CMS Note Mailing address: CMS CERN, CH-1211 GENEVA 23, Switzerland

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1 Available on CMS information server CMS NOTE 997/ The Compact Muon Solenoid Experiment CMS Note Mailing address: CMS CERN, CH-2 GENEVA 23, Switzerland January 997 Low p T electron identification in CMS A. Kharchilava )2) and P. Pralavorio ) Abstract We demonstrate that, with the fine granular electromagnetic calorimeter of CMS, electrons can be identified down to p T 2 GeV with an efficiency of more than 6%. Hadron contamination can be kept at a few percent level. Hence a substantial increase of B-physics potential of CMS is expected by enlarging the events statistic accessible at low luminosity runs of LHC. ) CRN, IN2P3 CNRS / ULP, Strasbourg 2) Institute of Physics, Georgian Academy of Sciences, Tbilisi

2 Introduction With LHC runs of low luminosity, L 33 cm?2 s?, CMS will be able to perform a wide range of B-physics []. This is due to the good capability of the detector to trigger on muons, to precisely measure particle momenta and secondary vertices. A study performed recently has shown that a first-level trigger on low transverse momentum (p T > GeV) electrons can be implemented [2]. The goal of this note is to show that in off-line analysis (or at a higher trigger level) one can efficiently recognize low p T 2 GeV electrons with a good purity, even if CMS is not optimized for it. This can be achieved thanks to the high-resolution and fine granular electromagnetic calorimeter (ECAL) made of PbWO 4 crystals, characterized by a small Molière radius. These properties allow to exploit local isolation of the electromagnetic showers in ECAL if electrons itself are (semi-)isolated. It is the case in a low-p T b-jet as illustrated in Fig., where the distribution of distances R = p between p T > 2 GeV electrons and their nearest associated particle with p ass: T > GeV is shown. In more than 95% of events, electrons are isolated within a cone size of R =.. Well identified electrons can be used for b-quark tagging, as well as for J=! e + e? reconstruction [3]. Implications of the current analysis for CP violation measurements with CMS are discussed in ref. [4]. This note is organized as follows. We first discuss the tools for CMS detector simulation in section 2 and compare Monte-Carlo results on ECAL and preshower performances with test beam data in section 3. Results obtained with the proposed electron finding algorithm are discussed in section 4. A -recovery procedure and a comparison of various clusterisation algorithms are presented in section 5. The impact of the first-level electron trigger on electron/hadron separation is given in section 6. Conclusions are summarized in section 7. 2 Detector simulation To simulate detector performance we use the CMSIM package version 8 (CMS8) [5]. The geometry implemented is described in the CMS Technical Proposal (TP) [6], except for the preshower set-up. Particle tracking in the detector media are performed in two ways: muons and hadrons are treated by standard GEANT tracking [7], whereas electromagnetic showers are parameterized [8]. Shower particles are traced down to either MeV for electrons and photons, or to MeV for hadrons and muons. The following data cards are used to describe the detector: ICVERS =, overall TP CMS detector version ITVERS = 2, tracker version IEVERS = 2, PbWO 4 crystal ECAL IEHITS =, semi-fast version of ECAL IHVERS = 42, semi-fast version of hadron calorimeter (HCAL) 2. Tracker The tracker geometry used corresponds to the TP version. On average 2 measured points are provided for a straight track and half of the measurements have stereo information. The material budget of the tracker varies from 2% to 4% of a radiation length (X ) depending on polar angle. The tracker cable structure in front of ECAL contributes additional 2% of X [9]. The primary vertex, i.e. the proton-proton interaction point, is smeared by a Gaussian with a of 5 m and 5.3 cm in XY -plane and Z-coordinate, respectively (Z-axis is parallel to the proton beam). Tracks are reconstructed by the Kalman filter method []. Each track has to pass the following quality requirements: at least six measured points (N fit ) per track, see Fig.2a; length of the reconstructed track larger than cm; 2 =NDF < 6, see Fig.2b.

3 A realistic pattern recognition algorithm is not currently available in CMSIM (Kalman filter is guided by Monte- Carlo hits). Therefore, for particles with p T > 2.5 GeV, we assume a reconstruction efficiency of 9% in case of electrons and 95% in case of muons and hadrons. Track parameters, e.g. momentum, polar angle (), azimuthal angle (), are given at the first measured point. To compute the parameters of a particle at the point of production (which we assume to be the primary vertex), we propagate the reconstructed track back to the primary vertex, accounting for bending in a solenoidal magnetic field of 4 T. Impact points in the preshower detector and in ECAL are also obtained by propagating the tracks in magnetic field, as well as the impact parameter the distance of closest approach of the particle to the primary vertex. The distribution of differences between generated and reconstructed angles and are shown in Fig.3a and Fig.3b, respectively. The resolutions obtained from a Gaussian fit are: =.8 mrad and = mrad. The non-gaussian tails seen in the distribution for electrons are mainly due to bremsstrahlung in the tracker material. In Fig.3c we give the ratio of reconstructed to generated p T for electrons and hadrons. For hadrons this ratio peaks at one, while electrons momenta are underestimated in more than % of cases due to bremsstrahlung. 2.2 ECAL We use the TP version of ECAL with crystals arranged in a projective geometry. The barrel region extends up to jj < :56, whereas endcap covers pseudorapidity range of jj < 2:6. Transverse granularity is = :45:45 in the barrel region and varies from to in the endcap region, depending on. The size of the barrel-endcap transition region is = :87 and is filled with a cable structure. The Molière radius of PbWO 4 medium is 2 cm; the depth of the crystals is about 26X. Uniform light collection in crystals is assumed and no digitization effects are included. The energy resolution is given by =E = a= p E b c=e; () where a, b and c are the stochastic, constant and noise terms, respectively; incident energy E is in units of GeV. Test beam data show that values of a = 5%, b = :5% and c = :2 can be easily achieved with the current design of the CMS ECAL when energy is collected in 33 array of crystals. In our analysis we pessimistically assume the values quoted above (see also section 3). Fig.4a shows the ECAL energy resolution for various values of a, b and c: full and dashed lines correspond to the noise term of c = :2, while dash-dotted and dotted lines represent resolutions with c =. It is clearly seen, that at low energies the resolution is dominated by the noise term. To simulate this term we add an energy equivalent of noise with E = 25 MeV per crystal and apply a 2 E zero suppression cut (unless stated otherwise). Simulation results are indicated by points in Fig.4b, when energy is collected in a 57 array of crystals with and without magnetic field as well as for various ways of the noise term treatment. In a 4 T magnetic field and with a zero suppression cut the Monte Carlo reproduces well the expected energy resolution. 2.3 Preshower in endcap The preshower layout in front of the endcap ECAL is schematically shown in Fig.5. It differs from the TP version, but corresponds basically to the 995 test beam design []. The preshower detector consists of 5.2 cm +.56 cm thick lead plates serving as an absorber, interleaved with the 33 cm 2, 3 m thick silicon detectors of 2 mm pitch. The total thickness of the preshower material corresponds to about 3X. The first and the second plane measure X- and Y -coordinates, respectively. An example of an electromagnetic shower initiated by a 3 GeV electron in the preshower detector is shown in Fig.6. In order to parameterize electron/photon energy deposition in thin silicon planes, we fit the results obtained with detailed GEANT simulation of the preshower response with the function: E Si = log( + ae) E b ; (2) where E (in GeV) and E Si (in MeV) are the incident and deposited energies, respectively; a and b are free parameters. Results of the fit are shown in Fig.7. This parameterisation of the energy deposited in silicon planes of the preshower detector was not tuned to reproduce the test beam data, thus results presented thereafter are pessimistic. Hadrons and muons are treated as minimum ionizing particles in silicon planes. Electronic noise with an energy equivalent of E = 2 kev per strip is superimposed on the signal. The energy threshold is set at 5 E [2]. 2

4 2.4 HCAL The hadron calorimeter description corresponds basically to the TP version, with a granularity = :87:87 for jj < 2: and two times bigger in 2: < jj < 2:6 region. The following features are of importance in our analysis: i) perfect matching between ECAL and HCAL trigger cells ( HCAL tower = 66 ECAL crystal array); ii) no massless gap between ECAL and HCAL instead, an approximate description of cables and service material in aluminum equivalent has been defined which is non-uniform in [3]. The energy resolution corresponds to the one quoted in the TP [6]: this is confirmed with the Monte-Carlo. =E = 65%= p E 6%; (3) Electromagnetic shower development in HCAL is parameterized as in ref. [4]. The hadronic part of shower is treated by GEANT. In order to take into account the energy deposited by neutral particles, HCAL is calibrated with pions of various energies. A linear fit through the simulated points is performed. The result is shown in Fig.8. An energy equivalent of electronic noise with E = 25 MeV per HCAL tower is added and a 3 E zero suppression cut is applied. 3 Comparison of Monte-Carlo and test beam data During the last two years several beam tests have been performed on PbWO 4 crystal matrix of the TP design geometry. We compare Monte-Carlo results to the data obtained in references [, 5]. For this particular purpose, we assume no magnetic field in our simulation; furthermore, the impact point of electrons is by definition the center of the crystal (as for the beam tests). 3. ECAL without preshower Results obtained from the Monte-Carlo for 5 GeV electrons and using two values for the stochastic term, a = 5% and 3%, are shown in Fig.9a and Fig.9b, respectively. Like for test beam data, no noise subtraction is applied. The energy collected in a 33 matrix, E(33), is about 3 GeV smaller than the incident beam energy because of shower leakage. In test beam data the energy sum in this matrix is shifted by hand to match the known incident energy. The corresponding distribution is shown in Fig.9c. From a Gaussian fit one obtains =E = :55% (i.e. a 5% stochastic term) and :36% (i.e. a 3% stochastic term) from Monte-Carlo and :23% from the 995 data. The more pronounced non-gaussian tails from simulations are mainly due to the assumed uniform light collection in crystals, as pointed out in ref. []. The energy deposited by 8 GeV pions in the same crystal matrix is shown in Fig.. Both, data and Monte-Carlo, show a prominent peak at zero and a few percent level plateau at higher energies. A longer tail is seen in the 994 data (Fig.b); it is understood as a consequence of direct ionization losses in Avalanche Photo Diodes [5]. With new Diodes this tail is reduced in 995 data (Fig.c). In our simulation the direct ionization effect is not implemented. This may explain the discrepancy with the data at very high values of deposited energies. 3.2 ECAL with preshower A few percent of the electron energy is lost in the lead of the preshower thus decreasing the energy collected in ECAL and degrading the energy resolution. To account for these effects we apply the energy correction procedure. The distributionof the energy deposited in both planes of preshower, E Si(+2) = E Si +E Si2, is shown in Fig.a. Here E Si and E Si2 stand for energies measured in the three hottest strips of the first plane and in the five hottest strips of the second plane of the preshower detector, respectively. Test beam and Monte-Carlo results (section 4.2) show that E Si(+2) contains more than 9% of total energy deposited in strips. The energy from a 33 matrix of crystals as function of the preshower energy is shown in Fig.b; a correlation is clearly established: the more energy is deposited in silicon the less energy is collected in the ECAL crystals. The energy correction procedure use information from each silicon plane separately: E corrected = E Si + E Si2 + E(3 3) (4) The distribution of uncorrected and corrected energies collected in a 33 array of crystals for 5 GeV electrons are shown in Fig.2a and Fig.2b, respectively. We see that after correction the mean value has increased and is equal 3

5 to the one obtained without the preshower detector (Fig.9a). The resolution has also improved from about 3:9% to 2:4%. The corresponding distribution for test beam data is shown in Fig.2c []. The energy sum is shifted in this case to match the known incident beam energy, i.e. 5 GeV. The energy resolution is better than the one obtained in our simulation. This is mainly due to the worse resolution we observe even without preshower in front of the ECAL (see previous section) and to the parameterisation we use for the energy deposited in silicon planes of the preshower (see section 2.3). With the 996 test beam data a better result on energy resolution,.% instead of.68%, has been obtained with the following design: 2.5X of lead, silicon plane and a shorter distance between the preshower detector and the crystals [6]. In the following, we apply a more simple energy correction procedure: E corrected = E Si(+2) + E(3 3) (5) because for low energy electron (E GeV), the dominant uncertainty comes from the parameterization (2) of the energy deposition in thin silicon planes. 4 Electron finding algorithm The electron finding algorithm is developed by making use of bb events generated with PYTHIA 5.7 [7]. The CTEQ2L structure functions [8] and the Peterson fragmentation functions [9] with b =.6 are used. bb pairs are generated with p b T > 2 GeV. No pile-up events have been superimposed since the study is devoted to low luminosity runs of LHC. In each event, we require at least one Bd. The following decay chain is then forced B d! J= K s! +? +? and selected according to the criteria described in ref. [4]. The accompanying B-hadron decays freely. The signal event is defined in case of b! e direct decay and background otherwise. Electrons from direct b-decays are called tagging electrons, e tag, because they tag the charge of the parent b-quark. In jj <2.6 region, about 7% of these electrons hit the barrel ECAL and 26% the endcap. The geometrical acceptance loss due to the barrel-endcap transition region is about 4%. An example of a signal event is displayed in Fig.3. In this particular case, one sees that, along with an e tag, there is a low-p T hadron, which deposits most of its energy in ECAL, thus faking another electron. Real electrons, e.g. from b! c! e cascades, Dalitz decays, -conversions, etc. are also sources of background. 4. Event preselection In a bb event we require at least one charged particle with p T > 2.5 GeV and jj <2.6, in addition to or coming from selected B d. In the subsequent analysis this particle(s) is (are) considered as possible etag candidate(s). A total of 2 generated events (6 signal events and 6 background events) are passed through the CM- SIM simulation package. We assume a branching ratio B(b! e)=. leading to a relative fraction of signal and background events of :9. This weight factor is taken into account when estimating signal contamination. Note that even in the signal event sample there are fake electrons representing internal background (see, e.g. Fig.3). In Fig.4a we show the generated p T spectra of electrons and hadrons. The events statistic corresponds to what is expected for an integrated luminosity of L int = 4 pb?. For p T > 2.5 GeV the number of hadrons is about 5 times larger than the number of electrons. Each e tag candidate has to satisfy the following criteria.. p T cut A track which passes quality cuts (see section 2.) must have a fitted p T > 2 GeV. About 5% of electrons are lost at this step, about half of them because of quality requirements. Such an inefficiency is mainly due to bremsstrahlung in the tracker material. 2. Impact parameter requirement The impact parameters, IP XY (in transverse plane) and IP Z (in Z-coordinate) must be less than 2 and 4 cm, respectively. These cuts reduce decay products of long lived particles and particles coming from secondary interactions. Distributions of IP XY and IP Z are shown in Fig.5a and Fig.5b, respectively. 4

6 3. ECAL cluster Each reconstructed track is propagated up to the ECAL surface. For electrons this extrapolated point may not match well the real impact point in case of late -radiation in the tracker. Thus, one proceeds in the following way. In the barrel, search for the crystal with the largest energy deposit in a region of = 57 array of crystals around the impact point. Collect the energy, E(57), in a = 57 array of crystals centered around this most energetic crystal. We take an asymmetric window in because the incident angle of a low-p T particle on the ECAL surface differs from 9 o (due to the bending in magnetic field) in spite of the projective geometry of crystals. In the endcap, a cluster is constructed around the hit crystal because of worse granularity and presence of preshower. Cut on cluster energy, E(57) > 2 GeV. 4. Track cluster matching The distance R E between the particle s impact point on the ECAL surface and the barycenter of the ECAL cluster has to be smaller than.7, see Fig.5c. We also require that there is only one track with p T > 2 GeV inside R E to avoid an ambiguity when tagging the b s. This requirement removes less than one percent of signal events because electrons in low-p T b-jets are (semi-)isolated, see Fig.. The distributionof generated p T after applying the preselection cuts 4 is shown in Fig.4b. At this step the hadron contamination is reduced by about 5 times compared to the initial ratio (Fig.4a), while the acceptance for signal electrons is about 8%. Results obtained at this step are summarized in tables and 2. Table : Cut values applied at each step of selection criteria Variables BARREL ENDCAP. 2 =NDF < 6 N fit 6 Event Length > cm p T > 2 GeV 2. jip XY j < 2 cm preselection jip Z j < 4 cm 3. E(57) > 2 GeV 4. R E <.7 5. S >.73 >.56 Electron/hadron 6. E Si > MeV E Si2 > 2 MeV separation 7. H=E <.4 <.4 8. E=p [.85;.5] [.85;.35] Table 2: Electron acceptance and hadron rejection factor of the selection criteria for particles with p T > 2.5 GeV. Inefficiencies due to pattern recognition and geometrical acceptance losses in barrel-endcap transition region are not taken into account. CUTS BARREL ENDCAP Relative Hadron Relative Hadron acceptance rejection acceptance rejection Event preselection Shower shape Preshower H=E E=p All cuts

7 4.2 Electron/hadron separation To further reduce hadron contamination other powerfull tools are used. 5. Shower shape Due to the fine granularity of the CMS ECAL and to a small Molière radius of the PbWO 4 crystals, an electron deposits most of its energy in a few crystals, see Fig.6. This results in a locally isolated electromagnetic shower which can be characterized by: S n = E(n hottest crystals)=e(5 7) (6) where E(n hottest crystals) is the energy sum in n crystals with the largest energy deposits. For the barrel region we show in Fig.7 hadron rejection factor versus electron acceptance for various values of n. Rejection factors and acceptances are quoted relative to the cuts applied previously. We see that for about 9% signal acceptance the optimal hadron rejection factor can be achieved for n = 3 or 4. In the following the value of S is calculated for the three hottest crystals. In Fig.8a distributions of S for electrons and hadrons are shown for the barrel region. A cut S > :73 reduces hadron contamination by a factor of three keeping 95% of the signal. Corresponding distribution for the endcap ECAL is shown in Fig.8b. The overlap between electron and hadron spectra is more pronounced in this case due to the presence of the preshower detector, which causes more developed, i.e. wider showers. A cut S > :56 is applied in the endcap region. At this step the signal to background ratio is about 2:3 (barrel) and :5 (endcap). 6. Preshower criterion Hadron contamination in the endcap region can be further reduced using the fact, that hadrons deposit less energy in the preshower than electrons. We extrapolate tracks up to the preshower silicon planes and search nearby for a strip with the largest energy deposit. Distributions of distances X and Y between the hottest strip and particle impacts are shown in Fig.9a and Fig.9b for their X- and Y -coordinates, respectively. We see that in most of the cases the hottest strip is found within 2:5 cm from the electron track. This is not the case for hadrons. The average energy deposit per strip in the first and second planes of the preshower detector are displayed in Fig.2. Most of the deposited electron energy is confined to three strips in the first plane and to five strips in the second plane. Distributions of the total energy deposit in the hottest strips of both planes of the preshower detector are given in Fig.2. The hadron spectrum peaks close to zero, while electrons deposit about 4 MeV on average in the first plane (7 MeV in the second plane). Requiring at least an energy of MeV (2 MeV) in the first (second) plane provides a hadron rejection factor of 8 keeping more than 9% of electrons. The signal to background ratio in the endcap region is now about 4:3. 7. H=E ratio Hadrons deposit most of their energy in HCAL. To exploit this fact, we compute the ratio H=E, where H is the energy sum in HCAL towers in a cone R around the particle direction and E is the energy E(57). First, we project the track direction onto the HCAL surface taking into account the bending in magnetic field. Distributions of energies deposited in HCAL towers by electrons and hadrons are shown in Fig.22a and Fig.22b, respectively. One clearly sees more activity behind the hadron clusters in contrast of the electron clusters. For the barrel region, the hadron rejection factor and the electron acceptance as function of H=E cut are shown in Fig.23a and Fig.23b, respectively, for various R=.2,.2 and.87. The optimal result is found for H=E <.4 with a R =.2. An electron acceptance bigger than 95% and a hadron rejection factor of.3 are achieved in the barrel region. In the endcap, a rejection factor of.4 is obtained with a H=E=.4 and R=.87 giving 99% electron acceptance. One should say, that the H=E requirement is strongly correlated with the preshower criterion. The low rejection power obtained with this criterion is mainly due to the strong magnetic field and dead material in the ECAL-HCAL transition region [3]. 8. E=p matching The ratio of the energy E(57) and the momentum p provided by the tracker is a very powerful tool for hadron rejection. This ratio is plotted in Fig.24a as function of the reconstructed p T for electrons. On the average, the E=p ratio is close to unity except for a tail seen at p T < 5 GeV. The main reason is the recovery of late -radiations; its 6

8 probability increases with p T as electrons are less bent in magnetic field and, consequently, radiated photons reach the ECAL surface closer to the electron impact. For comparison, in Fig.24b the E=p ratio versus p T is plotted for hadrons. In Fig.25a E=p distributions after event preselection cuts 4 are displayed for the barrel region. This ratio for electrons shows a narrow peak close to one, while hadrons populate lower values. For the endcap region the E=p ratio is shown in Fig.25b and Fig.25c, before and after correction for energy loss in the lead of the preshower (see section 3.2). Even after the correction procedure the electron/hadron separation is much worse than that in the barrel region. This is a consequence of the degradation of energy resolution in the endcap ECAL because of the preshower is located in front of it. The combined E=p spectrum for the barrel+endcap regions is given in Fig.26. To select electrons one keeps events in an interval centered at the electron peak. The hadron rejection factor versus the value of the E=p window cut is illustrated in Fig.27a for the barrel region. The signal acceptance curve is shown in Fig.27b. Depending on p T, a more optimal electron/hadron separation can be achieved by taking an asymmetric window around the maximum (see Fig.24). In our analysis the cut :85 < E=p < :5 is applied; 96% of signal events are kept and a rejection factor of 2 is achieved in the barrel region. For the endcap the optimal cut corresponds to the window :85 < E=p < :35. The corresponding signal acceptance is 9% with a hadron rejection factor of about 5. The signal to background ratios at this step are 5 and 5 in the barrel and endcap regions, respectively. Let us consider in more detail the usefulness of previously developed criteria (steps 5 7) for electron/hadron separation. In Fig.28a a distribution of E=p ratio after preselection cuts 4 is displayed. Selecting only on E=p in an interval centered at the electron peak the signal contamination would exceed 3% depending on cut value. Fig.28b illustrates the effect of the shower shape and preshower criteria (cuts 5 and 6); clearly, these two requirements reduce the background level by a factor of 4 in the region just near the electron peak. Fig.28c includes the optimal cut on H=E in addition; under the electron peak, the relative rejection factor for hadrons is only. for these low-p T particles, H=E criterion does not significantly improve the electron-hadron separation. All the selection criteria discussed above are listed in table ; the corresponding results are summarized in table 2. The electron acceptances are.72 in the barrel and.64 in the endcap regions, giving a global average of.7 for the total ECAL. These values do not include inefficiencies due to pattern recognition (a factor of.9 to be added) and to losses in the barrel-endcap ECAL transition region (.4 acceptance loss). Taking these factors into account we obtain an average electron acceptance of.6. Hadron rejection factors are 5 and 3 in the barrel and endcap regions, respectively. Worse results are obtained for the endcap compared to the barrel region because of the following reasons: ) a larger hadron activity and worse granularity result in an about five times larger particles density per crystal; 2) the presence of the preshower detector degrades the energy resolution of ECAL, leading to a less precise E=p matching and less reliable shower shape criteria. The remaining hadronic background comes mainly from two sources. First, hadrons which deposit all their energy in ECAL (see e.g. Fig.3) and second, incident charged particles which are accompanied by photons. A different source of background comes from real electrons and is discussed in detail in the following section. The p T spectrum obtained after all cuts of electron selection criteria is shown in Fig.4c. The electron finding efficiency is shown in Fig.29 as function of p T for the barrel and/or the endcap regions. Except for the first bin (2.5 GeV < p T < 5 GeV) efficiencies do not depend on p T. No significant -dependence of the electron finding efficiency is observed, except for the barrel-endcap transition region. 4.3 Electron sample purity For tagging purposes we consider events with only one electron tag candidate after all cuts. To characterize the purity of the sample we define the fraction W of wrong tags: W = N w =(N w + N g ); (7) where N w and N g are the number of events with wrong and good tags, respectively. Along with hadrons, real electrons may also contribute to wrong tags. Various sources of electrons are considered: 7

9 ) b! c! e cascade decay, 2) and Dalitz decays, 3) additional bb, cc pairs in the event. In the initial sample of 2 simulated events, we find all the above contributions, but with limited statistic. To estimate these backgrounds with a better accuracy a special study at the particle level (fast Monte-Carlo program) has been performed with a sample of more than 6 unbiased bb events. The efficiency of the electron finding algorithm as function of p T and is parameterized and is implemented into the fast Monte-Carlo program. Combined results from detailed (CMS8) and particle level simulations are summarized in Fig.3, where the fraction of wrong tags is shown as function of p T. One sees that hadron contamination is reduced to a few percent level and that the main contribution comes from cascade decays. Hadrons, Dalitz decays and extra b=c-quarks give correct tags in 5% of the cases, while b! c! e transitions yield dominantly wrong tags. This is taken into account when W is calculated according to (7). The curve in Fig.3 corresponds to the exponential fit. We also consider electrons from resonance decays and -conversions in the tracker material. The former contribute less than one percent because of their soft p T -spectra and due to small branching fractions into electrons, while conversions are strongly suppressed by impact parameter requirements. 5 Comparison of various clusterisation algorithms In addition to the fixed window algorithm (FW) there is another algorithm adopted by CMS which is based on dynamical clusterisation (DC) [2]. In this algorithm all crystals are ordered by decreasing energy deposition. The hottest crystal initiates the cluster. An adjacent by side crystal is joined to the cluster if it has lower energy deposition. The cluster is completed if there is no more adjacent crystal candidate. The whole procedure stops when all the crystals are assigned to a cluster. On average, 25 crystals are attached to one cluster with an energy of more than 2 GeV. 5. E=p matching The E=p ratio distributions for the barrel ECAL after applying preselection cuts 4 are shown in Fig.3a and Fig.3b for the fixed window and dynamical clusterisation algorithms, respectively. For a given interval around the electron peak, the best signal to background ratio is observed in latter case; it shows, however, larger tail for electrons at low values of E=p leading to a loss of the signal events. In the endcap region both algorithms give comparable results. 5.2 E=p matching with -recovery procedure In ECAL one can try to recover the photon(s) radiated by the electron. The recovery method is based on an estimation of the photon impact point in the ECAL, from the measured transverse momentum of the electron [2]. Depending on the charge of the electron, the maximal distance in azimuth between the electron and photon impact points ( max ) can be estimated assuming that the photon is emitted at the primary vertex. In an slice of crystal around the crystal hit by the electron and up to max we search for a cluster with significant energy and attach it to the original electron cluster. A detailed description of this recovery procedure using dynamical clusterisation algorithm (DCG) can be found in ref. [2]. In this case about 3 crystals are attached on average to one cluster of 2 GeV energy. A similar procedure is adopted for the fixed window algorithm: in an slice of crystal around the crystal hit by the electron and up to max we search for the most energetic crystal; around this crystal the energy, E(33), is collected in a 33 crystal array and is required to exceed.5 GeV; the new value of cluster energy is then the sum of E(57) and E(33) energies. This procedure is referred to as fixed window algorithm with -recovery (FWG) and is applied only in the barrel ECAL. 8

10 Results obtained in the barrel ECAL with these two algorithms after preselection cuts 4 are displayed in Fig.32. Both algorithms show larger hadronic tails compared to algorithms without recovery procedure; this is due to nearby accidental clusters which tend to increase hadron contamination. For example, the DCG algorithm gives as twice as much hadron background than the FW algorithm. In general, the minimal overlap between hadrons and electrons in E=p ratio distributions is achieved using the FW algorithm. We choose the fixed window algorithm (without -recovery procedure) to select low-p T electrons for the following reasons: ) for an optimal E=p window around the maximum it saves about 5% more signal events than dynamical clusterisation algorithms in the barrel ECAL; 2) in principal, the fixed window algorithm could be implemented at a higher trigger level. 5.3 Reconstructed versus initial electron energy In Fig.33a and Fig.33b we show distributions of the ratio of ECAL cluster energy to generated momentum for electrons using FW and FWG algorithms, respectively. All cuts of electron finding procedure are applied. The energy of a cluster reconstructed by the FWG algorithm is closer to the nominal energy of the electron, and the RMS of the distribution is smaller. For comparison, we show in Fig.33c an analogous distribution for the tracker. Despite the fact that this ratio peaks at one, we see a longer tail compared to the FWG algorithm. The reason is that electrons radiating in the beam pipe or the innermost layers of the tracker systematically give underestimated reconstructed momenta. The good results obtained from the FWG algorithm can be exploited, e.g. for effective mass reconstruction. One can proceed in the following way to profit from the good features of both algorithms: recognize electrons efficiently with the fixed window algorithm, and then recover the radiated photons with the fixed window algorithm with - recovery. 6 Impact of trigger on electron finding algorithm In ref. [2] a dedicated first-level, low-p T single electron trigger algorithm is described for the barrel region. It exploits the local isolation of the electron in a b-jet and absence of activity in HCAL behind the electron. The local isolation is defined using the following variable: R = E T (2 6)=E T (6 6); (8) where E T (66) is the transverse energy measured in a trigger cell, and E T (26) is obtained from a = 26 array of crystals. Out of 5 possible local regions the one with maximal R is determined. An event is kept if there is at least one trigger cell with R > :95. A detailed description of this algorithm can be found in ref. [2]. It allows to keep the QCD background trigger rate at an acceptable level of khz with a signal efficiency of 75% for p T > GeV. To study the impact of the trigger algorithm on electron/hadron separation, we generate another sample of bb events with a p T cut on generated b-quarks of 5 GeV and then apply the electron finding algorithm with the cuts described in section 4, except for the following: p T and E(57) more than 8 GeV and :9 < E=p < :35. The largest overlap between the trigger and electron finding algorithms is observed for the shower shape criterion. This is illustrated in Fig.34a, where we show the hadron rejection factor versus the threshold value S cut of the S parameter, with and without trigger requirement. For S cut > :73 the trigger algorithm has already reduced about half of the hadron contamination. This is due to the fact that both algorithms exploit local isolation of the electromagnetic shower. However, in case of the electron finding algorithm this is done in a more precise way thus reducing hadronic background by an additional factor of 2. The relative electron finding efficiency as function of p T is shown in Fig.34b with and without trigger. For p T > GeV, the average electron finding efficiency is bigger than 8% when the trigger is applied. This value has to be multiplied by the first-level electron trigger efficiency of 75%, resulting in an overall efficiency of 6% (to be compared to a 75% efficiency of electron finding algorithm alone at p T > GeV). 7 Conclusions The current study is performed with a GEANT-based simulation facility in which the implemented CMS detector essentially corresponds to the Technical Proposal design. The electron finding algorithm is optimized for low luminosity runs of LHC. With the CMS high-resolutionand fine granular ECAL made of PbW 4 crystals, characterized 9

11 by a small Molière radius, we demonstrate that electrons from b-jets with p T >2 GeV can be efficiently recognized. We find that: more than 2% of electrons are lost due to the material in front of the ECAL (2 6% of X depending on ) and to 4% geometrical acceptance loss due to the barrel-endcap transition region; the electron finding algorithm provides by itself more than 85% electron identification efficiency; a hadron rejection factor of >4 is achieved. Finally, this algorithm keeps about 6% of electrons from bb events with a signal to background ratio bigger than. This allows to tag b-quarks with a good purity: the hadron contamination is kept at a few percent level and the dominant source of wrong tags are real electrons. The current simulation for the preshower detector + ECAL gives worse results compared to that of the test beam data. Thus the performance obtained for the endcap region is pessimistic. Four different algorithms are examined to select low-p T electrons. The best electron/hadron separation and electron reconstruction efficiency are achieved with the fixed window algorithm when the cluster s energy is measured in a 57 crystal array. A good matching between the deposited energy in ECAL and the real momentum of the electron is obtained using the fixed window algorithm with -recovery. This can be exploited for effective mass reconstruction, e.g. for the decays J=! e + e? [3]. There is an overlap between first-level trigger and electron finding algorithms because both use local isolation of electromagnetic showers and an HCAL veto. Some of the steps of the selection procedure developed here could be implemented at a higher trigger level, e.g. more fine shower shape and more precise HCAL veto criteria as well as E=p matching (even with softer cut), when the energy of cluster is collected in a fixed window. At high energies, the Monte-Carlo results are verified by test beam data. It would be very desirable to have low energy electron and hadron data at 5 GeV, to cross-check the results obtained in this analysis. Acknowledgments We would like to thank Claude Charlot and Sasha Nikitenko for valuable support in software development. We are also thankful to David Barney, Philippe Bloch, Daniel Denegri, Ia Iashvili, Chantal Racca, Patrice Verrecchia for fruitful discussions. Special thanks to Jean-Louis Faure, Walter Geist, Yves Lemoigne and Martti Pimiä for carefully reading this manuscript. References [] D. Denegri et al., B physics and CP violation studies with the CMS detector at LHC, International Journal of Modern Physics A, Vol. 9, No. 24 (994) [2] C. Lourenço, A. Nikitenko and J. Varela, A low p T st level single electron trigger for beauty studies in CMS, CMS TN/95-97 [3] A. Kharchilava and P. Pralavorio, J=! e + e? Reconstruction in CMS, CMS TN/96-6 [4] A. Kharchilava and P. Pralavorio, Sensitivity to CP violation in CMS, CMS TN/96-7 [5] C. Charlot et al., CMSIM-CMANA Simulation Facilities, CMS TN/93-63, Version of December 7, 994 [6] CMS Collaboration, The CMS Technical Proposal, CERN/LHCC 94-38, 5 December 994 [7] R. Brun et al., GEANT-CERN Program Library, W53, October 994 [8] C. Charlot, Electromagnetic shower parameterization in CMSIM, CMS TN/94-32, X-LPNHE 95-5 [9] R. Ribeiro, Material Budget Calculation of the CMS Inner Tracker (Technical Proposal), CMS TN/94-36

12 [] S. Qian, Simultaneous Pattern Recognition and Track Fitting by Kalman Filtering Method for CMS Inner Tracker, CMS TN/96- [] D. Barney, Results from the 995 ECAL Test Beam with Preshower, CMS TN/96-6 [2] D. Barney, P. Bloch and V. Popov, Monte-Carlo Studies of Barrel ECAL with Preshower, CMS TN/ [3] A. Nikitenko and J. Varela, A simulation study of the ECAL / HCAL interface region, CMS TN/94-95 [4] V. Genchev and L. Litov, Fast simulation of the CMS hadron calorimeter using the parameterization of e.m. showers, CMS TN/94-49 [5] C.J. Purves, New values for electron / charged-pion Discrimination from the 95 CMS Electromagnetic Calorimeter Prototype, CMS TN/96-6 [6] Ph. Bloch, private communication [7] T. Sjöstrand, Comp. Phys. Comm. 82 (994) 74; PYTHIA 5.7 and JETSET 7.4, Physics and Manual, CERN-TH 72/93 [8] H.L. Lai et al., Global QCD Analysis and CTEQ Parton Distributions, Phys. Rev. D 5 (995) 4763 [9] C. Peterson et al., Scaling violations in inclusive e + e? annihilation spectra, Phys. Rev. D27 (983) 5 [2] P. Busson and C. Charlot, A method for Electron/Photon reconstruction in CMS PbWO 4 crystals ECAL, CMS TN/95-74 Figure captions Fig. distribution of the distance between electron and nearest particle, charged or neutral, in a b-jet. Fig. 2 a) number of fitted points per track; b) 2 =NDF distribution. Full and dashed lines correspond to electrons and hadrons, respectively. Fig. 3 a) the difference between generated and reconstructed polar angle; b) same for azimuthal angle; c) reconstructed over generated p T ratio. Fig. 4 ECAL energy resolution: a) the curves correspond to the TP parameterizations; b) solid curve corresponds to a TP parameterization and points are obtained with our Monte Carlo when energy is collected in 57 array of crystals. Fig. 5 the layout of the preshower in front of the endcap ECAL. Fig. 6 a shower initiated by a 3 GeV electron in preshower. Fig. 7 parameterization of the energy deposited in: a) first and b) second planes of preshower detectors. Points are obtained with detailed simulation. Fig. 8 calibration of HCAL. Points are obtained with detailed simulation. Fig. 9 a) and b) 5 GeV electron energy resolution obtained with Monte-Carlo for a stochastic term a = 5% and 3%, respectively; c) 995 test beam data. Fig. a) energy spectrum of 8 GeV pions obtained with Monte-Carlo; b) and c) 994 and 995 test beam data, respectively. Fig. a) distribution of energy deposited in silicon planes of preshower; b) energy measured in ECAL as function of energy deposited in silicon planes of preshower.

13 Fig. 2 a) and b) 5 GeV electron energy resolution obtained with Monte-Carlo without and with correction for the energy lost in the preshower, respectively; c) 995 test beam data. Fig. 3 a B d! J= K S! +? +? event display. Dotted lines represent photons. Fig. 4 a) p T spectrum of particles generated by PYTHIA; b) after preselection cuts is applied; c) after all cuts. Fig. 5 a) and b) transverse and Z impact parameters distributions, respectively; c) R E distribution. Fig. 6 average energy deposited in ECAL by: a) electrons and b) hadrons. Fig. 7 hadron rejection factor versus electron relative acceptance for shower shape cut. Fig. 8 shower shape parameter distribution in: a) barrel and b) endcap ECAL. Fig. 9 distance between track impact point and the most energetic strip in: a) first and b) second silicon planes of preshower. Fig. 2 average energy deposited per strip in: a) first and b) second silicon planes of preshower. Fig. 2 energy distribution in: a) first and b) second silicon planes of preshower after preselection cuts 4. Fig. 22 average energy deposited in HCAL behind: a) electron and b) hadron ECAL clusters. Fig. 23 a) hadron rejection factor and b) electron relative acceptance curves for H=E criterion for various R cone size. Fig. 24 p T -dependence of E=p ratio for: a) electrons and b) hadrons. Fig. 25 E=p distribution in: a) barrel; b) endcap before correction for energy lost in preshower and c) endcap after correction is applied. The cut values applied are indicated with arrows. Fig. 26 E=p distribution in barrel + endcap. Fig. 27 a) hadron rejection factor and b) electron relative acceptance curves for E=p criterion. Fig. 28 E=p distribution after cuts: a) 4, b) 6 and c) 7. Fig. 29 electron finding algorithm efficiency as function of p T. Inefficiencies due to pattern recognition and geometrical acceptance losses in barrel-endcap transition region are not taken into account. Fig. 3 fraction of wrong tags as function of p T. Fig. 3 E=p ratio distribution for various clusterisation algorithms in barrel ECAL: a) fixed window, b) dynamical clusterisation. Fig. 32 E=p ratio distribution for various clusterisation algorithms in barrel ECAL: a) fixed window with - recovery, b) dynamical clusterisation with -recovery. Fig. 33 reconstructed energy E in ECAL over generated momentum p ratio for: a) fixed window and b) fixed window with -recovery algorithms; c) reconstructed over generated momentum ratio. All selection procedure cuts are applied. Fig. 34 effect of first-level single electron trigger algorithm on: a) shower shape criterion, b) efficiency of electron finding algorithm. Inefficiencies due to pattern recognition and geometrical acceptance losses in barrel-endcap transition region are not taken into account. 2

14 .45 Electron Isolation in a b-jet: R e, ass. between e and closest particle Figure 3

15 Figure 2 4

16 Figure 3 5

17 .2. σ/e = a/ E b c/e a) a=5%, b=.5%, c=.2 a=2%, b=.5%, c=.2 a=5%, b=.5%, c= a=2%, b=.5%, c= Energy in a (5x7) array of crystals b) B = 4 T, no noise sup. B = 4 T, 2σ E noise sup. B = 4 T, no noise B = T, no noise a=5%, b=.5%, c= Figure 4 6

18 Silicon planes 2 X LEAD O X LEAD O C R Y S T A L S 45 mm 48 mm Figure 5 LEAD Si planes ECAL Figure 6 7

19 EM Parameterization in Preshower Figure 7 8

20 Calibration of HCAL Figure 8 9

21 Data Mean = 5. GeV σ/e =.23 % c) E (3x3) (GeV) Figure 9 2

22 b) c) Figure 3: Energy spectrum of 8 GeV? measured by 3 x 3 array of crystals. Upper plot is for '94 data, lower plot is for '95 data. Figure on E/p a very attractive proposition. In the test beam the momentum of the incident particles is known to a high precision (.%),the dominant error in E/p coming from the measurement of the energy. An E/p selection is possible by making a cut on the energy deposited in a 3 3 array of crystals. This is demonstrated in gure 4 which shows the energy spectrum of 8 GeV electrons with 2 vertical lines showing the events within 8 2 and 3 proposed cuts.

23 6 Mean Figure 22

24 Corrected Energy = E Si + E Si2 + E(3 3) Events per MeV Mean = 5.5 GeV σ/e =.68% Figure Data Corrected Energy in E 3x3 GeV c 23

25 pp! bb! e tag + B d(! J= K S) + X HCAL ECAL π e + π π + µ µ + Figure 3 24

26 Figure 4 25

27 Preselection in Barrel + Endcap Figure 5 26

28 Energy deposition in ECAL Figure 6 27

29 Shower shape cut in Barrel ECAL Figure 7 28

30 Shower shape criterion Figure 8 29

31 Figure 9 3

32 Figure 2 3

33 Energy deposition in Silicon planes Figure 2 32

34 Energy deposition in HCAL Figure 22 33

35 Figure 23 34

36 E/p matching in Barrel ECAL Figure 24 35

37 E/p matching after event preselection Figure 25 36

38 E/p matching after event preselection Figure 26 37

39 Figure 27 38

40 E/p matching in Barrel+Endcap ECAL Figure 28 39

41 Figure Figure 3 4

42 3 Mean Mean Figure 3 4

43 3 Mean Mean Figure 32 42

44 3 Mean RMS Mean RMS E Mean RMS Figure 33 43

45 Barrel ECAL Figure 34 44