Available on CMS information server CMS NOE 2003/006 he Compact Muon Solenoid Experiment CMS Note Mailing address: CMS CERN, CH-1211 GENEVA 23, Switzerland 24 March 2003 Study of H ττ with hadronic τ decays in CMS R. Kinnunen Helsinki Institute of Physics, Helsinki, Finland A. Nikitenko a) Imperial College, University of London, London, UK Abstract A detailed study for H ττ with fully hadronic final states in MSSM is presented with full simulation of the hadronic au rigger, identification of τ hadrons + ν in the tracker, τ tagging with impact parameter measurement, E miss measurement and Higgs boson mass reconstruction. he discovery range in the m A, tanβ parameter space is evaluated with parametrized impact parameter uncertainties from full simulation for b tagging. a) On leave from IEP, Moscow
1 Introduction In MSSM, the H and A couplings to the down type fermions are enhanced at high tanβ leading to a large branching fraction to bb and ττ pairs and to large production cross section in association with b quarks in pp bbh + X. As LEP [1] has excluded the low tanβ values, H ττ and H µµ have become the major discovery channels for heavy neutral MSSM Higgs bosons at LHC. For H ττ the final states ll, l + jet and two jets have been investigated in CMS [2, 3, 4]. he l + jet and two-jet final states have comparable branching fractions of 45.6% and 42.0%, respectively. For the ll channel the branching fraction is smaller (12.4%), which makes it useful only in the lower mass range m A < 300 GeV/c 2. A recent detailed study of the two-lepton channel with τ and b tagging with impact parameter measurement indicates that a visible signal can be still extracted with tanβ > 10 around m A 200 GeV/c 2 [2]. he two-jet final states are already shown to extend significantly the discovery range towards large masses m A 600-800 GeV/c 2 [4] and can be comparable in the tanβ reach to the ll and l + jet channels also at lower masses (m A 200 GeV/c 2 ) provided an efficient hadronic au rigger can be achieved. he searches in the three channels (ll, l + jet and two jets) can be eventually combined, which significantly extends the tanβ coverage, especially for m A < 200 GeV/c 2. his work is an update of the study of Ref. [4] with several important developments: Normalization of the cross sections and branching fractions to the results of exact one-loop calculations [5] and investigation of the sensitivity of the results to the SUSY parameters; Full simulation of the au rigger and off-line τ identification in the tracker; Full simulation of τ tagging with impact parameter measurement; Full simulation of the E miss measurement and Higgs boson mass reconstruction; Study of b tagging with parametrizations based on full simulation results. he main backgrounds are from Z, γ ττ, multi-jet production with jets faking τ s (thereafter called QCD background ), tt and W+jet events with W τν. he Z,γ ττ background can be reduced efficiently with b tagging thanks to the dominance of the associated production processes. he approximately 10 12 QCD di-jet events with E jet > 60 GeV for 60 fb 1 are a large potential background. o reduce the QCD and the W+jet background (one fake τ), the narrow shape and low multiplicity of τ hadrons + ν is exploited to obtain a rejection factor of > 1000 per jet. he b tagging gives another strong reduction ( 100) against the QCD di-jet background. Further reduction can be still obtained exploiting the τ lifetime with impact parameter measurements in one- and three-prong τ decays and τ vertexing in three-prong decays. Here results are shown for the impact parameter method. Good E miss measurement is necessary for efficient Higgs boson mass reconstruction. he amount of E miss in the signal events is however too small to allow the QCD di-jet background reduction to be comparable to that from b tagging with a cut on E miss. he tt background with W τν is irreducible against both τ and b tagging, as well against the E miss cut, but can be reduced with a central jet veto cut. Supersymmetry is potentially a source of large background as the τ s can be copiously produced in the decays of τ s, neutralinos and charginos in the squark and gluino cascades. One SUSY point has been tried in detail in which most of the τ s were found to be much softer than the signal τ s and less isolated because they are produced within multi-jet final states. hese τ s would be therefore rejected with energy and isolation requirements but a complete study of the SUSY parameter space has not been done to confirm generality of the statement. In the following, the expected searches for the heavy neutral MSSM Higgs bosons A and H are studied in the process H, A ττ, τ hadrons + ν. As leptons can be well identified in CMS, the leptonic decays of τ are excluded and are not discussed in the following. he A and H bosons are so degenerate in mass for large m A that their signals in the H, A ττ channel cannot be separated and are superimposed in this study. o simplify the discussion, the single charged hadron or the nearby charged (one or three) and neutral hadrons from τ hadrons + ν are often called a τ jet in the following. he simulation tools, the H ττ branching fraction and the production cross sections are briefly discussed first in Sections 2 and 3. he hadronic au rigger and the off-line τ identification in H ττ, τ hadrons + ν are discussed in detail in Sections 4 and 5. agging of b jets in bbh, measurement and Higgs boson mass reconstruction are discussed in Sections 6 to 8. Finally, the results of all the techniques discussed are merged to evaluate signal to background ratios in Section 9 and the conclusions are given in Section 10. E miss 1
2 Simulation tools he PYHIA6.1 [6] is used to generate events for the signal and for the backgrounds. he Higgs boson branching fractions are normalized to the results of the HDECAY program [5] and the signal cross sections to the results of the HIGLU (for gg fusion) and the HQQ (for gg bbh) programs [7]. Fast detector simulation is performed with the CMSJE package [8] which takes into account the detector resolutions as paramerizations obtained from full simulation studies, the acceptance and the main detector cracks. he GEAN-based full detector simulation package CMSIM [9] and the completee reconstruction package ORCA [10] are used to study the trigger issues, τ identification in the tracker, Higgs boson mass reconstruction and missing transverse energy for background rejection. Parametrizations based on the full detector simulations are exploited to study the b-tagging performance. A luminosity of 2 10 33 cm 2 s 1 is assumed. An average of 3.4 minimum-bias pile-up events is superimposed to each simulated event. 3 Branching fractions and cross sections Figure 1 shows the H ττ branching fraction as a function of tanβ for m A = 200 and 500 GeV/c 2 calculated with the HDECAY [5] program. he SUSY parameters are set to A t = 2450 GeV/c 2 (maximal mixing), M 2 = 200 GeV/c 2, µ = 300 GeV/c 2 and M g, q, l = 1 ev/c 2. he H ττ branching fraction is stable against the amount of stop mixing and the variation of slepton mass but is sensitive to M 2 and µ at large Higgs boson masses due to the opening of the neutralino and chargino pair production. For decreasing µ and M 2 the neutralinos and charginos become lighter and the decay thresholds move to lower m A towards the experimentally accessible H ττ range. Figure 1 also shows the variation of the ττ branching fraction as a function of the parameter µ, amounting to about 40% between µ = 200 GeV/c 2 and µ = 300 GeV/c 2. he variation as a function of M 2 is about 10 % for 120 GeV/c 2 < M 2 < 300 GeV/c 2. For lighter squarks and gluinos (M g = M q = 500 GeV/c 2 ), the branching fraction is enhanced by 14%. Figure 1: Branching fraction for H ττ as a function of tanβ for m A = 200 and 500 GeV/c 2 calculated with HDECAY for M 2 = 200 GeV/c 2, µ = 300 GeV/c 2 and A t = 6 ev/c 2. he dashed curve shows the branching fraction for m A = 500 GeV/c 2 with µ = 500 GeV/c 2 and the dash-dotted curve with µ = 200 GeV/c 2. Figure 2: Cross sections (LO) for gg H/A and gg bbh/a as a function of m A for tanβ = 30 with the CEQ4L structure functions and calculated with the HIGLU/HQQ package [7]. he two production mechanisms for the heavy neutral MSSM Higgs bosons at the LHC are the gluon-gluon fusion gg H (through loops of top and bottom quarks as well as squarks) and the production in association with b quarks in gg b bh. As the Higgs boson coupling to b quarks is enhanced at high tanβ (g Hbb cosα / cosβ and g Abb tanβ) the associated production dominates at high tanβ values and is about 90% of the total rate for tanβ > 10 and m H > 300 GeV/c 2. he LO cross sections for gg H/A and gg bbh/a as a function of m A for tanβ 2
= 30 calculated with the HIGLU and HQQ programs [7] and with the CEQ4L structure functions are shown in Fig. 2. he gluon fusion is mediated by quark and squark loops, and can be affected by stop mixing. However, due to the dominance of the tree-level associated production, and because only the CP-even Higgs is concerned by gluon fusion, the expectations for the heavy SUSY Higgs bosons are not too sensitive to the loop effects [11] in contrast to the lighter h production. he τ s in H ττ are produced with opposite helicity while in Z, γ ττ they are produced with the same helicity. In H ττ, when both τ decay to charged pions (and a neutrino), one of the pions tends to be emitted along the original τ direction and the other in the opposite direction (in the centre-of-mass frame of the τ s) while in Z, γ ττ both pions tend to be emitted simultaneously along the original τ direction or opposite to it. Due to the two possible spin configurations in the ττ final state the correlations are however not visible in the p spectra and are not simulated in this study. It has been checked that the selection efficiency does not change when the polarization effects are included. hey may be used in more dedicated variables (likelihood variables or neural network methods) to reduce further the Z, γ ττ and tt backgrounds as is proposed in Ref. [12]. 4 au trigger o exploit fully the two τ-jet final states, especially in the low ( 200 GeV/c 2 ) mass range, an efficient hadronic au trigger has been developed based on Level-1 calorimetric (ECAL+HCAL) selection, Level-2 electromagnetic calorimeter isolation [13] and a Level-3 tracking (isolation) with either pixel detector information [14] or regional tracking [15]. Updated results on the performance of the Level-1 and High-Level rigger (HL) au algorithms, obtained with the latest versions of simulation (CMSIM version 125) and reconstruction (ORCA version 6) software, are presented here for the luminosity of L= 2 10 33 cm 2 s 1. he Level-1 and HL trigger efficiencies are evaluated relative to the events selected at the PYHIA generator level (Section 5.1). For the isolation in the tracker, results obtained by exploiting only the pixel detector information are shown. he following definitions are used in the rest of the current section : he first (second) Level-1 τ jet is the first (second) jet in the τ-jet list provided by the Global Calorimeter rigger [16]. he jets in this list are ordered in E (the first jet has the highest E ); he first (second) calorimeter jet is a jet reconstructed at the HL in the calorimeter in the region centred on the first (second) Level-1 τ jet; he nominal pixel detector configuration with three barrel layers and two forward disks is called the full pixel detector whereas the start-up detector with only two barrel layers and one forward disk is called the staged pixel detector. 4.1 Level-1 au trigger he Level-1 au trigger is designed to enhance the efficiency to trigger the hadronically decaying τ s at low E values, in particular the τ s from the decays of low mass (200 300 GeV/c 2 ) Higgs bosons [13]. An updated version [17] of the Level-1 au trigger described in Refs. [13] and [16] is used in this study. Efficiency and purity of the first Level-1 τ jet for gg b bh, H ττ two jets (m H = 500 GeV/c 2 ) are shown in Figs. 3 and 4 as a function of p and η of the true (generator level) τ jet. he purity is defined as the fraction of the Level-1 τ jets being true τ jets. No Level-1 au trigger threshold is used. It should be pointed out that the purity (and efficiency) of the Level-1 τ jet depends on the topology of the physics channel studied and on the trigger thresholds; here only gg b bh is considered. he rates for the single and double Level-1 Jet and au triggers as a function of the thresholds are shown in Fig. 5. he Level-1 single au versus double au trigger thresholds are optimized in order to obtain an efficient trigger for both the two τ-jet final states from the gg b bh, H ττ and the single τ-jet final state from gb(g) H ± t(b), H ± τν τ-jet, t bjj for m H = m H ± = 200 GeV/c 2. he Level-1 trigger efficiency for the charged Higgs boson is evaluated relative to the events selected at PYHIA generation level with loose off-line analysis selection cuts on the τ jet: p τ jet > 80 GeV/c, η τ jet < 2.4 [18]. Figure 6 shows the iso-rate curves in the plane of E thresholds for the single and double au triggers. he efficiency points for H ττ and the H ± τν for m H = m H ± = 200 GeV/c 2 for a given multi-jet background rate are shown in Fig. 7. he working points for the Level-1 single and double au trigger rates of 3, 6, 8, an 9 khz 3
Efficiency and purity of first Level-1 τ jet 1.1 orca6. L=2x10 33 cm -2 s -1 1.05 1 0.95 0.9 0.85 efficiency 0.8 purity 0.75 Criteria of purity: 0.7 R(1st Level-1 τ jet - MC τ jet)<0.4 0.65 in gg bbh(500 GeV/c 2 ) two τ jets 0.6 0 50 100 150 200 250 300 p of MC τ jet (GeV/c) Efficiency and purity of first Level-1 τ jet 1.1 orca6. L=2x10 33 cm -2 s -1 1.05 1 0.95 0.9 0.85 efficiency 0.8 purity 0.75 Criteria of purity: 0.7 R(1st L1 τ jet - MC τ jet)<0.4 0.65 in gg bbh(500 GeV/c 2 ) two τ jets 0.6 0 0.5 1 1.5 2 2.5 η of MC τ jet Figure 3: Efficiency and purity of the first Level-1 τ jet for gg b bh, H ττ two jets as a function of p of the true τ jet for m H = 500 GeV/c 2. No Level-1 au trigger threshold is used. Figure 4: Efficiency and purity of the first Level-1 τ jet for gg b bh, H ττ two jets as a function of η of the true τ jet for m H = 500 GeV/c 2. No Level-1 au trigger threshold is used. are summarized in able 1. he thresholds quoted in parenthesis correspond to the true τ-jet transverse energy at which the efficiency of the trigger is 95%. hey are lower than the actual Level-1 thresholds since at Level-1 the energy corrections evaluated for the normal hadronic jets are applied for all type of Level-1 jets (Central, Forward and au) and therefore the energy of the Level-1 τ jet is overestimated. he relationship between the value of the threshold and the E of the generator-level τ jet is given by E (95%) = E (Level-1) 7 GeV. able 1: Working points of the Level-1 single and double triggers : the thresholds (absolute and 95% efficiency point) and the trigger efficiencies for H ττ and H ± τν for m H = 200, 500 GeV/c 2 and m H ± = 200 GeV/c 2 Rate 1 threshold (95%) 2 threshold (95%) ε(h ττ) ε(h ± τν) ε(h ττ) khz (GeV) (GeV) m H =200 GeV/c 2 m H ±=200 GeV/c 2 m H =500 GeV/c 2 3 93 (86) 66 (59) 0.78 0.81 0.90 6 82 (75) 60 (53) 0.87 0.84 0.92 8 78 (71) 57 (50) 0.90 0.85 0.93 9 76 (69) 56 (49) 0.91 0.86 0.93 he efficiency increases by 10 % when the rate for the single and double au trigger is increased from 3 to 6 khz and almost no gain is obtained increasing further the bandwidth. he working point at 3 khz is chosen as a baseline in this study. 4.2 High Level au rigger A further reduction of the QCD background rate by a factor 10 3 is possible at the High Level rigger. he QCD di-jet events were generated with PYHIA in several bins of p gen. he largest contributions to the Level-1 au rigger rate ( 85 95%) come from the following bins: 50 < p gen < 80 GeV/c, 80 < pgen < 120 GeV/c and 120 < p gen < 170 GeV/c. hese bins are used to evaluate the rejection factor of the HL against the QCD background. Both the signal and the QCD di-jet background samples are required to pass the Level-1 rigger selections described in Section 4.1. he first step of the HL is based entirely on the calorimetric information exploiting isolation in the electromagnetic calorimeter. he parameter P isol is defined as a sum over the transverse energy deposits in the electromagnetic 4
Level-1 rate, khz 10 2 10 1 Single and double Jet and au rates L=2x10 33 cm -2 s -1 1 Jet 2 Jet 10-1 1 au 10-2 2 au 60 80 100 120 140 160 180 200 Level-1 E threshold (GeV) Figure 5: Rates of the single and double Level-1 Jet and au triggers at L= 2 10 33 cm 2 s 1 calorimeter within 0.13 < R < 0.4, where R is the distance in the (η, ϕ) plane between each ECAL cell and the direction of the τ jet reconstructed at the HL. he τ identification at the HL starts with the reconstruction of a jet in the region centred at the Level-1 τ jet. he Iterative Cone algorithm [19] with a cone size of 0.6 is used. Only the calorimeter towers (with E > 0.5 GeV) within a cone of radius 0.8 around the Level-1 τ-jet direction are used to speed up the jet finding process. For each jet found, the electromagnetic isolation parameter P isol is calculated. Jets with P isol < Pisol cut are retained as τ candidates. he τ identification (at HL) in the calorimeter is called Calorimeter au rigger. he efficiency of the Calorimeter au rigger for H ττ two jets and for QCD di-jet events for different Pisol cut values is shown in Fig. 8; the calorimeter τ identification is applied to the first calorimeter jet in the event. he efficiency of the selection is almost independent of the Higgs boson mass. Details of the Calorimeter au rigger optimization can be found in Ref. [13]. he following High Level rigger stage uses also the tracker information to exploit isolation with track measurement. he tracks are searched for in a cone around the direction of the jet given by the calorimeter trigger. For the isolation (no tracks in the isolation cone accepted) the low-p tracks (in the GeV/c range) have to be reconstructed with good efficiency and with an acceptably low ghost rate. An accurate measurement of the track p is not needed. hese requirements can be met with a fast track-finding algorithm exploiting only pixel data [20]. he τ identification with the pixel detector [14] is called Pixel track au rigger. he efficiency of the Pixel track au rigger is shown in Fig. 9 varying the size of the isolation cone in the range 0.20 0.50. he Pixel τ identification is applied to the first calorimeter jet in H ττ and in the QCD di-jet events. he other parameters of the Pixel track au rigger are the size of the jet-leading track matching cone R m, the size of the signal cone R s around the leading track, the p thresholds for the tracks in the signal and isolation cones p m and pi (the definition of these parameters can be found in Ref. [14]); these parameters are optimized to yield the same efficiency for the one- and the three-prong τ jets in H ττ for m H 200 GeV/c 2. he typical parameter values are R s = 0.07, R m = 0.10, p m = 3 GeV/c, pi = 1 GeV/c. A comparison between the full and staged pixel systems shows that, for a constant QCD background rate, the signal efficiency in the staged scenario is reduced by approximately 10%. he complete HL selection for H ττ can be defined as the Calorimeter au rigger selection applied to the first calorimeter jet and the Pixel track au rigger selection applied to both calorimeter jets. he performance of this selection (called Calo+Pxl au rigger ) is presented below. he purity of the selected τ jets in gg b bh, 5
L1 double au threshold (GeV) 90 85 80 75 70 65 60 55 50 60 65 70 75 80 85 90 95 100 E (95%) L=2x10 33 cm -2 s -1 80 3 khz 75 6 khz 70 8 khz 65 60 55 50 9 khz 45 40 70 75 80 85 90 95 100 105 110 L1 single au threshold (GeV) ε(h 0 2τ 2jet) (%) 95 L=2x10 33 cm -2 s -1 90 85 3 khz 80 6 khz 75 8 khz 9 khz 70 70 75 80 85 90 95 ε(h + τν jet) (%) Figure 6: Iso-rate curves in the plane of the E thresholds for the single and double au triggers. Figure 7: Efficiency points for H ττ and H ± τν in hadronic final state for m H = m H ± = 200 GeV/c 2 for a given QCD di-jet background rate. ε(h(200, 500 GeV) ττ, τ 1,3h+X) 1.2 1.1 1 0.9 0.8 0.7 L=2x10 33 cm -2 s -1 Calo au rigger on first Calo jet M H =200 GeV/c 2 M H =500 GeV/c 2 0.6 0.5 0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ε(qcd bkg 50-170 GeV) ε(h(200, 500 GeV) ττ, τ 1,3h+X) 1 0.9 0.8 0.7 0.6 0.5 L=2 10 33 cm -2 s -1 Pxl au rigger on first Calo jet R S =0.07, R I is varied 0.2-0.5 R M =0.10 M H =200 GeV/c 2, staged Pxl M H =500 GeV/c 2, staged Pxl M H =200 GeV/c 2, not staged Pxl M 0.4 H =500 GeV/c 2, not staged Pxl 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 ε(qcd 50-170 GeV) Figure 8: Efficiency of the Calorimeter au rigger for the first calorimeter jet in H ττ two jets with m H = 200 and 500 GeV/c 2 and in the QCD dijet events. Figure 9: Efficiency of the Pixel track au rigger for the first calorimeter jet in H ττ two jets with m H = 200 and 500 GeV/c 2 and in the QCD dijet events for both the full and the staged pixel system. 6
H ττ is defined as the fraction of calorimeter jets being true τ jets. he purity of the first jet is high (0.98). o increase the purity of the second jet, the following algorithm is used. If the second Level-1 τ jet is not found in the list given by the Global Calorimeter rigger, or it is found but is too soft (E jet < 50 GeV) a new calorimeter jet, centred around the direction of the first Level-1 Central jet in the list, is reconstructed and taken as the second τ-jet candidate. he purity of the second τ jet increases with this method from 63% to 90% (for m H = 500 GeV/c 2 ). Exploiting the Calorimeter au rigger as a pre-selector before applying the Pixel track au rigger leads to a considerable reduction of the total CPU time per Level-1 event. he cuts are optimized by examining the background rejection of the Calorimeter au rigger step (S calo ), the efficiency for the signal and the CPU time required, while keeping the suppression factor of the overall High Level rigger selection at 10 3. he results of this study for m H = 200 GeV/c 2 are shown in able 2 for the full pixel system. he calorimeter suppression factor of 3 is found to provide the best signal efficiency for the total suppression factor of 10 3. he total time tot of the full HL path is then 59 ms per Level-1 event for a Pentium-III 1 GHz CPU. his time is well within the present HL constraint of 400 ms per one Level-1 trigger event. able 2: Signal efficiency and total CPU time for H ττ two jets (m H = 200 GeV/c 2 ) as a function of the Calorimeter au rigger background rejection factor. An overall suppression factor 10 3 for the hadronic jet background through the completee selection is maintained. Cut on the isolation parameter P isol (GeV) 10.4 7.6 5.6 4.6 4.0 3.4 3.2 2.6 Background rejection factor, S calo 1.0 1.5 2.0 3.0 4.0 5.0 6.2 7.5 10.0 tot = calo + pixel /S calo (ms) 110 85 72 59 52 50 45 43 41 Efficiency of Calo + Pixel au selection 0.35 0.37 0.40 0.42 0.40 0.39 0.37 0.36 0.35 Figure 10 shows the efficiency for the Calo+Pxl au rigger selection for the signal and for the QCD di-jet background. he size of the isolation cone R i is varied in the range 0.20 to 0.50, and the optimal suppression factor of three for the Calorimeter au rigger is used. For the total suppression factor of 10 3, there is a small difference in the efficiency between the staged and full pixel configurations at low luminosity. he HL efficiency for m H = 500 GeV/c 2 (with full pixel configuration) is almost the same (0.41) as for m H = 200 GeV/c 2 for the same total suppression factor of 10 3. Within statistical uncertainties, the HL efficiency for both the signal and the QCD di-jet background is independent of the Level-1 au trigger thresholds for 3 or 6 khz Level-1 bandwidth for τ s. 5 Off-line τ identification he τ identification in H ττ, τ hadrons + ν is based on low multiplicity (one to three charged hadrons), narrowness and isolation. In the study of Ref. [4], the τ-jet candidate (calorimeter jet E > 60 GeV) was required to contain one hard (p > 40 GeV/c) charged particle track within R < 0.1 around the calorimeter jet direction. By requiring this track to be well isolated in a cone of R < 0.4, the hadronic jets were suppressed by a factor of 3000 [4]. Here these results are updated with the track reconstruction efficiency from full simulation. More importantly, first results with the complete reconstruction algorithms and the trigger simulation are shown for the signal and for the QCD di-jet background in the E range of 50 GeV < E jet < 170 GeV where the contribution to the background is maximum. Only the one-prong hadronic τ decays (branching fraction 50%) were considered in Ref. [4]. Accepting all hadronic decays (branching fraction 65%) increases the signal rate by a factor of 1.7 with respect to the final states with one-prong hadronic τ s but the QCD di-jet background with three-prong jets is also significantly larger. However, this new background component can be suppressed by constraining the three tracks into a small cone in the centre of the jet. Figure 11 shows the R separation between the leading track (p > 40 GeV/c) and the other two tracks from H ττ, τ 3π with E τ jet > 60 GeV for m A = 500 and 200 GeV/c 2. For m A = 500 GeV/c 2, the decay hadrons are well contained within R < 0.03 (93%) while for m A = 200 GeV/c 2 such a narrow cone leads to a loss of 55% of the three-prong events. A constant trigger efficiency is obtained with a signal cone of R = 0.07, but it may not be possible to do so in the off-line analysis as the rejection power against hadronic jets deteriorates significantly with increasing the signal cone size (Section 5.1.1). 7
ε(h(200, 500 GeV) ττ, τ 1,3h+X) 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 L=2 10 33 cm -2 s -1 Calo+Pxl au rigger R S =0.07, R I is varied 0.2-0.5 R M =0.10 P em =5.6 GeV M H =200 GeV/c 2, staged Pxl M H =500 GeV/c 2, staged Pxl M H =200 GeV/c 2, not staged Pxl M H =500 GeV/c 2, not staged Pxl 10-3 10-2 ε(qcd bkg 50-170 GeV) Figure 10: Efficiency of the Calo+Pxl au rigger path for H ττ and for the QCD di-jet background when the size of the isolation cone is varied in the range 0.20 0.50. Results for m H = 200 and 500 GeV/c 2 are shown for the full and staged pixel scenarios. 5.1 Event reconstruction For the complete reconstruction, the ORCA version 6 is used. o study the QCD multi-jet background, fully simulated data samples with 50 GeV/c < p gen < 80 GeV/c, 80 GeV/c < p gen < 120 GeV/c and 120 GeV/c < p gen < 170 GeV/c (1.5 105 events each) are used. Events are generated with the preselection cuts E 1, E2 > 45 GeV, η 1, η 2 < 2.4. From these data samples only 9, 51 and 59 simulated events, respectively, survive the full trigger chain. When needed some results are shown also without trigger simulation to enhance the statistics. When the trigger is simulated, the HL τ jets are used as the τ-jet candidates. If the trigger is not simulated, the two hardest jets in a QCD di-jet event reconstructed in the calorimetry within a cone of 0.5 are chosen as τ-jet candidates. For the signal, the data samples for m H = 200 and 500 GeV/c 2 are used. he jets matching with the true τ jets are taken as τ-jet candidates if the trigger is not simulated. o estimate the jet rejection factor, expected to be 10 3 10 4, large numbers of QCD di-jet events have to be reconstructed. he reconstruction of all tracks in the event is too time consuming for this study. he two possibilities for fast reconstruction in the current ORCA software have been exploited: (i) the use of the pixel lines (tracks reconstructed in the pixel detector with the two hit recovery [20]) inside the two hardest calorimeter jets as seeds for the track reconstruction in the full tracker; (ii) the use of the regional tracking method to reconstruct the tracks inside the two hardest calorimeter jets with pixel hits as seeds. For the regional tracking method, the primary vertex z-position (longitudinal coordinate) is first determined with the pixel lines inside the hardest jets. he track reconstruction area is chosen within the jet reconstruction cone ( φ = η = 0.5) and within a window of 0.5 cm centred at the z-position of the primary vertex and 0.5 mm for the tolerance of the transverse impact parameter. his reconstruction region yields an efficient reconstruction inside the whole jet isolation cone. he two tracking methods are found to have similar performance. In the following mainly the results obtained with the regional tracking method are presented. 5.1.1 τ identification in the tracker For the off-line τ identification the leading charged particle track is first searched for in the τ-jet canditate defined at the High Level rigger or (if the trigger is not simulated) in the reconstructed calorimeter jet within R(track,jet axis) < 0.1. o include the three-prong τ decays, a small signal cone of size r centred around the leading track is defined. he signal cone is required to be isolated within a larger isolation cone of size R. he cone is defined 8
Figure 11: R between the leading track and the two other tracks from τ 3π ± + nπ 0 + ν for E τjet > 60 GeV, p > 40 GeV/c for the leading track and p > 1 GeV/c for the two other tracks for m A = 500 and 200 GeV/c 2. Figure 12: Efficiency for the three-prong τ selection (isolation, p hard > 40 GeV/c, three tracks in the signal cone) for signal events with m A = 200 and 500 GeV/c 2 versus the efficiency for hadronic jets with E τ jet > 60 GeV as a function of the isolation cone size. he signal cone size is varied between 0.02 and 0.07. to be isolated if no track with p >1 GeV/c is found in the area limited by the signal cone and R. For the Pixel track au rigger, the size of the signal cone is taken to be 0.07 and that of the isolation cone is 0.35. able 3 shows the efficiency of the off-line isolation criterion with these cone sizes for the events passing the full trigger chain for H ττ two jets for m A = 200 and 500 GeV/c 2 and for the QCD di-jet events in the bins 80 GeV/c < p gen < 120 GeV/c and 120 GeV/c < p gen < 170 GeV/c. In the signal events the τ s are isolated and thus 96-97% of them are found isolated when reconstructed in the full tracker. Since the track multiplicity in the hadronic jets can be large the increased reconstruction efficiency in the whole tracker relative to the reconstruction efficiency in the pixel detector leads to only 70-80% of the jets, found isolated at the HL, isolated also in the subsequent off-line reconstruction. In able 3, the isolation efficiency calculated with respect to the leading track as well as with respect to the jet direction are listed. No significant difference is found between the two methods and in the following the isolation is performed around the leading track direction. able 3: Off-line isolation efficiency for H ττ two jets with m A = 200 and 500 GeV/c 2 and for QCD di-jet events passed the full trigger chain. he isolation parameters r and R are chosen to be r = R s = 0.07, R = R i = 0.35 as in Pixel track au rigger. he isolation is applied around the leading track direction and around the jet direction. Isolation around leading track Isolation around jet direction m A = 200 GeV/c 2 0.920±0.006 0.918±0.006 m A = 500 GeV/c 2 0.944±0.004 0.945±0.004 < 120 GeV/c 0.512±0.076 0.488±0.076 < 170 GeV/c 0.625±0.077 0.625±0.077 QCD, 80 GeV/c < p gen QCD, 120 GeV/c < p gen As shown by fast simulation studies [4], the p cut of the leading track p hard > 40 GeV/c leads to an efficient QCD multi-jet rejection without too large a loss of signal events. It is therefore used in the following. A p hard cut optimization as a function of the Higgs boson mass can lead to a better signal-to-background ratio. For instance, the high E jets for the large Higgs boson mass range could be suppressed efficiently with an addional cut r τ = p max /Ejet > 0.4. An isolation cone with R = 0.4 is chosen. he three-prong τ selection is sensitive to the choice of the signal cone size r. For a small signal cone size, the efficiency for m A = 200 GeV/c 2 decreases due to the tracks from τ decay falling outside the isolation cone. For m A = 500 GeV/c 2, very narrow signal cones can be used due to strongly boosted τ jets. For hadronic jets, larger signal cone leads to a rapidly increasing QCD di-jet background as can be seen from Fig. 12, which shows the efficiency of the three-prong τ selection for signal 9
events with m A = 200 and 500 GeV/c 2 versus the efficiency for the hadronic jets varying the signal cone size between 0.02 to 0.07. In the following r = 0.04 is chosen. able 4 shows the τ-jet full selection efficiency for the signal events with m H = 200 and 500 GeV/c 2 generated with the process gg bbh, H ττ two jets. he off-line selection is less efficient for m H = 200 GeV/c 2 due to a softer leading track and less boosted τ jets. For easier comparison with the fast simulation results, to be discussed in Section 5.2, the off-line selection efficiencies are shown in able 5 for the signal events without the HL selections taking as τ-jet candidates the calorimeter jets matching the true τ jets. he efficiencies are shown for the events passing the cuts E j1 > 93 GeV and Ej2 > 66 GeV on the calorimeter τ-jet energy emulating the Level-1 single and double au rigger thresholds. able 4: Selection efficiency from full simulation and complete reconstruction for gg bbh, H τ τ with m A = 200 and 500 GeV/c 2. Shown are the production rate with tanβ = 30, the efficiencies for preselection, Level-1 and Calo+Pxl au rigger and off-line τ identification (E cuts, isolation, p cuts). Also shown are the efficiency and the numbers of events expected in 60 fb 1 for the full (trigger + off-line) one- and one- or three-prong selections. he last three rows show the total off-line efficiency with variable p cuts. m A = 200 GeV/c 2 m A = 500 GeV/c 2 σ(a,h) BR(H τ τ) BR(τ hadrons) 9.53 pb 0.188 pb E j1, Ej2 > 45 GeV, η j1, η j2 <2.4 30.9% 74.9% Level-1 and HL Calo+Pxl au rigger 32% 36% Off-line τ identification > 60 GeV 66.3% 91.4% Isolation 60.6% 84.2% p max > 40 GeV/c 21.0% 53.6% >40 GeV/c, one track in r <0.04 8.3% 19.5% E j1, Ej2 >40 GeV/c, one or three tracks in r <0.04 11.4% 36.2% otal efficiency (preselection, trigger, off-line τ identification) >40 GeV/c, one track in r <0.04 0.54% 4.8% >40 GeV/c, one or three tracks in r <0.04 0.75% 8.9% Events for 60 fb 1 >40 GeV/c, one track in r <0.04 3088 541 >40 GeV/c, one or three tracks in r <0.04 4273 1006 Off-line τ identification with variable p cut p max >40 GeV/c and p max /Ejet >0.4 20.0% 33.9% isol., p max >40 GeV/c, p max /Ejet >0.4, one track in r <0.04 8.1% 13.1% isol., p max >40 GeV/c, p max /Ejet >0.4, 10.8% 23.8% one or three tracks in r <0.04 able 5: Off-line τ selection efficiency for H ττ with m A = 200 and 500 GeV/c 2 with complete reconstruction, when the selections are applied on the true calorimeter τ jets with E j1 > 93 GeV and Ej2 > 66 GeV. he High Level rigger selections are not used. m A = 200 GeV/c 2 m A = 500 GeV/c 2 Isolation 42.8% 61.2% p max > 40 GeV/c 21.5% 49.3% > 40 GeV/c, one track in r <0.04 5.5% 12.7% > 40 GeV/c, one or three tracks in r <0.04 7.9% 23.3% he trigger and off-line selection efficiencies for the two QCD di-jet samples with 80 GeV/c < p gen < 120 GeV/c and 120 GeV/c < p gen < 170 GeV/c are shown in able 6. No events survive the off-line selection with the present simulated statistics. Statistics of > 107 events per p gen -bin would be needed for a detailed estimate of the QCD di-jet background. For the time being, this background can only be estimated with a parametrization of the rejection factor as a function of E jet under the assumption that the two jets are independent. For this study, the full trigger chain cannot be used as it is asymmetric between the two jets. Figure 13 shows the hadronic jet efficiency 10
able 6: Cross section and efficiency for the trigger and off-line τ identification for the QCD di-jet events. 80 GeV/c < p gen < 120 GeV/c 120 GeV/c < pgen < 170 GeV/c σ 3.6 10 6 pb 6.1 10 5 pb Level-1 and Calo+Pxl au rigger (2.2 ± 0.3) 10 4 (2.8 ± 0.4) 10 4 E j1, Ej2 > 60 GeV 72.9% 70.2% p max > 40 GeV/c 0.093±0.044 0.175±0.060 Isolation 0.140±0.052 0.225±0.066 p max > 40 GeV/c, Isolation 0.047±0.032 0.050±0.034 one or three tracks in r <0.04 < 0.023 < 0.025 as a function of E jet for the one-prong and the one- or three-prong selections. he statistics of the reconstructed events are limited here to 20000 for the two p gen bins. he results are shown for the signal cone r = 0.04, isolation cone R = 0.4 and for p max > 40 GeV/c. he rejection for the one- or three-prong hadronic jets is weaker in the high E region due to the more collimated τ -like configuration in the three-prong component. Figure 14 shows the hadronic jet efficiency as a function of E jet with an addional cut r τ = p max /Ejet > 0.4 and keeping the cut p max > 40 GeV/c to avoid a less efficient rejection of low E hadronic jets. he rejection against the high E jets clearly improves with a small ( 20%) loss of signal events at m A = 500 GeV/c 2 as can be seen from able 4. he p cuts for the other two tracks in the three-prong jets could be also optimized (p >1 GeV/c is used here) for better signal to background ratios. Figure 13: Efficiency for the off-line τ selection ( r < 0.04, p max > 40 GeV/c) for hadronic jets without trigger simulation within 50 GeV/c < p gen < 170 GeV/c as a function of E jet. Figure 14: he same as in Fig. 13 but with an addional variable p cut, p max /Ejet > 0.4. 5.2 τ identification with fast simulation he simulated samples for gg bbh, H ττ presently exists only for the signal and for a limited p range 50 GeV/c < p gen < 170 GeV/c of the QCD di-jet background. herefore the signal to background ratios cannot be estimated entirely with full simulation. In the following, the results of Section 5.2 are reproduced with the fast simulation applying the Level-1 trigger thresholds. For the track reconstruction efficiency, parametrizations based on full simulation are used [9]. able 7 shows the efficiency for the τ identification in the signal events gg bbh, H ττ, τ hadrons + ν for 11
m A = 200 and 500 GeV/c 2 with an event generation identical to that used for the fully simulated data samples. For 20% of the signal events at m A = 200 GeV/c 2, a matching true τ jet is not found. It is due to the τ s falling outside the detector acceptance and to occasional hard neutrinos from τ decays, which lead to low hadronic τ energy, insufficient to trigger the jet reconstruction. For m A = 500 GeV/c 2, these effects become small and the matching efficiency is high ( 93%). he results of able 7 can be compared directly to those of able 5 with full simulation and complete reconstruction, but without the trigger simulation. he τ-identification efficiency (isolation, p cuts, one or three prongs) is in a good agreement within 4% for m A = 200 GeV/c 2 while for m A = 500 GeV/c 2 the fast simulation yields about 20% higher efficiency. he inefficiency of the complete reconstruction may be due to the high track density in the τ jet for m A = 500 GeV/c 2. More elaborated track reconstruction methods than the standard one used in this work are now in progress in CMS [21] for the reconstruction of high-e τ jets. he total selection efficiencies (trigger and off-line) of able 4 include the calorimeter isolation performed at the trigger level and are then expected to be somewhat lower than those from fast simulation (able 7). he differencies in the final efficiencies in able 4 with respect to able 7 (larger by 1.4 for m A = 200 GeV/c 2 and smaller by 1.9 for m A = 500 GeV/c 2 ) can be explained by the different jet energy scales in the Level-1 au trigger and in the fast simulation but it requires more detailed investigations. able 7: otal production rate and selection efficiency from fast simulation for H, A ττ for m A = 200 and 500 GeV/c 2 with the Level-1 trigger thresholds. he total efficiency and numbers of events for 60 fb 1 are also shown. m A =200 GeV/c 2 m A =500 GeV/c 2 σ(a,h) BR(H τ τ) BR(τ hadrons + ν) 9.53 pb 0.188 pb Matching τ jets 79.7% 92.6% E j1 > 93 GeV, Ej2 > 66 GeV 8.3% 63.0% τ identification Isolation 39.0% 62.8% p max > 40 GeV/c 22.2% 51.8% >40 GeV/c, one track in r <0.04 5.7% 15.2% >40 GeV/c, one or three tracks in r <0.04 8.3% 29.9% otal efficiency >40 GeV/c, one track in r <0.04 0.38% 8.9% >40 GeV/c, one or three tracks in r <0.04 0.55% 17.4% Events for 60 fb 1 >40 GeV/c, one track in r <0.04 2174 1004 >40 GeV/c, one or three tracks in r <0.04 3145 1965 p max >40 GeV/c and p max /Ejet >0.4 20.6% 41.1% >40 GeV/c and p max /Ejet >0.4, one track in r <0.04 5.2% 12.3% isol., p max >40 GeV/c and p max /Ejet >0.4, 7.5% 23.8% one or three tracks in r <0.04 isol., p max Figure 15 shows efficiencies from fast simulation for the one and for the one- or three-prong selections ( r = 0.04, R = 0.40 and p max > 40 GeV/c) as a function of E jet for hadronic jets generated within 50 GeV/c < pgen < 170 GeV/c as for the full simulation and complete reconstruction in Fig. 13. Both simulation results are in agreement, thus largerly confirming the earlier fast simulation for H, A ττ two jets [4]. Figure 16 shows the efficiency from the fast simulation for a more complete QCD di-jet generation within 50 GeV/c < p gen < 470 GeV/c. he increasing efficiency factor for E > 100 GeV for the partial event generation in Figs. 13 and 15 turns to fall for higher E values for the one-prong selection and remains constant for the one- or three-prong selection. he study of Ref. [4] was performed with the default PYHIA structure functions (CEQ2L) and underlying event simulation. he data samples for the full simulation are generated with the CEQ4L structure functions. More importantly, a different structure for the multiple interactions is used with increased regularization scale for the transverse momentum in the multiple interactions. As a consequence, the number of charged particles with p > 1 GeV/c is increased from 3.2 particles with the default generation to 5.7 particles per rapidity unit in the central region, which affects the isolation. he efficiency of the isolation cuts in the signal events decreases by about 10% compared to the default generation used in Ref. [4]. All the fast simulation results shown in this work are performed with the parameters identical to those used for the fully simulated data samples. he example shows that a significant uncertainty on the final result may come from the physics description at the event generation 12
Figure 15: Efficiency for the τ selection with fast simulation ( r = 0.04, R = 0.40, p max > 40 GeV/c) on hadronic jets within 50 GeV/c < p gen < 170 GeV/c as a function of E jet. Figure 16: he same as in Fig. 15 but for 50 GeV/c < p gen < 470 GeV/c. level. 5.3 τ tagging with impact parameter he study of Ref. [2] has shown that the (small) τ lifetime (cτ 90 µm) can be exploited with impact parameter measurement in A, H ττ two leptons to reduce the backgrounds where the leptons originate from W or Z decay. For A, H ττ two jets, the impact parameter measurement can be used to further reduce the QCD di-jet background. he small difference between the track impact parameters in the τ jets and in the hadronic jets can be better exploited combining the measurements into one variable: σ 12 = σ ip (τ 1 ) 2 + σ ip (τ 2 ) 2 (1) where σ ip (τ 1 ) and σ ip (τ 2 ) are the impact parameter significances for the leading tracks in the two τ jets. Figure 17 shows the distribution of σ 12 for H ττ two jets with m A = 500 GeV/c 2 and for the QCD di-jet events with E > 60 GeV and p max > 40 GeV/c. he minimum number of hits in the track reconstruction is set to five. Requiring more hits could improve the QCD multi-jet rejection by removing part of the accidental large impact parameters in the hadronic jets [22]. he efficiencies for the cuts σ 12 > 3 and σ 12 > 5 for the QCD di-jet events are shown in Fig. 18. he signal efficiencies for m A = 500 GeV/c 2 averaged over the E jet values for these two cuts are 75 and 54%, respectively. he corresponding efficiencies for m A = 200 GeV/c 2 are 65 and 35%. he background contains a component with truely large impact parameters, from the decays of b and c hadrons from gluon splitting processes. he fraction of hadronic jets with heavy flavour decays in the E range studied here is found to be at the level of 3% for b s and 4% for c s, with a tendency to increase with E jet [22]. he sign of the impact parameter relative to the jet direction is not taken into account in this study and may give an improvement in the signal to background ratio. A detailed study on τ tagging with impact parameter measurement in H ττ is in progress [22]. he three-prong hadronic jets can also be suppressed with τ vertex reconstruction. Studies have started and indicate that a rejection factor of 5 can be obtained against the three-prong hadronic jets with an efficiency of 70% for the τ s [23]. About 90% of the hadronic jet production at LHC arises through the gluonic processes, gg gg, gq gq and gg qq. herefore no correlation is expected between the charges of the leading tracks in the two jets in contrast to signal τ jets. his feature can be used to obtain a further rejection of 2 against the QCD multi-jet background without any significant loss of signal events. he efficiency for the signal events is 98% for the one-prong τ s and 13
94% when the three-prong τ s are included. (he charges of the three tracks are added.) he efficiency for the QCD background is shown in Fig. 18 as function of the energy of the harder of the two jets. Figure 17: Distribution of σ 12 from full simulation for the one-prongτ decays in A, H ττ two jets with m A = 500 GeV/c 2 and for the one-prong hadronic jets in the QCD di-jet events with E > 60 GeV. Figure 18: Efficiency of the cuts σ 12 > 3 and σ 12 > 5 and of the charge correlation cut for the QCD di-jet background from full simulation. 6 b tagging in bbh he b jets in bbh are soft and distributed over a wide rapidity range. Figure 19 shows the E distribution within η jet < 2.4 for the reconstructed true b jets (b quark within R(b,jet) < 0.4) in bbh with m A = 200 GeV/c 2. he p distributions for the associated b quarks including both b and b are also shown in the figure. Figure 20 shows the corresponding η distributions for E jet > 20 GeV. he efficiency to find two reconstructed jets with E jet > 20 GeV within the tracker acceptance ηjet < 2.4 (excluding the τ jets) matching with the two b quarks ( R(jet,b quark) < 0.4) is very low ( 5%). he efficiency to find at least one such jet matching with a b quark is 36%. hese efficiencies could be somewhat improved with a wider jet reconstruction cone for the non-τ jets (0.5 used in this study for all jets). Hence the b-tagging efficiencies are relatively low for bbh even with a perfect impact parameter measurement, and tagging methods without jet reconstruction (reconstructing secondary verteces, for instance) could be more efficient. Parametrizations based on full simulation are used here for the impact parameter uncertainties. he b jets are searched for within the jets with E > 20 GeV and η < 2.5. A simple method of counting significant tracks inside a jet is used. he jet is tagged as a b jet if it contains at least two tracks with p > 1 GeV/c and σ ip > 2. Only one tagged b jet per event is required as the efficiency to find the second b jet in the signal events is very small. his trick allows a veto on the second jet to be used, so as to reduce the tt background containing two hard b jets. able 8 shows the efficiency to find at least one jet with E > 20 GeV (excluding the two τ jets), the efficiency that at least one of these jets is b-tagged and the purity of the tagging defined as a fraction of tagged b jets being true b jets ( R(tagged jet, b quark) < 0.4). No significant difference is found by demanding the tagged b jet to be the one with the best tagging probability or that with the highest E. 7 E miss measurement in H ττ two jets he QCD multi-jet background could be further reduced with a cut in E miss. he magnitude of Emiss in the signal events is however relatively modest, even for a heavy Higgs boson as can be seen from Fig. 21 showing the E miss distribution for m A = 200 and 500 GeV/c 2 after the main event selection cuts (E j1, Ej2 > 60 GeV). For m A = 200 GeV/c 2, in particular, the E miss of the selected events is so modest that no cut in E miss (well above the E miss resolution) is efficient. Figure 21 also shows the E miss distribution for the QCD di-jet events from fast simulation (these distributions are not used in the following event selection as the fast simulation may not be accurate for 14
Figure 19: p distribution for b quarks and E distribution for the reconstructed first and second true b jet ( R(jet,b quark) < 0.4) with η jet < 2.4 for bbh, m A = 200 GeV/c 2 with E τ jet1 > 93 GeV, E τ jet2 > 66 GeV. Figure 20: η distribution for b quarks and η distribution for the reconstructed first and second true b jet ( R(jet,b quark)<0.4) with E jet > 20 GeV for bbh, m A = 200 GeV/c 2 with E τ jet1 > 93 GeV, E τ jet2 > 66 GeV. able 8: Efficiency for finding a b-jet canditate (excluding the τ jets), efficiency for finding a b-tagged jet and the tagging purity for pp bbh, H ττ with m A = 200, 500 and 800 GeV/c 2, for Z ττ, QCD di-jet and tt backgrounds. Process Reconstructed jet Reconstructed b-tagged jet tagging purity A, H ττ, m A =200 GeV/c 2, tanβ=20 40.5% 15.3% 93.1% A, H ττ, m A =500 GeV/c 2, tanβ=30 46.1% 19.9% 93.7% A, H ττ, m A =800 GeV/c 2, tanβ=40 46.4% 20.3% 95.9% Z,γ ττ, m ττ >130 GeV/c 2 45.4% 2.1% QCD di-jet events, E jet >60 GeV 44.4% 1.5% tt, W τν 91.3% 52.0% 97.5% the small E miss values). he E miss measurement in H ττ two jets has been studied with full simulation, including jet energy corrections and is discussed in detail in Ref. [24]. his study yields a rejection factor of 13 from the cut E miss > 40 GeV for the QCD di-jet events with E j1,j2 > 60 GeV. As the measurement of small E miss values is sensitive to a number of detector effects, the rejection factor as obtained from full simulation is used in the following fast simulation study for the QCD di-jet background. However, as is shown in the following, a cut in E miss is not necessary if b tagging is used in the associated production channels. he E miss reconstruction is still required to be as accurate as possible to ensure the best H ττ mass reconstruction resolution. 8 Higgs boson mass reconstruction While a precise E miss measurement may not be needed for the reduction of the QCD multi-jet background, it becomes mandatory for the reconstruction of the Higgs boson mass in H τ τ events. Starting from the fact that the two neutrinos from the τ decays are emitted close to the directions of the τ jets, the Higgs boson mass can be expressed as M H = 2 E τ1 E τ2 (1 cosθ jj ) (2) where E τ1 and E τ2 are the τ energies given by E τ = E τ jet +E ν and E ν is the neutrino energy reconstructed from E miss and the jet energy components, by projecting the p miss vector onto the directions of the two τ jets. he angle θ jj is the space angle between the two τ jets. he mass resolution is thus proportional to the E miss resolution and 15