Search for the Standard Model Higgs boson via H ττ llνννν channel in CMS

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1 Scientifica Acta, No. 1, 3 17 (8) Search for the Standard Model Higgs boson via H ττ llνννν channel in CMS Umberto Berzano I.N.F.N. sezione di Pavia, Italy berzano@pv.infn.it A study of observing potential of the Standard Model Higgs produced via Vector Boson Fusion in the decay H ττ llνννν has been done using a full simulation of the CMS experiment. Higgs mass has been reconstructed using an approximation of the τ decay products direction and evaluating the visible fraction of the τ momenta. Some selection criteria based on Vector Boson Fusion topology have been studied in order to suppress the main background processes. he statistical significance has been evaluated for the eµ final state using a consistent sample of Monte Carlo mass distributions and fitting them with a binned likelihood approach. For a Higgs boson with a mass of 15 GeV/c and an integrated luminosity of 3 fb 1 a significance of 4.σ has been obtained. 1 Introduction Search for the Higgs boson and, hence, for the origin of electroweak symmetry breaking and fermion mass generation, remains one of the primary tasks of present and future high energy physics experiments. Direct searches at LEP and fits to accurate electroweak data suggest that the Higgs mass should be in the range 114 < m H < 85 GeV/c. hus searches and preliminary studies for the discovery of a low mass Higgs boson are the target of strong analysis efforts. he ability to either discover or establish the non-existence of Higgs bosons with masses up to 1 ev is one of the main goals of the next generation colliders, such as the Large Hadron Collider (LHC) at CERN. Four experiments will exploits LHC beams; in particular, the ALAS [1] and the CMS [] detectors are being assembled in order to search for the Higgs boson and new Physics beyond the Standard Model. At LHC several Higgs production processes can occur, the most probable being: gluon fusion, vector boson fusion and top associated production. he dominant production process is expected to be the gluon fusion; in the low mass range the vector boson fusion Higgs production has a significantly lower cross section (about % of the gluon fusion), nevertheless it has the advantage of additional informations in the event other than the decay products. he signature of vector boson fusion events is provided by energetic quark jets in the forward/backward direction together with the suppressed hadron activity in the central region [3]. For a Standard Model Higgs boson with a mass below the threshold of the decay into vector bosons, the process H τ τ is expected to have a considerable branching fraction. his decay channel can thus be searched for already in the first years of data taking and it is very important for the Higgs boson coupling studies. In this analysis both τ s are considered to decay leptonically, thus the signal fraction is just the 1.4% of the total H ττ events but the process has a cleaner signature than the lepton+τ-jet final state. We search for the vector boson fusion production of Higgs boson decaying into τ pairs with τ decaying leptonically (hereafter labelled as qqh, H ττ ll). Signal and Background Simulation For the present analysis, full simulation signal samples are needed. he signal samples were generated with PYHIA 6.3 Monte Carlo generator [4] with vector boson c 8 Università degli Studi di Pavia

2 4 Scientifica Acta, No. 1 (8) (WW and ZZ) fusion channels to produce the Higgs particle. he Higgs boson was forced to decay into a τ pair and τ leptons are then forced to decay into electrons or muons. In order to have both accurate kinematics and polarization, τ decay is obtained using AUOLA libraries [5]. A set of four different Higgs mass values is considered, i.e.: 115, 15, 135 and 145 GeV/c. Higgs production cross sections are calculated with VVH [6], Higgs decay branching ratios are evaluated at Next to Leading Order (NLO) with HDECAY [7]. In able 1 expected cross section values for Higgs production, Higgs decay and fully leptonic τ decays are reported; the last row collects the number of events generated for each signal sample. able 1: Calculated NLO cross section values of Higgs production and decays for different Higgs mass values. M H [GeV/c ] σ(qqh) [fb] σ(qqh) BR(H ττ) [fb] σ(qqh) BR(H ττ) BR(τ e, µ) [fb] event numbers he CMS detector response is simulated using GEAN4 [8]. he information about energy deposition and geometrical position is stored into detector dependent quantities, called hits, which contain all the details needed to simulate the detector response. Finally the effects of pile-up at low luminosity are added; pile-up events from the previous 5 and following 3 bunch crossings are superimposed to the on-time crossing in order to mimic the electronic readout behaviour and to take into account the energy pile-up in the CMS calorimeters. he final products are digitized hits (called digis), which are used as input for trigger and reconstruction simulations. he digis are supposed to be equivalent to real raw data collected by CMS. Background processes to qqh, H ττ ll are characterized by two energetic jets, two leptons and considerable missing energy in the final state. At present, the considered backgrounds are: t t W bw b with W l, Quantum ChromoDynamics (QCD) production of Z and γ decaying into ττ + jets and ElectroWeak (EW) ττ + jets. Z/γ µµ, ee decays are a potentially dangerous backgrounds for µµ, and ee final states, thus QCD Z/γ µµ, ee + jets and EW µµ, ee + jets are taken in account as well. he NLO cross section values for each background process are listed in able. In the third column the generator used are listed and in the fourth column the numbers of generated events for each sample are given..1 he channel t t W bw b, W e, µ, τ Given the H decay signature, the main physics background arises from t t production, due to the large top production cross section at the LHC and because the branching ratio BR(t W b) is essentially %. he leptonic decay of the W s leads to a signature similar to the signal. Due to the appearence of two b- jets that can mimic the forward vector boson fusion jets, t t events contribute to the background already at Leading Order (LO). Anyway, for QCD processes, soft gluon radiation occurs mainly in the central region of the detector. A veto against additional jets in such region can reject much more QCD backgrounds than electroweak signals. he t t background has been generated into several groups of samples with the main generator software packages, i.e.: PYHIA, OPREX [9], Alpgen, MadGraphII and CompHEP []. W bosons are forced to decay into leptons only; furthermore no kinematical preselections are applied. he NLO cross section for this process is assumed to be 86. pb.. QCD Z/γ ττ, µµ, ee plus or 3 jets he QCD Z/γ + jets production has a large cross section at the LHC. For electron and muon pairs in the final state, the Z-resonance peak can be vetoed by applying a cut on the invariant mass of the same flavour c 8 Università degli Studi di Pavia

3 Scientifica Acta, No. 1 (8) 5 able : Calculated cross section values of background processes. process σ [fb] generator events no. Pythia, oprex, t t W bw b, W l 86 Alpgen, CompHEP, MadGraph QCD Z τ τ +j 17.7 ALPGEN 4 QCD Z τ τ +3j 31. ALPGEN 63 EW τ τ +j 99 MadGraph 13 QCD Z µµ+j 9.8 ALPGEN 4 QCD Z µµ+3j 5. ALPGEN 63 EW µµ+j 98 MadGraph 13 QCD Z ee+j 6.8 ALPGEN 4 QCD Z ee+3j 51.7 ALPGEN 63 EW ee+j 98 MadGraph 13 di-lepton pair; τ pairs in the final state from Z τ + τ represent a potentially serious background for the Higgs search in the ττ decay mode. he QCD jets production of this process is quite complex to simulate: it is chosen to exploit the matrix element (ME) calculation in Alpgen [11] generator to produce multi-jet events. In order to produce a correct simulation of QCD multi-jet processes, it has been chosen to split the events into two groups: the -jet and the 3-jet events. In the -jet events sample only the exclusive QCD production of jets is allowed whereas in the 3-jet events sample an extra parton emission is allowed. Only events with M ττ > 7 GeV/c are considered and a selection on the two most energetic jets in the event is applied: η j1 j > 4., M j1 j > 6 GeV/c, p j > GeV, η j < 5. and r j1 j >.5, where j 1 and j are two highest p jets and r j1j is the jet separation in the η φ plane. he samples are then processed with PYHIA to produce the hadronization. o avoid double counting, a specific algorithm developed by M. Mangano [1] is runned at PYHIA level. For the Z/γ ττ samples the AUOLA package was used in PYHIA to force both τ leptons into leptonic decay. Resulting final cross sections are expected to be 31.5 fb for Z/γ ττ ll + 3 jets and 17.7 fb for Z/γ ττ ll + jets, 5. fb and 51.7 fb for Z/γ µµ + 3 jets and Z ee + 3 jets respectively and 9.8 fb and 6.8 fb for Z/γ µµ + jets and Z/γ ee + jets respectively..3 Electroweak production of lepton pairs plus jets he electroweak process Z/γ +jets is very similar to the signal process qqh. Since Z is a vector particle and the Higgs boson is scalar, the angular distributions between the scattered quarks must differ. A cut on the azimuthal separation between the tagging jets, φ jj, could be useful to reduce electroweak Zjj background which tends to produce back-to-back jets. he inclusive EW τ τ jj background source is produced with MadGraphII [13]. A preselection is applied on the kinematics of the jets at generator level: p j > GeV/c and M jj > 5 GeV/c. Further preselection cuts are applied on jets and τ s, given the limit of detector acceptance and requirements of c 8 Università degli Studi di Pavia

4 6 Scientifica Acta, No. 1 (8) event reconstruction: η j < 5., R jj >.5, R ττ >.4. Final cross section is expected to be 99 fb as given in able. 3 Event Reconstruction he signature of the process under investigation is characterized by two energetic jets in the backward/forward region of the detector coming from the Vector Boson Fusion (VBF) production that can be used to tag the process (hereafter called tagging jets ), and by the lack of hadron activity in the central region due to the electroweak nature of the VBF process. For both τ leptons, only the leptonic decay is considered, thus muons, electrons and four neutrinos are present in the final state and have to be reconstructed. As neutrinos cannot be detected, a considerable missing amount in the energy balance of the event is expected. 3.1 rigger Selection he considered process (H τ τ ll) is characterized by two light leptons in the final state, ee, eµ and µµ, thus a quite clean leptonic signature can be exploited to trigger the signal events. Assuming that CMS is running with the trigger described in ref. [14], events are required to pass at least one of the following trigger streams, both in Level 1 (L1) and in High Level rigger (HL): single-electron, double-electron, single-muon, double-muon. hus, the considered trigger streams are combined with an OR logic. At present, no combined single-electron/single-muon dedicated trigger stream has being developed in the CMS simulated trigger code, thus the eµ final state has to be triggered by the combination of single-electron and single-muon streams. With this choice, the High Level rigger gives 4.8% of positive responses for a 115 GeV/c Higgs mass and 47.4% for a 145 GeV/c Higgs mass. 3. Jet Reconstruction Jet reconstruction is a fundamental item in this analysis since VBF Higgs production is clearly identified by the presence of two jets in the backward/forward region of the detector (at high pseudorapidity values) and by a lack of jet activity in the central region. Moreover, jets are used to estimate the transverse missing energy. Jets are reconstructed starting from the identification of an energy cluster in both electromagnetic and hadron calorimeters. he reconstruction approach is based on an iterative cone algorithm on ECAL+HCAL calorimeter towers with a cone radius R =.5; with transverse energy E tower >.5 GeV and total energy E tower >.8 GeV. A Monte Carlo calibration is applied to establish the right energy scale over the complete pseudorapidity range [15] agging Jet Selection VBF tagging jets are expected to be quite energetic and in the forward/backward regions of the detector. he two most energetic jets are specifically selected as follows: tagging jets must be in opposite hemispheres, η j1 η j <, must be well placed in the HCAL acceptance, η j1,j < 5.; must be both energetic in the transverse plane, E j1,j > 3 GeV must be well separated in η j1j in order to reduce QCD background: i. e. η j1j >4. must have a large di-jet invariant mass, M j1j > 8 GeV/c finally the Higgs scalar nature implies that no angular separation between quarks is preferred whereas quarks from the vector boson Z production tend to be back to back; thus a cut on the azimuthal angle is applied, ( φ j1 j <.4). c 8 Università degli Studi di Pavia

5 Scientifica Acta, No. 1 (8) 7 cross section [fb] 3 Higgs signal EW ττ + j QCD Z + 3j, Z ττ QCD Z + j, Z ττ tt cross section [fb] 3 Higgs signal EW ττ + j QCD Z + 3j, Z ττ QCD Z + j, Z ττ tt η jj φ jj Fig. 1: Left plot: distribution of η jj for signal and backgrounds. Right plot: distribution of φ jj for signal and backgrounds. In Fig. 1a the distributions of pseudorapidity gaps η j1 j for Higgs signal with mass M H = 15 GeV/c and for four backgrounds. hey are normalized to cross sections and are shown in log scale. he backgrounds are: QCD Z/γ +(3) jets, EW ττ+jets and t t production. Energetic jets from QCD Z/γ +(3) jets background appear to be more separated in pseudorapidity than signal due to the preselection cut η jj > 4. applied at generator level. he two background processes with and 3 jets have the same shape, just rescaled for the relative cross section. EW ττ+jets distribution has a shape very similar to the signal one but with maximum value between 3 and 4 but about 17 times larger. It is worth to observe that a large amount of t t background events has a small pseudorapidity separation of the two most energetic jets with maximum value at about 1, thus it is efficiently rejected by this cut. Fig. 1b shows the azimuthal separation φ j1j distributions normalized to cross sections and in log scale. For Higgs signal the azimuthal separation shows a quite flat distribution. For QCD Z/γ +(3) jets φ j1 j is larger with increasing the separation; they have the same shape, just rescaled for the cross section values. EW ττ+jets background shows a larger φ separation: the distribution at φ j1 j =3 is an order of magnitude larger than at φ j1 j =1.5. hus it is efficiently rejected by the φ j1 j <.4 cut. 3.. Central Jet Veto In VBF Higgs production no colour exchange is possible between the two scattered quarks, thus no energetic hadron activity is expected in the central region of the detector. his peculiarity can be exploited to reject the QCD background which is expected to have a large gluon radiation in this region. hus, it is required that no additional jet with transverse energy larger than a fixed threshold lies in the central region between the two tagging jets: (η min +.5) < η j3 < (η max.5) where η j3 is the pseudorapidity value of the 3rd most energetic jet in the event and η min and η max are the pseudorapidity values of the two tagging jets; a.5 margin is required to avoid the counting of soft radiation near the two most energetic tagging jets. A threshold is applied on reconstructed tranverse energy of the 3rd jet without any calibration is fixed to 15 GeV. c 8 Università degli Studi di Pavia

6 8 Scientifica Acta, No. 1 (8) 3.3 ransverse Missing Energy Reconstruction he easiest way to recover the transverse missing energy is to consider the transverse energy measured in the calorimeter towers and sum them up: E miss towers = E i (1) his formula does not take into account muons which only deposit a small portion of their energy in the calorimeters. hus, if there are muons in the considered event, their energy has to be subtracted in order to determine the right missing E. Missing transverse energy reconstruction using only calorimeter towers, eq. (1), is deteriorated by the non linear calorimeter response due to the sizable e/h ratio of the towers themselves. hus, to improve E miss reconstruction, jet energy corrections are applied. he following formula can be used to reconstruct the missing transverse energy in the calorimeters [16]: E miss = j (E ) jet j C jet j i + i (E ) tower i C tower i () Here the first sum runs over all reconstructed jets in the calorimeter and the second sum runs over all calorimeter towers not used in jet reconstruction. he calibration coefficients C jet j and Ci tower are energy correction factors and are pseudorapidity and transverse energy dependent. We call type 1 correction if only jet corrections are applied (Ci tower = 1); we call type correction if both jet and tower corrections are considered. In this analysis E miss with type 1 correction is used. In such case, E miss becomes: ( = E tower + ) (E,jet Calib E,jet) Raw (3) E miss where E,jet Raw is the transverse jet energy without any calibration and ECalib,jet is the transverse jet energy after calibration corrections. E tower is the transverse energy sum in the calorimeter towers. Reconstructed missing energy with jet correction has a average resolution of 13%. 3.4 Electron Reconstruction and Selection Electron candidates are obtained combining an ECAL supercluster with a reconstructed track in the racker system. he following set of identification selections is also applied: electrons are required to have transverse momentum P > GeV/c electrons have to deposit a negligible amount of energy in the HCAL: E HCAL /E ECAL <.5 electron track transverse momentum and ECAL supercluster transverse energy E SC have to match in energy/momentum: E SC /p k >.8; 1/E SC 1/p tk <. electron clusters have to be isolated: Iso SC <. he cluster isolation Iso SC is defined as the sum of the transverse momentum of all the tracks which lie inside a cone in the η φ plane with R = η + φ =.35 radius and outside a cone of R veto =.1 (called veto cone) around the electron track direction divided by the cluster transverse energy measured in the ECAL: Iso SC = 1 E SC.1< R<.35 p track t (4) c 8 Università degli Studi di Pavia

7 Scientifica Acta, No. 1 (8) 9 he track matching the supercluster cannot be taken in the sum as it is supposed to come from the electron. A veto cone is defined in order to exclude the electron track from the sum. his selection has a 69% efficiency for all reconstructed electrons matched with Monte Carlo electrons coming from τ decay and 76% for the matched reconstructed electrons that pass HL. 3.5 Muon Reconstruction and Selection Muon reconstruction is performed starting from the muon candidate trajectory reconstructed with the CMS muon detector system and extending it back to the central silicon tracker. It is required that the muon candidates are isolated and have a transverse momentum P > GeV/c. Muon isolation Iso µ is calculated using reconstructed tracks in the tracker: the transverse momentum of the tracks that lie in a cone with radius R =.5 around the muon track direction are summed and the result is compared to a threshold value: Iso µ = R<.5 P track < P threshold (5) In this analysis the momentum threshold is fixed to 4 GeV/c. he considered selection has a 74% efficiency for all reconstructed muons and a 85% efficiency for the muons passing HL. 4 Higgs Mass Reconstruction he di-lepton final state is characterized by two charged leptons in the central region and missing transverse momentum from neutrinos. he following basic selections are applied: isolated leptons with opposite charge are required to lie in between the forward jets: η jmin < η l < η jmax (6) as the Higgs decay products are boosted, closed lepton pairs are considered, thus it is required that the two lepton separation in the η φ plane has to be R ll <.4 reconstructed missing energy is requested to be E miss > GeV. In order to reduce further QCD background, a cut on tranverse energy balance of the process is applied. he tranverse total energy is given by the module of the -dimensional vectorial sum of all the transverse momenta of the final state objects (i.e.: electrons, muons, jets and missing transverse momentum): P total = P l1 + P l + P j1 + P j + P miss (7) For signal events P total is small while for QCD backgrounds it has more pronounced tails due to an enhanced jet activity which is not taken into account in the sum. hus it is required that P total < 5 GeV/c. he kinematics of the Higgs boson decay results into high energetic τ s, therefore the directions of all final state leptons are close to the originating τ direction. It is thus possible to approximate the τ direction to that of the measured lepton (collinear approximation). Under this assumption, the transverse momentum of the Higgs boson can be evaluated by the vectorial sum of the charged lepton transverse momenta and the missing transverse momentum (see Fig. ). he next step is to evaluate the visible fractions of the two τ momenta, that is the τ momentum fractions carried by the two charged leptons, x τi : x τi = p lepti p τi, i = 1,. (8) c 8 Università degli Studi di Pavia

8 Scientifica Acta, No. 1 (8) Fig. : Scheme of the momentum vectors in the analyzed process. Collinear approximation is applied on the Higgs decay products. hey can be expressed in terms of the calculated transverse momentum of the Higgs boson and the measured transverse momenta of the charged leptons: x τ1 = p lept1,x p lept,y p lept1,y p lept,x p Higgs,x p lept,y p Higgs,y p lept,x (9) x τ = p lept1,x p lept,y p lept1,y p lept,x p Higgs,y p lept1,x p Higgs,x p lept1,y () he reconstruction works only if the τ leptons are not emitted back-to-back in the transverse plane. For τ decays the reconstruction must yield < x τ1, < 1. his condition can be used to reject background events. For instance, in t t production, the collinear approximation is not valid for leptons originating from W s because the W bosons and the top quarks receive only modest boosts. In this case a significant fraction of events is reconstructed with x τ1 < or x τ <. Many other events end up in the unphysical region x τ > 1. hus selected events must fulfill the relations: x τ1, x τ > x τ 1 + x τ 1 < 1 o show explicitly the difference in the visible fraction of the τ momentum distrubutions between signal and QCD background, in Fig.s 3 the scatter plots of x τ1 and x τ for Higgs signal (Fig. 3a) and t t production (Fig. 3b) are compared: while the signal events are concentrated in the central circular sector, t t events (and in general QCD processes) are spread all over the entire area. Once the visible fractions of the τ momenta are known, the invariant mass of the τ pair is given by m ττ = m ll xτ1 x τ (11) where m ll is the invariant mass of the two leptons in the final state. In Fig.s 4 the ττ invariant mass distributions are shown for each Higgs mass value considered in this analysis. he mass distributions are fitted to a gaussian curve: the mean values show a shift of the value about 5 GeV above the nominal Monte Carlo mass values, due to a systematic overestimation of missing energy. he resolution is extimated to be about 13%. It is dominated by the missing energy resolution whose contribution is about 75% of the total resolution. c 8 Università degli Studi di Pavia

9 Scientifica Acta, No. 1 (8) 11 t1x1 3 Higgs signal (15 GeV/c ) t1x1 3 tt production t1x t1x Fig. 3: Left plot: x τ1, x τ scatter plot for 115 GeV/c Higgs signal. Right plot: x τ1, x τ scatter plot for t t+jets background. H115 Entries 63 Mean RMS 16.1 χ / ndf / 9 6 Constant ± 5.3 Mean ±.7 Sigma 14.6 ±.6 H15 Entries 664 Mean RMS χ / ndf 7.98 / 9 6 Constant 97.9 ± 5.3 Mean ±.7 Sigma ± H135 Entries Mean RMS.4 6 χ / ndf 9.3 / 9 5 Constant ± Mean ±.9 3 Sigma 18.3 ±.9 m ττ [GeV/c ] m ττ [GeV/c ] H145 9 Entries Mean RMS χ / ndf / 1 5 Constant 84.1 ± Mean ±.8 3 Sigma 18.1 ±.7 m ττ [GeV/c ] m ττ [GeV/c ] Fig. 4: Reconstructed ττ invariant mass for different Higgs mass values: 115 (mean value = 118.5), 15 (mean value = 13.), 135 (mean value = 14.), 145 (mean value = 149.3) GeV/c. 4.1 Selection Efficiency and Expected Number of Events he cumulative cross sections and the relative efficiencies of each reconstruction and selection step for signal events are reported in able 3. c 8 Università degli Studi di Pavia

10 1 Scientifica Acta, No. 1 (8) able 3: Cross section σ and relative efficiency (in brackets) of the complete selection chain for Higgs signals (Higgs mass from 115 to 145 GeV/c. Selection 115 H 15 H 135 H 145 H step σ (%) σ (%) σ (%) σ (%) σ (fb) L1 trigger 9.48 (68.9) 3.65 (7.8) 16.6 (7.6) 9.15 (74.4) HL (59.) (61.1).9 (6.) 5.81 (63.6) ll selection 4.63 (6.5) 3.68 (5.4).5 (4.8) 1.35 (3.) E miss cut 4.7 (9.) 3.44 (93.6).4 (93.7) 1.8 (94.6) M ττ rec (79.5).83 (8.) 1.98 (84.6) 1.8 (85.1) V.B.F. sel..79 (3.).71 (5.).49 (4.9).7 (5.1) jet veto.69 (87.6).63 (87.8).43 (86.7).6 (96.) E balance.54 (78.).6 (77.).3 (6.6).18 (7.) tot. eff. 1.6% 1.45% 1.36% 1.49 % For signal events, the main reduction steps are the trigger response, the di-lepton selection and the VBF selection. he di-lepton low efficiency is caused by the electron and muon selections and by the R ll cut. In the VBF selection the steps that depress significantly the number of signal events are the pseudorapidity separation cut and the di-jet invariant mass cut. he total selection efficiencies for the inclusive leptonlepton (ll) final state for Higgs boson masses of 115, 15, 135, 145 GeV/c respectively, are given in the last row of able 3. ables 4 and 5 collect the cumulative cross sections and the relative efficiencies of each selection step for the backgrounds described in Sect.s and 3. Results depend on the process and on the applied preselection. able 4: Cross section σ and relative efficiency (in brackets) of the complete selection chain for the considered backgrounds with ττ channel. Selection QCD Z3j QCD Zj EW ττjj t t step σ (%) σ (%) σ (%) σ (%) σ (fb) L1 trigger (47.3) 5.7 (39.7) (59.9) (78.7) HL 69.6 (47.1) 3.6 (46.5) 74.9 (41.8) (7.5) ll selection (.7) 4.4 (18.7) 5.1 (7.) (.) E miss cut 1.65 (87.9) 3.8 (86.9) 4.59 (88.) (86.7) M ττ rec (67.9) 3.3 (79.) 3.11 (67.7) (7.) V.B.F. sel (19.).65 (1.4).39 (11.9).66 (.4) jet veto.7 (4.8).6 (93.1).8 (7.6).85 (3.) E balance.8 (4.3).49 (81.5).14 (5.).48 (56.3) tot. efficiency.9 %.38 %.5 %.55 3 % In able 4 cross sections for the background events with τ τ final states are summarized. rigger selection is useful on all backgrounds but t t bw bw process which is characterized by highly energetic leptons in the final state. his process, which is the dominant background, is then strongly reduced by di-lepton selection and by real τ reconstruction cuts which are included in the M ττ reconstruction. VBF selection is very useful to reduce EW τ τ background and t t production, the latter being further reduced successfully by the jet veto. QCD production of Z/γ background is reduced by VBF selection as well; it is worth to remind that a loose VBF selection is applied at generation level. his QCD background is then reduced by the di-lepton selection. he E balance cut is useful to reject backgrounds with an enhanced c 8 Università degli Studi di Pavia

11 Scientifica Acta, No. 1 (8) 13 able 5: Cross section σ and relative efficiency (in brackets) of the complete selection chain for the considered backgrounds with µµ and ee channels. µµ final state Selection QCD Z3j µµ QCD Zj µµ EW µµjj step σ (%) σ (%) σ (%) σ (fb) L1 trigger (7.5) (65.) 8.4 (94.1) HL (85.4) (87.1) 6.8 (93.) ll selection (9.8) (7.) (43.5) E miss cut (19.5) 14.4 (8.8). (19.6) M ττ rec..7 (1.1).3 (16.5).37 (.7) V.B.F. sel. 1.9 (17.7).5 (.6).1 (5.17) jet veto.65 (34.1).15 (6.).6 E balance. (33.3). (4.).4 (66.7) tot. efficiency.86 %.96 %.13 1 % ee final state Selection QCD Z3j ee QCD Zj ee EW eejj step σ (%) σ (%) σ (%) σ (fb) L1 trigger (71.3) (65.7) (66.) HL 66.5 (59.5) (55.6) 8.9 (55.4) ll selection (31.) 4.1 (7.7) 3.64 (8.1) E miss cut (19.9).68 (.3) 3.47 (11.3) M ττ rec (19.3).7 (1.).73 (1.1) V.B.F. sel (13.7).9 (4.).4 (5.9) jet veto.3 (17.5).5 (5.). (5) E balance.13 (4.9) - - tot. efficiency.5 % - - jet multiplicity, i.e.: QCD Z/γ + 3 jets and t t. he low relative efficiency of the EW ττ background is actually due to a statistical fluctuation caused by the limited statistics available. In able 5 cross sections for the background events with µµ and ee final states are given. It is worth to observe that the cross sections we start from for QCD processes are three orders of magnitude larger than signal cross section. For the analyzed backgrounds, trigger selection is less efficient in rejection as final state leptons are quite energetic. Anyway, as electron cuts in leptonic trigger streams are tighter, backgrounds with electron pair in the final states are more suppressed. he cut on missing energy and the real τ reconstruction selection are crucial steps in the suppression of these processes. As no neutrino is present in the final state, the cut on missing energy is really useful to reject events with Z or γ decaying directly into muon and electron pairs. Furthermore, as there is no τ decay, the cuts on the calculated visible fractions of τ momentum reject efficiently these events. Using the selection method described above the expected number of events can be calculated for integrated luminosities of 3 and 6 fb 1 and summarized in able 6. he 6 fb 1 results are two times the 3 fb 1 ones and are reported here just for completeness, thus we do not comment on them. In the upper part of the table the expected event numbers for signal are given. For a Higgs boson with M H = 115 GeV/c the expected number is 16., less than for the M H = 15 GeV/c case even if the latter has a lower cross section, anyway this result can be interpreted as a statistical fluctuation. As for background, the contribution of EW processes (7), () and (13) is low. he main contribution to background expected c 8 Università degli Studi di Pavia

12 14 Scientifica Acta, No. 1 (8) able 6: he expected number of events for different integrated luminosities. no. process 3 fb 1 6 fb 1 (1) 115 GeV/c Higgs () 15 GeV/c Higgs (3) 135 GeV/c Higgs (4) 145 GeV/c Higgs (5) QCD Z τ τ +3jets (6) QCD Z τ τ +jets (7) EW τ τ +jets (8) QCD Z µµ+3jets (9) QCD Z µµ+jets () EW µµ+jets (11) QCD Z ee+3jets <1.4 <.8 (1) QCD Z ee+jets 1..4 (13) EW ee+jets <.6 <1. (14) t t WbWb event number comes from t t production (14) and from QCD production of Z decaying into τ pairs, i.e.: (5) and (6). For each of these processes, event number is about three times the expected signal events with M H = 145 GeV/c (4). Processes with electron pairs in the final state [i.e.: (11), (1) and (13)] give a negligible contribution to the background expected number of events. he distribution of the invariant mass of the reconstructed τ s is shown in Fig 5 for the signal sample with M H = 15 GeV/c and all background processes. Events/5 GeV/c 5-1 L = 3 fb 4 3 Higgs signal (M = 15 GeV/c ) H QCD Z ττ + (3)j QCD Z µµ + (3)j QCD Z ee + (3)j EW ττ + j EW µµ + j EW ee + j tt bwbw m ττ [GeV/c Fig. 5: Reconstructed ττ invariant mass for background and Higgs signal; considered Higgs mass value is 15 GeV/c. ] c 8 Università degli Studi di Pavia

13 Scientifica Acta, No. 1 (8) 15 5 he H ττ eµ final state he eµ final state has less background sources thus making it easier to separate signal from background. With the above analysis, about signal events and about 16 background events are expected to be reconstructed at an integrated luminosity of 3 fb 1. In Fig. 6 the signal and background distributions are shown for a signal sample with M H = 15 GeV/c. A gaussian curve is used to fit the signal distribution, whereas, for the resonance peak from the Z/γ decays, a Breit-Wigner function is used. Events from t t production are expected to be spread over the whole mass range but with the considered statistics their contribution is included in the Breit-Wigner tails. Events/5 GeV/c.5-1 L = 3 fb Higgs signal (M = 15 GeV/c ) H QCD Z ττ + (3)j EW ττ + j tt bwbw m ττ [GeV/c Fig. 6: Reconstructed ττ invariant mass for background and Higgs signal in the eµ final state assuming a Higgs mass value of 15 GeV/c. ] For an integrated luminosity of 3 fb 1 the number of signal events is very modest. hus, in order to extract statistical significance, we use ensembles of "Monte Carlo experiments". Starting from the distribution shape shown in Fig. 6, an experiment is built by making each bin fluctuating according to a Poisson distribution with the smeared bin value as a mean. It is reasonable that, in the initial analysis on real data, one is confident about the background shape but not about the absolute normalization. In this case, data can be fit with a sum of the signal and background shapes, presumably known, with the signal fraction as a free parameter. hus, as a model of the probability density function (pdf) in the signal+background hypothesis, we use: α F S + (1 α) F B (1) where F S is the pdf of the signal, which is a Gaussian and F B is the pdf of the background, which is a Breit-Wigner and α is the signal fraction. In order to extract the overall statistical significance of the signal a likelihood-ratio-based method has been used. Hence, to evaluate the CMS discovery potential for the Higgs boson in the considered fully leptonic channel, we use the likelihood-ratio estimator S L : S L = ln(l S+B /L B ) (13) where L S+B is the maximum likelihood value obtained in the signal+background binned likelihood fit, and L B is the maximum likelihood value from the binned background-only hypothesis fit. It is proven c 8 Università degli Studi di Pavia

14 16 Scientifica Acta, No. 1 (8) [18] that eq. (13) provides the significance in the common sense of number of standard deviations used in High Energy Physics. It is worth to observe that with this method the main systematic contributions are authomatically taken into account. Results for each mass values are summarized in able 7. able 7: Resulting significance for each considered Higgs mass with an integrated luminosity of 3 fb 1 and 6 fb 1. Higgs mass significance significance [GeV/c ] at 3 fb 1 at 6 fb Statistical significance for a Higgs boson with M H =115 GeV/c yields a value of.7, considerably less than the one obtained for the 15 GeV/c case, even if the former has a larger cross section. his value is affected by a modest separation between Higgs signal and Z resonance peak. An improvement in the mass resolution, which means an improvement in missing energy reconstruction, would help for sure in the separation between signal and background Z peak, thus increasing the statistical significance. On the other hand, Higgs bosons with M H = 135, 145 GeV/c are better separated but have a significantly lower expected cross sections. hus the 15 GeV/c mass case, for which the statistical significance yields a value of 4., would be a good compromise between the two situations. 6 Conclusions he possibility of observing in CMS the Standard Model Higgs boson via the qqh, H τ τ lepton+lepton channel has been considered for four different Higgs mass values in the low mass range (M H = 115, 15, 135, 145 GeV/c ). For this analysis the main background sources have been considered, i.e.: the reducible background t t+jets and the irreducible background arising from QCD and electroweak Z boson production with associated jets which can mimic the vector boson fusion quark jets. An effective rejection of these processes can be achieved by using the properties of the vector boson fusion (VBF) process i.e.: the topological and kinematical properties of the two tagging jets and the suppressed hadron activity in the central region. he Higgs mass is reconstructed using an approximation of the visible leptons directions and calculating the visible fractions of the τ momenta. he selection efficiency of the signal events is about 1.4% and the expected number of signal events at 3 fb 1 is about 16 for a light Higgs with a mass value of 115 or 15 GeV/c. Since the eµ final state channel is the most promising due to the reduced background contribution, the statistical significance has been evaluated using a binned likelihood method on an ensemble of "Monte Carlo experiments". Assuming an integrated luminosity of 3 fb 1, the statistical significance is about 4 for a Higgs particle with M H =15 GeV/c. For M H =115 GeV/c, which has a larger cross section, the significance drops to.7. Acknowledgements At the end of this work, I would like to thank Alexandre Nikitenko and Cristina Riccardi for their fundamental help in this analysis. I would like to thank also all the guys from CMS Higgs group. References [1] he ALAS Collaboration, ALAS echnical Proposal, CERN/LHCC 94-43, CERN (1994). [] he CMS Collaboration, CMS echnical Proposal, CERN/LHCC 94-38, CERN (1994). [3] J.D.Bjorken, Phys.Rev.47D (1993) 1. c 8 Università degli Studi di Pavia

15 Scientifica Acta, No. 1 (8) 17 [4] PYHIA Project, torbjorn/pythia.htm [5] S. Jadach, J. H. Kuhn, Z. Was, Comp. Phys. Comm. 64 (1991) 75. [6] M. Spira, VVH programme, [7] M. Spira, HDECAY, Comp. Phys. Comm. 8 (1998). [8] Geant4, html [9] S.R. Slabospitsky, L. Sonnenschein, Comp. Phys. Comm. 148 () 87. [] A.S. Beyaev et al., CompHEP-PYHIA interface: integrated package for the collision event generation based on ex act matrix elements, hep-ph/13. [11] M. Mangano et al., ALPGEN, a generator for hard multiparton processes in hadronic collisions, hep-ph/693 [1] M. Mangano, Merging multijet matrix elements and shower evolution in hadronic collisions, cern.ch/mlm/talks/lund-alpgen.pdf [13] F. Maltoni,. Stelzer, MadEvent: Automatic event generation with MadGraph hep-ph/8156 [14] CMS Collaboration, he ridas Project echnical Design Report. Volume : Data Acquisition and High-Level rigger, CERN/LHCC /6. [15] CMS Collaboration, CMS Physics echnical Design Report. Volume I: Detector Performance and Software, CERN/LHCC 6/1 [16] A. Nikitenko, S. Kunori, R. Kinnunen, Missing ransverse Energy Measurement with Jet Energy Corrections, CMS NOE 1/4 (1). [17] S.Bityukov, N.Krasnikov, Mod.Phys.Lett.A 13 (1998) 335 [18] S.S. Wilks, Annals of Math. Stat. 9 (1938) 6. c 8 Università degli Studi di Pavia