx z (beam) calorimeterboxtrigger 1 trigger 2target i npu t tr acke r ou t pu t t r acke r u v ~ c m Figure 1 . Setup scheme: the gray boxes represent the silicon layers; the black box represents the graphitetarget; the blue boxes represent the scintillating layers.
Several geometrical configurations were tested, which differ one from the other by the numberof 8 mm thick graphite targets, the output tracker lever arm and the number of u and v ( 𝜋 /
4) stereolayers. In the setup used for the present analysis 6 (10) silicon planes were placed in front (behind)of a single target (see fig. 1). The output stage was ∼ . ∼
35 mradangular acceptance upper limit. Further details on the apparatus can be found in [7]. The targetwas a 10x10 cm graphite layer, 8 mm thick. It was installed on a custom plastic holder, coupledto the Newport rail via a Bosch mechanical support. The coincidence between the signals of twoplastic scintillator trigger counters (with size 10 ×
10 cm , shown in fig. 1), together with thebeginning-of-spill and end-of-spill signals delivered by the SPS , allowed a clean trigger of muons The typical SPS cycle for fixed-target (FT) operation lasts at least 14.8 s, including 4.8 s spill duration, i.e. the timeduring which the beam is slowly extracted. The number of FT cycles is about 2-3 per minute depending on LHC fillingsand constraints by other users. – 2 –assing inside the acceptance of the tracker.
The electromagnetic calorimeter
In the data set analysed in this paper, the calorimeter was a com-pact array of 3 × ∼ . × . ( . × . ) cm and 23 cm length. They were read out by Photonis XP1912 PMTs [8] biased at 850 V. The crystalswere obtained by machining bigger spare blocks of the L3 endcap calorimeter and were arrangedas shown in fig. 2; such a configuration minimizes the dead regions in the detector active volumeto the (cid:46) Figure 2 . Scheme of the BGO calorimeter.
The transverse size of the electromagnetic calorimeter covered an angular acceptance of about15 mrad on each side from the center of a Si layer. The detector performance in terms of lin-earity and energy resolution is shown in fig. 3. The measured energy resolution is 𝜎 ( 𝐸 )/ 𝐸 = [( 𝑎 /√ 𝐸 (cid:1) + 𝑐 (cid:3) / with 𝑎 = ( . ± . ) % and 𝑐 = ( . ± . ) %. Further details on thiscalorimeter and on its characterization can be found in [7].Given the finite range of the acquisition chain, when high-energy electrons impinge on thecalorimeter, saturation may occur: in this case, the response of a single detector channel wascapped at a maximum value, which corresponds to ∼
11 GeV. This results in an overall upper limitin the measurement of the output electron energy of ∼
20 GeV.
Figure 3 . Calorimeter response linearity (left) and energy resolution (right) as a function of the detectorsignal pulse height (PH). ADC stands for Analog-to-Digital Counts. – 3 – he beam
The data were taken parasitically while COMPASS was running with pions of 190GeV energy. The muons originated mainly from the decays of the pions stopped in the beam dumpat the end of the COMPASS spectrometer. The hadron content at the location of the test setup wascompletely negligible.The resulting energy profile of the muons entering the test apparatus is shown in fig. 4, showinga peak at around 187 GeV with a tail. The divergence along the horizontal (vertical) direction is ∼ . . ∼ . × particles per spill. Figure 4 . Calculated energy profile of the muons beam reaching the test apparatus and originating from 𝜋 decays in the COMPASS dump. Simulation
The MonteCarlo sample used for the analysis consists of 150’000 𝜇 − 𝑒 elasticscattering events generated within the FairRoot [9] framework and simulated using GEANT4 [10].The geometry and material properties of the detector used in 2018 testbeam described above,have been implemented in GEANT4, with the simplification of defining a single-block calorimeterinstead of the 9 crystals in the real setup. The distributions of the incoming beam 𝑥 and 𝑦 positionhave been chosen to match that of the reconstructed incoming tracks in data events with non-zerocalorimetry deposit.The incoming muon beam has been taken to be a monoenergetic beam of 187 GeV, the tail has notbeen considered in the simulation (c.f. fig. 4 ).The 𝜇 − 𝑒 events have been generated based on Leading Order (LO) calculations, and the trackpropagation and simulation have been done with GEANT4.Hits registered in the Si detectors were subsequently translated to their frame of reference andsmeared by a Gaussian distribution with sigma corresponding to uncertainties determined from themeasured data. The total energy deposited by an event in the calorimeter corresponds to the sumof the signals of all crystals. The operation of the test run lasted ∼ ∼
2M triggers. Morestringent requirements were then applied on the presence of an incoming track and enough hits inthe 10 planes after the target to allow the reconstruction of at least two tracks. All these criteriareduced the sample to ≈
94k events.
Alignment
All the tracking layers, including stereo ones, were aligned based on the collection ofgood quality reconstructed tracks with at least ten hits. The ( 𝑥, 𝑦 ) position of the first layer wastaken as a reference. The shift in ( 𝑥, 𝑦 ) plane and the rotation angle of other layers around the 𝑧 axis were determined with respect to the reference layer. An iterative procedure was applied. The 𝑧 positions of layers were taken from the measured values of a geometrical survey. In one iterationthe layers were aligned one-by-one. A track was refitted excluding a given layer and the sum of theresiduals of all tracks from the collection was minimized with respect to 𝑥 and 𝑦 shift and rotationangle of the excluded layer. The iteration was finished when the change in the parameters of alllayers was below a given threshold. The distributions of the residuals obtained for final parameterswere then fitted using a single Gaussian distribution to determine the resolutions of individuallayers. The resolutions varied from 15 to 37 𝜇 m, with the spread mainly due to the intrinsic qualityof the sensors and the readout chain. Tracking algorithm
The scattering of high-energy muons on atomic electrons of a low-Z targetthrough the elastic process is characterized by a simple topology. Three tracks are expected to bereconstructed in the detector, i.e. the incident muon before the target and outgoing electron andmuon after the target.The track reconstruction is performed separately in detector parts before and after the target. First,the two-dimensional (2-d) tracks are searched for independently in 𝑥 - 𝑧 and 𝑦 - 𝑧 projections. In thenext step, accepted 2-d track candidates are combined into three-dimensional (3-d) tracks. Thenthe track fit is performed including hits in the stereo layers. The elastic 𝜇 - 𝑒 scattering event isobtained from reconstructed 3-d tracks: the track reconstructed before the target and the two tracksreconstructed after the target are checked for compatibility to belong to the common interactionvertex. The interaction vertex is constrained to the center plane of the target. Track reconstruction
The 2-d track finding is performed in each projection, by constructing pairsfrom all the combinations of hits in 𝑥 and 𝑦 layers separately. For each pair of hits, a 2-d line in 𝑥 - 𝑧 or 𝑦 - 𝑧 projections is determined. To maximize the efficiency, all the hits compatible with thestraight line within a relatively wide window corresponding to 10 times the sensor resolution, arecollected. A fit is then applied to the selected combinations, after removing outliers. The set of 2-dtrack candidates is sorted according to the number of collected hits and the 𝜒 of the fit. In the lastphase a clone killing procedure is applied as follows: only the best tracks with unique combinationsof hits are accepted. At least 3 hits in each projection are required. All pairs of track candidates, in 𝑥 - 𝑧 and 𝑦 - 𝑧 projections, are combined into 3-d track candidates. The compatible hits from stereolayers are included and the track fit is performed. An iterative fitting procedure is applied using theleast square method. After each iteration, hits more than 5 𝜎 away from the fitted line, are removed,and the fit is repeated until no outlier is found. As no unique combination of hits forming 3-d linesis imposed up to this point, the collections of tracks may contain clones, where clones are defined as– 5 –hose track candidates containing common hits. The clone removal procedure is applied as follows:the tracks are sorted according to the number of hits and 𝜒 per number of degrees of freedom NDFof the least square fit ( 𝜒 / 𝑁 𝐷𝐹 ). The tracks with the largest number of hits are accepted first. Forthe same number of hits the candidate of best quality is taken using the 𝜒 / 𝑁 𝐷𝐹 criterion. Afteraccepting a track, the hits used by that track are marked as used. Then the next track from the sortedlist is searched for and accepted if it contains the required number of hits (3 hits in 𝑥 projection and3 hits in the 𝑦 projection) not used by any track already accepted. The final collection of tracks withunique set of hits is passed to the last stage of the event reconstruction. Reconstruction of 𝜇 - 𝑒 scattering events The set of reconstructed tracks is used to search forevents with the elastic 𝜇 - 𝑒 scattering topology. In the first step all combinations of track pairsreconstructed after the target are checked to be compatible with intersecting inside the target. Thena third track, incoming to the target and passing close to the intersection point, is searched for.For the three tracks initially compatible with muon-electron scattering, a dedicated vertex fit isperformed to obtain the best possible accuracy for the scattering angles of the outgoing muon andelectron. To take into account multiple scattering, the momentum of tracks has to be estimated.For the small ( < . 𝜇 − 𝑒 elastic scattering, the observed scattering angleof the electron can be used to estimate its momentum. The expected value of the momentum isassigned to the electron candidate using the knowledge of the beam momentum and of the two-bodykinematics. The other track from the pair after target is assumed to be the muon. For such outgoingmuons the expected momentum is high enough to neglect multiple scattering, defined as describedabove. A dedicated kinematic fit of the vertex is performed, based on a constrained least squaremethod. The common ( 𝑥 𝑣𝑡 𝑥 , 𝑦 𝑣𝑡 𝑥 ) position, at the middle 𝑧 coordinate of the target, is enforced.The uncertainties of the hits assigned to the electron track are estimated using the predicted multiplescattering. The uncertainties due to detector resolutions and multiple scattering, from all materialfrom target up to the 𝑧 position of a given hit, are added in quadrature neglecting the correlations.The least square fit uses the 3-d line slopes of the three tracks and ( 𝑥 𝑣𝑡 𝑥 , 𝑦 𝑣𝑡 𝑥 ) as free parameters.The total 𝜒 used for minimization, is the sum of the 𝜒 contributions from all hits of the threetracks. The total vertex 𝜒 /NDF, referred to as 𝜒 𝑣𝑡 𝑥 , will be used through the paper. Its distributionis shown in fig. 6(a).The angular resolution for the two outgoing tracks is then determined from the MonteCarlosimulation, as the 𝜎 of the Gaussian function fitting the difference between the true angle and thereconstructed angle, plotted in fig. 5 as a function of the true emission angle. For muons it turnsout to be quite flat around 0.080 mrad, while for electrons it varies significantly as a function of theangle (i.e. the energy) from 0.100 to 0.900 mrad, mainly due to multiple scattering.The sample of ∼
94k events reduced to ∼
56k events after the final alignment and by requiringonly one incoming track, a total deposit in the calorimeter > 0, and enough hits in the tracker toreconstruct at least 2 tracks in the final state. Once the full reconstruction was performed, requiringat least three hits per plane and per track, and fitting a common vertex, 8556 events remain.– 6 – .25 0.50 0.75 1.00 1.25 1.50 1.75 [mrad] () [ m r a d ] without kinematic fitwith kinematic fit e [mrad] ( e ) [ m r a d ] without kinematic fitwith kinematic fit Figure 5 . Angular resolution as a function of the scattering angle for ( 𝑙𝑒 𝑓 𝑡 ) muons and for ( 𝑟𝑖𝑔ℎ𝑡 ) electrons.
Selection of 𝜇 - 𝑒 scattering events Two loose initial cuts are applied at the first stage of theanalysis and will be included in all further cuts described in this paper: i) the 𝜒 𝑣𝑡 𝑥 <
10 cut,determined from fig. 6(a), and ii) a cut on the electron emission angle rejecting events with 𝜃 𝑒 > 𝑒 > 1 GeV, which implies an angular cut at 𝜃 𝑒 ≈
35 mrad. Thecomparison of the data with the simulated elastic events traced through the experimental setup withGEANT4 is then valid in first approximation.The effect of these initial loose cuts is shown in the first three raws of table 1.
The specific kinematics of elastic scattering events requires that the events are planar, and that thetwo angles of the outgoing 𝜇 and 𝑒 are strongly correlated. The acoplanarity ( 𝐴 ), defined as theangle between the incoming muon and the plane of the two outgoing particles, is shown in fig. 6(b)for measured data and simulated elastic events, after the cut at 𝜒 𝑣𝑡 𝑥 < 𝜃 𝜇 , 𝜃 𝑒 ) is shown in fig.7 at this stage of the selection. In the measureddata (fig.7(a)) there is clearly a contribution from background, visible outside the correlation curve.The data plot of ( 𝜃 𝑒 , 𝜃 𝜇 ) in fig.8(a) shows also the deposited energy in the calorimeter, whichapproximately corresponds to the energy of the electrons .A variable 𝐷 𝜃 , which estimates the elasticity of a reconstructed event, is defined as the minimumangular distance of the measured event to the expected theoretical kinematic curve, and is calculatedfor a given incoming muon beam energy. This variable was introduced and used in the NA7experiment [11] to reject and estimate backgrounds. The distribution of 𝐷 𝜃 is shown in fig. 9(a) fordata and for simulated elastic events. Based on the simulation, a cut was set at − . < 𝐷 𝜃 < . The calorimeter structure doesn’t allow the separation of muon and electron deposited energies. – 7 – igure 6 . (a): 𝜒 𝑣𝑡 𝑥 distribution. (b): acoplanarity distribution. Data are in blue with error bars, the simulatedand reconstructed elastic events are the red histogram and are normalized to the observed number of eventsin data. Figure 7 . (a) kinematical correlation for data and (b) for simulated elastic events. this cut is applied, 3235 events remain, and their kinematic correlation is shown in fig. 9(b). Infig. 8(b) the information on the deposited energy in the calorimeter for these events is also shown.For comparison, an alternative set of selection criteria was applied, requiring a 𝜒 𝑣𝑡 𝑥 < 𝐴 | < 0.00035 cuts, and no cut on 𝐷 𝜃 . This set of cuts yields 3427 events.The summary of event yield at each selection step is given in table 1, where the definitions of thetwo final data samples, sample 1 and sample 2, are given.The selected events have been compared with elastic events generated with LO cross sectionand simulated with GEANT4.The correlation plot resulting from the selection of sample 2 is shown in fig. 10, to be comparedwith the one in fig. 9(b). – 8 – igure 8 . Measured angles of the outgoing muon and electron, with the color code representing the energydeposited in the calorimeter. (a) for measured data after the initial cuts on 𝜒 𝑣𝑡 𝑥 <
10 and 𝜃 𝑒 <
30 mrad, and(b) the measured data after imposing the additional cut on | 𝐷 𝜃 | < . Figure 9 . (a): 𝐷 𝜃 , defined in the text, for data and simulated elastic events normalized to the number ofevents observed. (b): The kinematical correlation in data, after the cut on 𝐷 𝜃 . Table 1 . Event yields after each step in the selection. The bottom two raws are alternatives, defining twodifferent samples, labelled sample 1 and 2, used in the analysis.
Selection criteria number of events
Initial sample 8556 𝜃 𝑒 <
30 mrad 6355 𝜒 𝑣𝑡 𝑥 <
10 4267
Above criteria and: sample 1: |D 𝜃 | < . 𝜒 𝑣𝑡 𝑥 < < . 𝜃 𝑒 is shown in fig. 11(a) and the acoplanarity in fig. 11(b) forsample 1. – 9 – igure 10 . The kinematical correlation for sample 2 (defined in table 1): in measured data (a), and inMonteCarlo (b). Figure 11 . Comparison data/MonteCarlo for the electron emission angle (a) and the acoplanarity (b). Thesimulated events have been normalized to the number of observed events. Sample 1 is defined in table 1.
The correlation between the electron energy 𝐸 𝑒 and 𝜃 𝑒 is shown in fig. 12. The measured correlationis well described by the simulation. The band of events in fig. 12 with 𝐸 𝑒 < large angle it misses the calorimeter partially or completely; when it is emitted at small angle ( < 𝜃 distribution ( cf. – 10 – igure 12 . Correlation between the reconstructed angle 𝜃 𝑒 and the deposited energy in the calorimeter,assumed to be 𝐸 𝑒 for measured data (a). For simulated events (b), in the MonteCarlo no detailed simulationis done for the calorimeter and the energy corresponds to the true energy deposited in the calorimeter. fig. 9) to roughly estimate it. The main contribution comes from below the kinematical curve, andit contains radiative events, pair production from the muon track, and migration of events from theregion 𝜃 𝑒 >
30 mrad. The events above the theoretical curve come mainly from badly measuredevents.Using only the left side events, the extrapolation under the signal region − . 𝐷 𝜃 < . 𝜇𝑒 + 𝑒 − , will provide the right way to understandthe level and the shape of this background.To this end, the implementation of a more comprehensive simulation of the muon electromagneticinteractions in GEANT4 to better estimate the level and the behaviour of background remaining inthe signal region is necessary.Finally, we compare the ratio of number of events in two different angular regions after thedifferent selection cuts. The two angular regions are defined as 𝜃 𝑒 < < 𝜃 𝑒 < 𝛼 , the small angular region will bewhere these corrections would appear. Given the low event statistics collected in this test beammeasurement, present results provide only preliminary and rough information. The comparisonof measured event yields to LO MonteCarlo simulation is given in table 2. The large statisticaluncertainties in the measured data make it difficult and premature to draw conclusions regardingthe level of agreement. In a test beam measurement performed parasitically behind the COMPASS spectrometer in theCERN North Area, elastic scattering 𝜇 - 𝑒 interactions were studied. This preliminary investigation– 11 –ngular region 𝜒 < | 𝐴 | < . | 𝐷 𝜃 | < . 𝜃< 𝜃 = −
20 mrad . ± . . ± . . ± . . ± . Table 2 . Ratios of number of events measured in two different angular regions, satisfying two sets ofselections cuts, as indicated. The comparison is made with LO simulated 𝜇 - 𝑒 elastic scattering events (inparenthesis). Errors are statistical only. was aimed mainly to explore the ability to select a clean sample of elastic scattering events inview of designing an experiment to measure the hadronic contribution to the running of 𝛼 . Theexperimental test setup had a resolution worse than the one planned to be used in MUonE [2], buteven in these conditions, we were able to select a clean sample of elastic events.Several other running conditions were different in this test with respect to the planned MUonEconditions, such as the high intensity and the shape of the beam requested by MUonE, and thereforesome experimental aspects could not be adressed.This study however suggests the importance of an adequate calorimeter, to understand theelectrons emitted in the range of a few GeV, and the determination and behaviour of the background.A crucial point for a future precise measurement of the differential cross section of the elastic 𝜇 - 𝑒 process is the upgrade [12] of GEANT4, at present under test. The upgrade concerns the muonpair-production interactions 𝜇 → 𝜇𝑒𝑒 for which an accurate angular distribution of the electrons ofthe pair has been implemented. This upgrade is available in version 10.7 of the GEANT4 package,currently in the process of being validated. Acknowledgments
We warmly thank the COMPASS collaboration for their kind willingness to let us run parasiticallybehind their detector, and in particular Vincent Andrieux for his active help. We also thank theLNF-BTF and the PADME collaboration for giving us the BGO calorimeter, and the LNF-SPCM,whose Tommaso Napolitano and Fabrizio Angeloni provided the mechanical support structure.
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