Application of the Tau Identification Capability of CMS in the Detection of Associated Production of MSSM Heavy Neutral Higgs Bosons Souvik Das Cornell University (September 11, 2006)
Decays of the Tau Lepton To detect a tau lepton, it is important to know what its major decay channels are. It has six major decay channels, two of which are leptonic and four hadronic. We tabulate them and their branching ratios below in Table 1. Leptonic Decays Channels Hadronic Decay Channels Decay Products Branching Ratio τ τ One Prong Jet Two Prongs Jet e ν eν τ 17.84±0.05% µ ν µ ν τ 17.36±0.05% τ τ τ τ π ν τ 10.90±0.07% π π 0 ν τ 25.50±0.10% π 2π 0 ν τ 9.25±0.12% + π π π ν 8.99±0.08% Kaonic, Pionic and other Jet decays 10.16% τ Table 1 Bayesian addition of probabilities tells us that in the event of two tau decays, the following will be the branching ratios for the general products tabulated below in Table 2. Branching Ratio jet + jet + missing energy 42% µ + jet + missing energy 22.5% e + jet + missing energy 23.1% e + e + missing energy 3.2% e + µ + missing energy 6.2% µ + µ + missing energy 3% Table 2 We will study the first three decay channels in this review.
Level One Algorithms for Tau Triggering A dedicated Level One Trigger exists for tau decays. It is hoped to provide efficient triggering on a low mass Higgs decaying to two tau leptons that decay hadronically. Using the Electromagnetic and Hadronic Calorimeters Figure 1 1. A generic array of 12x12 calorimeter towers is considered around an active spot. 2. It is divided into nine 4x4 regions as shown. 3. Each 4x4 region has a tau-veto bit associated with it. If more than 2 towers are active in the ECAL or HCAL, this tau-veto bit is set. Every tower has a programmable threshold of activation. For the ECAL it is typically 2 GeV and for the HCAL it is typically 4 GeV. 4. A generic jet is labeled a tau-jet if none of its nine tau-veto bits is on. 5. The four highest E T jets and the four highest E T tau-jets are sent to the global trigger for consideration as trigger objects. Figure 2 Figure 3 The efficiency of this algorithm as a function of E T is shown in Figure 2. It may be noted that efficiency is high (~0.7) for 50<E T <100 GeV, but drops off to 0.5 for 200<E T <250 GeV. It could be attributed to the firing of neighbouring trigger towers when a high E T tau-jet is incident. The efficiency of this algorithm as a function of pseudorapidity is shown in Figure 3. Once again, it is because an higher angle of incidence tends to activate a broader cluster of trigger towers.
High Level Algorithms for Tau Triggering Using the Electromagnetic Calorimeter As demonstrated before, the pions produced when a 40 GeV tau decays is highly collimated within 0.1 steradians. We exploit this fact in the first High Level Trigger that is done with the ECAL. The algorithm is outlined below: Figure 4 Define R 2 = η 2 + Φ 2 1. Use the jet axis as found by ECAL and HCAL in Level One Trigger. 2. Find the amount of transverse energy deposited in a region of R = 0.4 around it. 3. Subtract from that the energy found within R = 0.1 and call it P isol. cut E T ET = Pisol < Pisol R< 0.4 R< 0. 13 4. If the result of step 3 exceeds the parameter P isol cut then reject the jet else pass it. P isol cut as a parameter of this algorithm is varied and the efficiencies of tau-jet and QCD-jet acceptance for various ranges of E T is plotted in Figure 4. Figure 5 It can be seen that the rejection of QCD jets and the acceptance of tau-jets is most efficient at P isol cut 5 GeV.
Figure 6 Keeping P isol cut = 5 GeV/c, the efficiency of tau-jet identification was plotted as a function of E T in Figure 6. Different decay channels are plotted with different lines. A general decrease of efficiency with increasing transverse energy was noted. It may be attributed to more spraying of the jets at higher energy. Figure 7 Keeping P isol cut = 5 GeV/c and E T > 30 GeV, the efficiency of tau-jet identification was plotted as a function of η in Figure 7. Once again, a higher angle of incidence results in the jet traveling through more tracker material and activating a wider cluster of trigger towers in the calorimeter, thus reducing the efficiency of this algorithm. An isolation requirement based on information from the hadron calorimeter results in worse performance in addition to larger systematic errors.
Using the Silicon and Pixel Trackers Figure 8 The principle of tau-jet identification using the silicon and pixel trackers is outlined below with reference to the diagram in Figure 8. 1. The direction of the tau-jet axis is determined by jet reconstruction in the calorimeter outlined before. 2. A Matching-Cone of solid angle R m is drawn around the Jet-Axis. 3. Only tracks within the Matching-Cone with transverse momentum greater than p T m are considered. 4. The track with the highest transverse momentum is called the Leading-Track. 5. A Signal-Cone of solid angle R S is drawn around the Leading-Track. 6. All tracks within the Signal-Cone which have a z-impact parameter less than z tr are considered part of the tau-jet. There must be either 1 or 3 such tracks corresponding to 1 or 3 pions. 7. An Isolation-Cone of solid angle R I is drawn around the Jet-Axis. 8. All tracks within the Isolation-Cone that have z-impact parameters less than z tr away from the Leading Track and with transverse momentum greater than p T I are considered. If they are solely found within the Signal-Cone, the High Level Trigger accepts it.
Figure 9 It can be seen from Figure 9 that an Isolation-Cone size of 0.45 steradians rejects 1 in 2 QCD jets and is probably an optimum value. At the High Level Trigger, this Tracker Isolation is applied to both jets. The first jet defines the primary vertex and all tracks of both jets must originate from there, or else they are deleted. At the High Level Trigger, the tracks are not entirely reconstructed using both the Silicon and Pixel Detectors. Instead only the Pixel Detector is used to roughly reconstruct tracks from as little as 3 pixel hits. Essentially, 2 of the 3 hits are used first and matched in r-φ and z-r to establish track candidates. The matching cuts are optimised for tracks of p T ~1 GeV/c. Valid pixel pairs are matched with the 3rd pixel hit forming pixel-tracks. The momentum of these pixel-tracks is reconstructed without a primary vertex constraint. A list of primary vertices where tracks cross the z-axis is drawn up. Primary vertices (and their tracks) with at least 3 tracks are kept, and the rest are deleted. The High Level Trigger sequence described was used to study the decay of a Higgs boson to two taujets. RM was set to 0.1, p T ltr was set to 3 GeV/c and R S =0.07. Ri was varied as a free parameter.
Figure 10 Figure 10 shows the efficiency of accepting signal versus efficiency of accepting QCD multi-jet events. The Tracker Isolation was applied to only the first jet. Two Higgs Boson masses of M H = 200 and 500 GeV/c 2 were used. R i is varied from 0.2 to 0.6 in steps of 0.05. Figure 11 Figure 11 shows the same with Tracker Isolation applied to both jets. The first jet gets to decide the primary vertex. One can see a significant suppression of QCD jets.
Event Generation and Pre-Selections Offline Selection and Analysis H/A/h τ+τ- µ, jet Analysis The gluon-gluon fusion followed by associated Higgs production from b-jets that decays into two taujets was done in PYTHIA. The tau leptons were decayed using TAUOLA and events with one muon and one hadronic jet were selected. The Drell Yan background of Z/γ * decaying to two tau-leptons followed by further decay to a muon, hadronic jet and missing energy was done in PYTHIA. This event was produced in two ranges of invariant mass: 40 < m ττ < 120 GeV/c 2 and m ττ > 120 GeV/c 2. ττbb events were produced using PYTHIA in two energy ranges: 60 < m ττ < 100 GeV/c 2 and m ττ > 100 GeV/c2 The W + jet background was produced with p T > 20 GeV/c. The number of events after all selection had been estimated to be less than one, therefore SUSY background was considered negligible and not generated. The pre-selections at generation level were chosen in a way that signal events were likely to pass the trigger selection. The muon from the signal was isolated with no charged particles of p T > 1 GeV/c within a solid angle of 0.2 around its trajectory. The tau-jets were isolated with at most one other charged particle of p T > 1 GeV/c within a solid angle of 0.4 and without 0.1 from its trajectory. The leading track of the tau-jet was required to have p T > 3 GeV/c 2. Offline Selection Tau-jet identification offline uses the same algorithms (Calo-Pxl) and parameters in the High Level Trigger but with fully reconstructed tracks from the Silicon and Pixel Trackers instead of 3-point pixel-tracks. Instead of using the Jet-Axis as defined by the calorimeters in Level One, the sum of the momenta of reconstructed tracks is used. Additionally one or three tracks are required in the Signal- Cone. The Leading-Track is required to have p T > 10 GeV/c in case of one track and p T > 20 GeV/c in case of three tracks. To ensure that we are looking at associated bbh(a) production, one of b-tagged jet with E T > 20 GeV is required. The b-tagging efficiency including finding the jet is 17% for M A = 200 GeV/c 2 and 27% for M A = 500 GeV/c 2. Events containing the decay of a nearly on-shell W into a µ + ν are suppressed by a cut of 60 GeV/c 2 on the transverse invariant mass of the muon and missing transverse energy. All events containing more than just the tau and b jets in η <2.5 with E T > 20 GeV were rejected. This is called the Central Jet Veto and it reduces the tt background. EHCAL A threshold of 0.2 on the ratio f = is required to reject energetic electrons that may be pltr produced in tt and Wt backgrounds. It is seen to retain 90% of signal events while rejecting 95% of electrons. A cut on the upper value of f to 1.1 rejects jets with a large fraction of neutral hadrons. 80% of the signal events are retained while 50% of W+jet and bb events are rejected. r ϕ. Events with muons and jets back to back were rejected with a cut of cos( ( p r, ) > 0. 9962 And so were events with negative reconstructed neutrino energy. T E T
Efficiencies of Signal and Background The production cross sections and individual selection efficiencies for signals of M A = 200 and 500 GeV/c 2 are shown in Table 3. Table 3 The production cross sections and individual selection efficiencies for the background reducible processes are shown in Table 4. Table 4
The production cross sections and individual selection efficiencies for the irreducible background processes are shown in Table 5. Table 5 The systematic uncertainty of the number of non Z/γ * events is estimated to be 12%. The Z/γ * consists of two parts: the ττbb process and the Drell Yan ττ process. The jet scale uncertainty and b-tagging uncertainty contributes to an estimated 8% uncertainty in the number of ττ processes. A 15% uncertainty is estimated for the ττbb process. Reconstruction of the Higgs and Discovery Reach The reconstructed ττ mass distribution is shown in Figure 12. 20 fb -1 worth of data was simulated. Figure 12 As one can see, this channel is good for reconstructing a low mass Higgs around 200 GeV/c 2 but not a heavy Higgs around 500 GeV/c 2. The discovery reach through this channel in the M A tan β plane with 30 fb -1 worth of data in the maximum m h scenario is shown in Figure 13. The 5σ discovery area without the uncertainty in the background is bordered with the solid curve. The same with the uncertainty in the background is bordered with the dashed curve.
Figure 13 H/A/h τ+τ- e, jet Analysis Event Generation The gluon-gluon fusion followed by associated Higgs production from b-jets that decays into two taujets was done in PYTHIA. The tau leptons were decayed using TAUOLA and events with one electron and one hadronic jet were selected. The appreciable backgrounds that mimic the signal come from: Z/γ* -> ττ -> e + τ (jet) + missing energy bb Z/γ*, Z/γ* -> ττ -> e + τ (jet) + missing energy tt -> bbw 1 W 2, W 1 -> τ (jet) + missing energy, W 2 -> e + missing energy or W 2 -> τ, e, missing energy and τ -> e + missing energy W 1 t -> bw 1 W 2, W 1 -> τ + missing energy, W 2 -> e + missing energy or W 2 -> τ, e, missing energy and τ -> e + missing energy. (Generated with TOPREX.) The backgrounds that can fake the signal where a hadronic jet or an electron can be identified as a τ- jet are: W+jet, W-> e + missing energy Z/γ* -> e + e - bb Z/γ*, Z/γ* -> e + e - tt -> bbw 1 W 2, W 1 -> jet + jet, W 2 -> e + missing energy All tau decays were generated with TAUOLA. Offline Selection The isolated electron from the decay of one of the tau leptons was first searched for. The reconstructed electrons were first required to be isolated in the tracker demanding that no track with p T > 1 GeV/c was found within the solid-angle R = 0.4 around the electron trajectory. The ratio of hadronic cluster energy to electromagnetic energy was required was cut with E < 0. 2 The ratio of HCAL E EM
supercluster energy to track momentum was given a threshold E sup ercluster p track > 0. 8. The purity of the selected electrons was found to be 97.5%. The tau-jet identification was identical to the one used in ττ -> µ + jet analysis. E A threshold of 0.35 on pltr jets, similar to the threshold used in ττ -> µ + jet analysis. HCAL f = was used to reject highly energetic electrons that may be faking The charges of the tau-jet and electron were required to be opposite. At least one jet from the event was required to be a b-jet with E T > 20 GeV and η < 2.5. This reduces the tt background. This veto efficiency was found to be 60% for the signal and 5% in the background. r ϕ. Events with electrons and jets back to back were rejected with a cut of cos( ( p r, ) > 0. 9962 T E T Efficiencies of Signal and Background Table 6 shows the number of signal events with tan β = 20 and M A = 130 500 GeV/c 2 that remain after all the selection cuts are made. The remaining effective cross section (percentage efficiency) is tabulated corresponding to each selection method. Table 6 Table 7 shows the cross section of Drell Yan background processes trickling through the selections. It may be noted that the efficiency is almost three orders of magnitude less than signal efficiency.
Table 7 Table 8 shows the cross section for backgrounds involving Ws trickling down through the selections. Table 8 Background Uncertainties The uncertainty of the background selection can be split into the uncertainties in electron identification, calorimeter energy scales in identifying tau jets and b-tagging uncertainties. There was also an uncertainties in the cross sections of the various backgrounds. And finally there is the 3% uncertainty in beam luminosity. After accounting for all of the above, the uncertainties were estimated at 8.1% for Z/γ*, 15.9% for bbz/γ*, 11.1% for tt, 14.0% for Wt and 14.5% for W+jet events. Reconstruction of the Higgs and Discovery Reach The reconstructed invariant ττ mass distribution for M A = 200 GeV/c 2, tanβ = 20 and M A = 300 GeV/c 2, tanβ = 25 for 30 fb -1 worth of data are plotted in figures 14 and 15 respectively. The dashed line shows the sum of the Z/γ* and bbz/γ* backgrounds.
Figure 14 Figure 15 Figure 16 Figure 16 shows the 5σ discovery areas for this channel of exploration in the M A -tanβ plane for simulations without and with systematic uncertainties. 30 fb -1 integrated luminosity worth of data was taken.
Event Generation and Preselections H/A/h τ+τ- jet, jet Analysis PYTHIA was used to generate the signal event from gluon gluon fusion to the production of tau leptons as well as the background events of tt, Drell Yan production of Z/γ* that decay into tau-jets, W+jet, and Wt. In the background events mentioned all W and Z/γ* were forced to decay into tau leptons. The TAUOLA package was used for the decay and hadronisation of tau leptons. The ττbb background was generated with COMPHEP and propagated to PYTHIA for showering and hadronisation and decay of tau leptons. The Z/γ* generation was split into three bins of invariant mass 80 < m ττ < 130 GeV/c 2, 130 < m ττ < 300 GeV/c 2 and m ττ > 300 GeV/c 2. The W+jet background was generated with p T > 65 GeV/c. All events were preselected at generation level to have two tau-like jets. A jet is selected as tau-like if it has E T > 50 GeV, η < 2.4 and the transverse momentum of the leading track p T > 30 GeV/c. Offline Selection E T > 50 GeV was required on both tau-jets for M A = 200 GeV/c 2. For higher Higgs Boson masses asymmetrical cuts were used on the two jets: 100 and 50 GeV for M A = 500 GeV/c 2, 150 and 50 GeV for M A = 800 GeV/c 2. This is seen to reject QCD jets more effectively. Tau identification was done using Tracker Isolation described before. The parameters used were stricter than the ones at High Level Trigger and are R m =0.1, R S =0.04, R i =0.5, p T ltr =35 GeV/c and p T i =1 GeV/c. One or three charged tracks in the signal cone were required for low mass Higgs while effective background rejection was possible with the strict condition of only one charged track in the signal cone. The two tau-jet candidates were required to have opposite charges. At least one b-tagged jet was required in the event. Signal and Background Efficiencies Table 9 shows the efficiencies at the trigger and offline levels of event selection. N tracks = 1 or 3 for M A = 200 GeV/c 2 and N tracks = 1 for M A = 500 and 800 GeV/c 2. The QCD multi-jet background efficiencies are tabulated in Table 10. The selections were factorised into three groups. The first group included the Level One and calorimetric tau-jet reconstruction at High Level and Offline. The second and third groups were applied independently so as to decrease the statistical uncertainties. The second group is the tau-jet isolation at HLT and offline. Group three are those for the extra b-tagged jet and Higgs mass reconstruction. Table 11 summarises the number of expected events with 60 fb -1 and efficiencies of the selections for the some of remaining background events.
Table 9
Table 10 Table 11
Reconstruction of the Higgs and Discovery Reach Figure 17 Figure 18 Figure 17 shows the reconstructed invariant m ττ masses for the signals of M A = 200 GeV/c 2 and tanβ = 20 while Figure 18 shows the same for M A = 500 GeV/c 2 and tanβ = 30 for the maximum m h scenario. The thick solid line is the isolated signal. The normal solid histogram is the signal + background. The dashed histogram is the reducible QCD-jet background. The solid-dashed histogram is the irreducible background. The reaches of 5-σ discovery in the M A -tan β plane with and without systematic uncertainties are shown in Figure 19. Figure 19