Precise top mass determination using lepton distribution at LHC

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by  Sayaka Kawabata

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Precise top mass determination using lepton
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distribution at LHC
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- SayakaKawabata
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e InstituteofConvergenceFundamentalStudies,
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SeoulNationalUniversityofScienceandTechnology,Seoul01811,Korea
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E-mail: [email protected]

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We present a new method to measure a theoretically well-defined mass of the top quark at the
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simulationanalysisofthetopmassreconstructionwiththismethodfortt lepton+jetschannel
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. attheleadingorder. We estimate severalmajoruncertaintiesin thetop massdeterminationand
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8thInternationalWorkshoponTopQuarkPhysics,TOP2015
14-18September,2015
Ischia,Italy
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
Precisem determinationusingleptondistributionatLHC
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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
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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)
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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
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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].
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Precisem determinationusingleptondistributionatLHC
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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).
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