The purpose of this work is the development of a new analysis technique that allows the determination of differential cross sections with respect to arbitrary kinematic variables. This is illustrated for top quark pairs production where two leptons are present in the final state together with two neutrinos that cannot be detected. By estimating the t¯t invariant mass and the angle between

the top quarks in the t¯t rest frame, the sensitivity to the presence of new physics is demonstrated. This technique, based on the matrix element method, makes the

optimal use of the experimental information given a set of theoretical hypotheses

Mattelaer, O.

Pin, Arnaud

English

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DOI 10.1393/ncc/i2012-11254-1Colloquia: TOP2011IL NUOVO CIMENTO Vol. 35 C, N. 3 Maggio-Giugno 2012Determination of differential cross sections from tt¯ fully leptonic,using the matrix element methodA. Pin(∗) and O. MattelaerCosmology, particle physics and phenomenology (CP3), Universite´ Catholique de LouvainChemin du cyclotron, 2 B-1348, Louvain-la-Neuve, Belgiumricevuto l’ 1 Marzo 2012pubblicato online il 5 Giugno 2012Summary. — The purpose of this work is the development of a new analysistechnique that allows the determination of differential cross sections with respectto arbitrary kinematic variables. This is illustrated for top quark pairs productionwhere two leptons are present in the final state together with two neutrinos thatcannot be detected. By estimating the tt¯ invariant mass and the angle betweenthe top quarks in the tt¯ rest frame, the sensitivity to the presence of new physicsis demonstrated. This technique, based on the matrix element method, makes theoptimal use of the experimental information given a set of theoretical hypotheses.PACS 14.65.Ha – Top quarks.1. – IntroductionEvidences for new physics in top quark pair production are predicted in many theoriesand can be observed by estimating differential cross section with respect to arbitraryquantities. However, in high energy collider physics, some observables cannot be fullyreconstructed using the detector information only. Techniques like kinematical fitting(KF) or matrix weighted template (MWT) have been developed to handle this difficulty— see for example [1]. This is for instance the case for top quark pair production, wheretwo leptons are present in the final state together with two neutrinos that cannot bedetected.In this proceeding, we present a technique named Differential Matrix Element Method(DMEM) [2] which estimates differential cross section using for each event a density ofprobability. This method will be developed in sect. 2. Section 3 presents first results inthe case of standard model hypothesis and afterwards in presence of an additional vectorboson decaying in a top-quark pair (e.g., Z ′ → tt¯). Finally the efficiency of this methodis quantified.(∗) Email: arnaud.pin@uclouvain.bec© Societa` Italiana di Fisica 229230 A. PIN and O. MATTELAER2. – Differential matrix element method (DMEM)The matrix element method [3] is a model-dependent technique providing a prob-ability that an observed event is compatible with a partonic configuration. The wholetheoretical information is used to constrain the unobserved kinematic variables. A weightis allocated to each event considering a specific theoretical frame, parametrized by α. Itcan be computed as the integral over all the possible partonic state of these probabilitiesas described by(1) P(pvis|α) = 1σα∫dx1dx2f(x1)f(x2)dΦ|Mα(p)|2W (p, pvis),where |Mα(p)|2 is the square of the matrix element at leading order for tt¯ productionand decay, f(·) is the parton density function, W (p, pvis) is the transfer functions anddΦ is the measure of phase space. The technique has been adapted to be able to esti-mate differential cross sections by estimating the probability density functions (pdf) ofarbitrary variables as(2)∂P∂m(pvis)|m0 = 1σ∫dx1dx2f(x1)f(x2)dΦ|M(p)|2W (p, pvis)× δ(m(pvis) −m0).Differential cross section estimator are built by combining all the normalized eventpdf’s, 1PdPdm . We dubbed this technique, Differential Matrix Element Method (DMEM)and implemented it in a private version of MadWeight [4]. An analysis based ona similar method was performed at CDF II to search resonant productions of tt¯ pairsdecaying semileptonically with an integrated luminosity of 4.8 fb−1 [5].3. – Prospect at LHCIn order to observe the feasibility of the techniquesMadGraph [6] samples of tt¯ eventsdecaying in the di-muons channel have been generated (√s = 14TeV) and passed throughPYTHIA [7] with ISR activated. A fast detector response simulation is performed usingDelphes [8]. Some selection criteria are applied, events are required to have exactly twojets with transverse momentum larger than 30GeV, and of two opposite-sign leptons withpT > 20GeV. Additionally, a transverse missing energy larger than 30GeV is required.Looking at the transfer function on jets energies, a double Gaussian shape allows toreproduce the resolution as simulated by Delphes (see fig. 1). Lepton energy as observedparticles directions are well reconstructed and parametrized by δ functions. We observedthat the differential curve, obtained with the DMEM, reproduces the theoretical curveswithout any significant bias as represented by fig. 1.A theoretical frame [9] with a spin-1 resonance decaying in tt¯ (Z ′ → tt¯ → lbνlbν)has been chosen to illustrate the efficiency of the method by the reconstruction of twodifferential cross section. The first one is the tt¯ invariant mass spectrum and the secondone the angle in the centre of mass frame cos(θ∗tt¯). The considered model includes aZ ′ with a mass of 1TeV. Several configurations have been tested according to differentcontaminations NZ′Ntot = (2, 3, 5, 8, 10)%. It is important to stress that the square matrixelement used in eq. (2) is the standard model one. Samples of 5000 events have beenanalyzed, corresponding to an integrated luminosity of 5 fb−1.The tt¯ invariant mass spectrum shows the presence of new resonances as illustratedby fig. 2. Selecting the events contributing above 700GeV in this spectrum, the angularDETERMINATION OF DIFFERENTIAL CROSS SECTIONS FROM TT¯ FULLY LEPTONIC 231Fig. 1. – Left: Probabilty of (Eparton − Ejet) obtained by the jet energy transfer function,W (Ep,Ejet), estimated with 100000 jet-parton pairs. Right: Mtt¯ normalised differential crosssection of 5000 top-quark pair events decaying in fully leptonic channel. The theoretical curveis the expected one at tree-level when neither ISR and UE are taken into account.Fig. 2. – Normalized differential cross section for Mtt¯ and cos(θ∗tt¯) for several samples of 5000events (5 fb−1) containing different ratios of Z′ events. Standard Model expected curves havebeen estimated on a sample of 100000 events.distribution cos(θ∗tt¯) was built. This variable is sensitive to the spin of the new physicsdecaying in top-quark pairs [9]. Deviations from the standard model are clearly visible,on both distributions, when the ratio of new physics increases. The shape of the cos(θ∗tt¯)distribution is in agreement with what is expected for a spin-1 hypothesis.To be able to quantify these tendencies, a χ2 estimator has been defined. Since eachevent provides a binned pdf, all bins are correlated to each other. Using 100000 tt¯ fullyTable I. – Confidence level for standard model exclusion computed on several samples for dif-ferent contamination of Z′ events.NZ′Ntot2% 3% 5% 8% 10%C.L. for S.M. exclusion 72% 95.6% > 99.998%232 A. PIN and O. MATTELAERleptonic events theses correlations have been computed. The χ2 is constructed as∑ijC−1ij(xi − xthi )σi(xj − xthj )σj,where i and j are the bins, σi the variance of bin i and Cij the covariance matrix element.This estimator is converted to a confidence level value of standard model exclusion,as shown in table I. With an integrated luminosity of 5 fb−1 looking at selected eventsamples, containing 2% of Z ′, the standard model is excluded at 72%. Increasing thenew physics proportions in the samples, the standard model can be excluded at 99.998%above 5% of Z ′ events.4. – ConclusionsFor top physics at LHC, MadWeight in combination with the Differential MatrixElement Method provides variables sensitive to new resonances decaying in top quarkspairs. The deviations observed in the tt¯ invariant mass spectrum have been quantified toestimate the power to discriminate between the standard model and beyond. Moreover,the angular variable cos(θ∗tt¯) provides information about the spin of the resonance. Thecurrent integrated luminosity recorded by CMS/ATLAS is sufficient to perform a firstanalysis with this method.REFERENCES[1] The CMS Collaboration, “First measurement of Top quark mass in pp collisions at√s = 7TeV”, in CMS PAS TOP-10-006 (2010).[2] Mattelaer O., “A New Approach to Matrix Element Re-Weighting” UCL Thesis: Ecoledoctorale en sciences, 220 (2011).[3] Kondo K., J. Phys. Soc. Jpn., 57 (1988) 4126.[4] Artoisenet P., Lemaˆıtre V., Maltoni F. and Mattelaer O., JHEP, 12 (2010) 068.[5] CDF Collaboration, Phys. Rev. D, (2011) 072003.[6] Alwall J. et al., JHEP, 09 (2007) 028.[7] Sjostrand T., Mrenna S. and Skands P., JHEP, 05 (2006) 026.[8] Ovyn S., Rouby X. and Lemaˆıtre V., “Delphes, a framework for fast simulation of ageneric collider experiment” arXiv:0903.2225v3 (2010).[9] Frederix R. and Maltoni F., JHEP, 01 (2009) 047.

Determination of differential cross sections from t¯t fully leptonic, using the matrix element method

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Determination of differential cross sections from t¯t fully leptonic, using the matrix element method

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