Table Of Content

6 1 Precise top mass determination using lepton 0 2 distribution at LHC n a J 8 2 ] h p - SayakaKawabata p e InstituteofConvergenceFundamentalStudies, h SeoulNationalUniversityofScienceandTechnology,Seoul01811,Korea [ E-mail: [email protected] 1 v 4 We present a new method to measure a theoretically well-defined mass of the top quark at the 8 6 LHC.Thismethodusesleptonenergydistributionandhasaboost-invariantnature.Weperforma 7 simulationanalysisofthetopmassreconstructionwiththismethodfortt lepton+jetschannel 0 → . attheleadingorder. We estimate severalmajoruncertaintiesin thetop massdeterminationand 1 0 findthattheyareundergoodcontrol. 6 1 : v i X r a 8thInternationalWorkshoponTopQuarkPhysics,TOP2015 14-18September,2015 Ischia,Italy (cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ Precisem determinationusingleptondistributionatLHC t 1. Introduction The top quark mass appears in a variety of discussions, as an important input parameter to perturbative predictions within and beyond the Standard Model (SM). Well-known examples are electroweak precision fits [1] and evaluation of the SM vacuum stability [2]. To reduce errors in thesepredictions, anaccurate valueofthetopquarkmassisdesired. ThetopquarkmasshasbeenmeasuredattheTevatronandLHCusingkinematicdistributions oftt decayproducts. Theirrecentcombined resultis173.34 0.76GeV[3]. However,ithasbeen ± aproblem thatthemeasured massisnotwell-defined inperturbative QCD.Thereason isthatthe- oreticaldescriptionsforthekinematicdistributions ofjets,whichareimplementedinMonte-Carlo (MC) simulations, rely on approximations and phenomenological models with tuned parameters. In this sense, the measured mass is often referred to as “MC mass” and should be distinguished fromtheoretically well-definedmassessuchasthepolemassandtheMSmass. Thepole massis defined as the pole position of the top quark propagator in perturbation the- ory. Reflecting the fact that there is nopole inthe propagator in non-perturbative QCD,the quark pole mass is sensitive to infrared physics and exhibits bad convergence properties in perturbative expansions. It is known that this difficulty can be avoided by using short-distance masses repre- sented by the MS mass. The relation between the pole mass and the MS mass is known up to four-loop order in QCD [4]. The pole and MS masses have been determined at the Tevatron and LHCmainlyfromtt crosssectionmeasurements. Thepresentaccuracyofthetopquarkpolemass isaround2GeV[5],whichisevenlarger thanthatoftheaboveMCmassmeasurements. Thissituationdemandsamoreprecisedetermination ofatheoretically well-definedtopquark mass. WiththeaimofdeterminingthetopquarkpolemassandtheMSmassaccuratelyattheLHC, wepresentanewmethodtomeasurethetopmass. Thismethodusesleptonenergydistributionand is called “weight function method.” Weperform asimulation analysis ofthetop massreconstruc- tion with this method at the leading order. This analysis will be a basis for further investigations withhigher-order QCDandothercorrections included. 2. Weightfunction method TheweightfunctionmethodwasfirstproposedinRef.[6]asanewmethodforreconstructinga parentparticlemass,andappliedtotopmassreconstructionattheLHCinRef.[7]. Thismethodhas twofeatures: usingonlyleptonenergydistributionandhavingaboost-invariantnature. Theformer allows extraction of a theoretically well-defined top quark mass. The latter reduces uncertainties related totopquarkvelocitydistribution. Using the top decay process t bℓn , the top quark mass can be reconstructed only from → lepton energy distribution D(E ). The procedure for the top mass reconstruction with the method ℓ isasfollows. 1. Computeaweightfunction givenby 1 W(E ,m)= dE D (E;m) (oddfn.ofr ) , (2.1) ℓ Z 0 EE (cid:12) ℓ (cid:12)er =Eℓ/E (cid:12) (cid:12) 2 Precisem determinationusingleptondistributionatLHC t 185 Signalstat. error 0.4 +1.5 180 Factorization scale(signal) LV 1.4 e 175 − G PDF(signal) 0.6 H recmt170 nn == 23 Jetenergyscale(signal) +00..20 165 n = 5 − n = 15 Background stat. error 0.4 160 165 170 175 180 Table 1: Estimates of uncertainties in GeV Inputtopmass HGeVL fromseveralsourcesinthetopmassreconstruc- tion. Resultsfortheweightfunctionwithn=2 Figure 1: Reconstructed top quark mass as a are shown. The signal statistical error is for function of the input mass. Weight functions 100fb 1andforthesumofthelepton(e,m )+jets used in this analysis correspond to n = 2,3,5 − events. The background statistical error is also and15inEq.(3.1). Thebluelineshowsmrec= minput. t for100fb−1. t whereD (E;m)isthenormalizedleptonenergydistributionintherestframeofthetopquark 0 withthemassm. Onecanchooseanarbitraryoddfunction for(oddfn.ofr )inEq.(2.1). 2. Construct a weighted integral I(m), using lepton energy distribution D(E ) in a laboratory ℓ frame: I(m) dE D(E )W(E ,m). (2.2) ≡Z ℓ ℓ ℓ 3. ObtainthezeroofI(m)asthereconstructed mass: I(m=mrec)=0. (2.3) Note that the function W(E ,m) can be computed theoretically and the definition of the recon- ℓ structedmasscorresponds tothatofmwhichyouusedinthecalculation oftheD (E;m)instep1. 0 The method is based on two assumptions that the top quarks are longitudinally unpolarized1 and on-shell. Deviations fromtheseassumptions shouldbeincorporated ascorrections. 3. Simulationanalysis In order to estimate experimental viability of the top mass reconstruction with the weight function method at the LHC, we perform a simulation analysis at the leading order, taking into account effects of detector acceptance, event selection cuts and background contributions. We generate tt m +jets events for the signal process. Forthe background events, weconsider other → tt,W+jets,Wbb+jetsandsingle-top production processes. ThecenterofmassenergyoftheLHC isassumedtobe√s=14TeV.Wechoose fortheoddfunction ofr inEq.(2.1) (oddfn.ofr ) = ntanh(nr )/cosh(nr ), (3.1) withn=2,3,5and15. SeeRef.[7]forfurtherdetailsofthesetupofthisanalysis. 1ThelongitudinalpolarizationofthetopquarksproducedinttpairattheLHCisatsub-percentlevel[8]. 3 Precisem determinationusingleptondistributionatLHC t Theleptonenergy distribution D(E )isdeformedbyvariousexperimental effects. InRef.[7] ℓ we examined various possible sources of such experimental effects and presented a way to cope with them. In particular, lepton cuts cause severe effects and we devised a method to solve this problem. Fig.1showsthereconstructed massasafunctionoftheinputtopmasstothesimulation events. The reconstructed masses are consistent with the input masses taking into account MC statistical errors and effects of the top width in this analysis. In Table 1 we show estimates of uncertainties from several sources in the top mass determination. The dominant source in this estimates is the uncertainty associated with factorization scale dependence. Although the method originallyhadaboost-invariantnature,duetoexperimentaleffectsthisnatureispartlyspoiled. This results inthescale uncertainty aswellasthePDFuncertainty. Theseuncertainties areexpected to bereducedbyincluding next-to-leading ordercorrections inthismethod. Acknowledgements I would like to thank Y. Shimizu, Y. Sumino and H. Yokoya for fruitful collaborations. This research wassupported by BasicScience Research Program through theNational Research Foun- dation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant No. NRF-2014R1A2A1A11052687). References [1] M.Ciuchini,E.Franco,S.MishimaandL.Silvestrini,JHEP1308,106(2013)[arXiv:1306.4644 [hep-ph]];M.Baaketal.[GfitterGroupCollaboration],Eur.Phys.J.C74,3046(2014) [arXiv:1407.3792[hep-ph]];G.F.Giudice,P.ParadisiandA.Strumia,JHEP1511,192(2015) [arXiv:1508.05332[hep-ph]]. [2] G.Degrassi,S.DiVita,J.Elias-Miro,J.R.Espinosa,G.F.Giudice,G.IsidoriandA.Strumia,JHEP 1208,098(2012)[arXiv:1205.6497[hep-ph]];D.Buttazzo,G.Degrassi,P.P.Giardino,G.F.Giudice, F.Sala,A.SalvioandA.Strumia,JHEP1312,089(2013)[arXiv:1307.3536[hep-ph]]. [3] [ATLASandCDFandCMSandD0Collaborations],arXiv:1403.4427[hep-ex]. [4] P.Marquard,A.V.Smirnov,V.A.SmirnovandM.Steinhauser,Phys.Rev.Lett.114,no.14,142002 (2015)[arXiv:1502.01030[hep-ph]]. [5] G.Aadetal.[ATLASCollaboration],Eur.Phys.J.C74,no.10,3109(2014)[arXiv:1406.5375 [hep-ex]];S.Chatrchyanetal.[CMSCollaboration],Phys.Lett.B728,496(2014)[Phys.Lett.B 728,526(2014)][arXiv:1307.1907[hep-ex]];G.Aadetal.[ATLASCollaboration],JHEP1510,121 (2015)[arXiv:1507.01769[hep-ex]]. [6] S.Kawabata,Y.Shimizu,Y.SuminoandH.Yokoya,Phys.Lett.B710,658(2012)[arXiv:1107.4460 [hep-ph]];S.Kawabata,Y.Shimizu,Y.SuminoandH.Yokoya,JHEP1308,129(2013) [arXiv:1305.6150[hep-ph]]. [7] S.Kawabata,Y.Shimizu,Y.SuminoandH.Yokoya,Phys.Lett.B741,232(2015)[arXiv:1405.2395 [hep-ph]]. [8] W.Bernreuther,M.FueckerandZ.G.Si,Phys.Rev.D74,113005(2006)[hep-ph/0610334]; W.BernreutherandZ.G.Si,Phys.Lett.B725,115(2013)[Phys.Lett.B744,413(2015)] [arXiv:1305.2066[hep-ph]]. 4