Latest theory developments for top pair production, generators and showering

0.29 MB·

by  Emanuele Re

Latest theory developments for top pair production,
generators and showering
6
1
0
2

r
a
M Emanuele Re∗
RudolfPeierlsCentreforTheoreticalPhysics,
8
1 UniversityofOxford,1KebleRoad,Oxford,UK

] Laboratoired’Annecy-le-VieuxdePhysiqueTheorique(LAPTh),
h 9chemindeBellevue,Annecy-le-Vieux,France†
p
- E-mail: [email protected]
p
e
h
I summarize the state of the art of cross-section computations and of available simulation tools
[

for top-quark pair production in hadron collisions. Particular emphasis is put on recent theory
2
v developmentsrelevantforLHCphenomenology.
7
4
6
3
0
.
1
0
6
1
:
v
i
X
r
a
8thInternationalWorkshoponTopQuarkPhysics
14-18September,2015
Ischia,Italy
Speaker.
∗
†currentaddress
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommons
Attribution-NonCommercial-NoDerivatives4.0InternationalLicense(CCBY-NC-ND4.0). http://pos.sissa.it/
Latesttheorydevelopmentsfortoppairproduction,generatorsandshowering EmanueleRe
1. Introduction
Top Physics is a central part of the LHC Physics programme, as shown for instance by the
variety of topics and results presented at this conference. The large value of the cross sections
to produce top quarks at the LHC allows an experimentally accurate extraction of its properties.
On the other hand, the final state arising from its decay products makes top-quark production
processes a background for several BSM searches. For these reasons it is extremely important
to have predictions for total and differential cross sections that are precise enough to match the
experimental accuracy. It is also crucial to model as accurately as possible subleading effects by
includinghigher-ordercorrectionsintoeventgeneratorprograms.
In this paper I review the state of the art of computations and simulation tools for top-quark
pairproduction,thatisthedominantmechanismforproducingtopquarksattheLHC.Insection2
Ifocusonresultsfortotalanddifferentialcrosssectionsatpartonlevel,whereassection3reviews
thecurrentresearchactivitydevotedtotheimprovementofsimulationtools.
2. Recentimprovementsinthecomputationoftotalanddifferentialcrosssections
In this section I will first summarize recent highlights in the computation of the tt¯total and
differentialcrosssectionsinQCD(sec.2.1-2.2). Inthelastpart(sec.2.3)Igivethestateoftheart
forfullydifferentialpredictionswheretopquarkdecayproductsareincluded.
2.1 Fixedorderresults
A landmark result for top quark Physics at the LHC
1111....77775555 CCCCzzzzaaaakkkkoooonnnn,,,, HHHHeeeeyyyymmmmeeeessss,,,, MMMMiiiittttoooovvvv ((((2222000011115555)))) NNLO
wasobtainedbytheauthorsofref.[1],thathavecomputed
NLO
1111....5555
for the first time the exact next-to-next-to-leading order LO
(tTbiNaohtNneivsLσeetOorset)e,sruQuieslCtsisn,Dgswhtciohtowherrsgeaucobftoaitodirranlcoystvigtoeoornlotashdpcehcaoetmomntvoaeenlrpgignreeucnslneuccneseitrvoetdefaiticnhnrteoyrspesbfe.arst[neu2dcr]s--. d/dp [pb/GeV]d/dp [pb/GeV]d/dp [pb/GeV]d/dp [pb/GeV]σσσσT,tT,tT,tT,t 01 01 01 010..0..0..0...7 2.7 2.7 2.7 25515551555155515 PPPPmMµmMµmMµmMµFFFFP P P P tStStStS,,,,====→→→→TTTTRRRR1111WWWW//// 77772222mmmmtttt33330000ttttt-t-t-t-....0000∈∈∈∈++++33338888{{{{XXXX 0000GGGG....eeee5555VVVV,,,,1111,,,,2222}}}}
whengoingfromoneordertothenextone. Theagreement 0000....22225555
betweentheoryanddataisalsoremarkablygood,asshown 0000
0000 55550000 111100000000 111155550000 222200000000 222255550000 333300000000 333355550000 444400000000
insevDeirfafelrteanlktisaaltdtihstirsibcuotniofenrsenfocre.tt¯productionarenowalso NNLO/NLO 011. ..9112
0 50 100 150 200 250 300 350 400
known at NNLO in QCD. They were first published for 1.6
the forward backward top asymmetry in ref. [3], and, very NLO/LO 011. ..8124
recently, for other (more exclusive) observables [4]. The 0 50 100 150 200 250 300 350 400
pT,t [GeV]
importance of the latter results can not be underestimated.
Figure 1: The top quark transverse
NNLO/NLOdifferentialKfactorsaregenerallynotflat, as
momentum at LO, NLO and NNLO,
illustrated for instance the plot in fig. 1, where it is shown
and the associated K-factors (LHC,
thatNNLOcorrectionschangesizeablytheshapeofthetop
√S=8TeV).Figurefromref.[4].
quark p spectrum.1 In the tail region several studies by
T
ATLASandCMShaveshownanunsatisfactoryagreementbetweendataandNLO-matchedevent
1Ithastobenoticedthough,thatafixedrenormalizationandfactorizationscaleisusedintheseresults.
2
Latesttheorydevelopmentsfortoppairproduction,generatorsandshowering EmanueleRe
generators, with the latter overshooting the measured cross section. By including NNLO correc-
tions, the agreement is significantly improved, as also shown in ref. [4]. An important refinement
ofthesedifferentialresultswillbeitscombinationwiththeNNLOdifferentialcomputationofthe
topdecay,thatwasperformedinrefs.[5,6].
For completeness I also recall that significant progress towards the computation of NNLO
QCD corrections to total and differential tt¯cross sections was also made by other groups [7, 8].
Forinstancethecrosssectiondσ/dpT,tt¯forthetransversemomentumofthetoppairisnowknown
inthesmall p limitatthenext-to-next-to-leadinglogarithmicorder[9,10]: stepstowardsagener-
T
alizationofthe“q -subtraction”methodtoperformaNNLOcomputationwithcoloredfinalstates
T
havestartedtobetaken[8],thankstotheavailabilityoftheseresults.
2.2 All-orderresults
When thett¯system is produced just above threshold, effects due to multiple soft-gluon radi-
ation become relevant. In this phase-space region large logarithmically-enhanced corrections of
the form αnlogmX appear, where X is a kinematic function that vanishes when the tt¯system is
s s s
produced exactly at threshold. Thanks to factorization properties of phase space and production
matrixelementsinthesoftregion(thelatterbeingnottrivialfortt¯duetocolorflow),theperturba-
tive expansion can be reorganized suitably, by computing systematically the log-enhanced terms,
andresummingthemtoallorders.
Several groups performed soft-gluon threshold resummation at next-to-next-to-leading loga-
rithmic (NNLL) accuracy [11, 12, 13, 14, 15], using different formalisms and different functional
formsforX ,andinonecasealsoresummingCoulombeffects[14]. NNLLresummationhasalso
s
been matched to the exact NNLO computation mentioned in sec. 2.1: this accuracy represent the
stateoftheartforσ ,andisavailableinpubliccodesasTOP++[1]andTOPiXS[16].
tot
Resummedresultscanalsobeusedtoguessthesizeofthefirstunknowntermatfixedorder:
until the exact NNLO result was available, approximate NNLO results have been computed by
severalgroups. Nowadaysthenaturaldevelopmentistotryandcomputeσ atapproximateN3LO.
tot
Thishasbeenachieved,usingdifferentapproaches,inref.[17],aswellasinref.[18](inthelatter
paper,high-energyresummationwasusedtogetherwiththresholdresummation).
2.3 Fullydifferentialcomputations,includingtop-quarkdecays
Since top quarks can not be detected, σ and differential distributions for stable top quarks
tot
can not be directly compared with data without some extrapolation. In this respect, differential
resultsthatincludealsothefinalstatedecayproductsareoffundamentalimportance,andarealso
a central ingredient for the latest developments of modern event generators, to be discussed in
sec. 3. The more accurate fixed-order results for describing the fully exclusive final state arising
from“toppair”productionanddecayarethosepresented,awhileago,inrefs.[19,20,21,22,23].
Despitetherebeingdifferencesamongthecomputations, allthesepapersessentiallycontainfully
differentialNLOresultsfortheprocess2 pp W+W bb¯,wherealloffshellnesseffectsaswellas
−
→
interference among double-, singly- and non-resonant diagrams are taken into account exactly up
2ThroughoutthedocumentwiththisnotationitisimpliedthatleptonicW decaysareincluded.
3
Latesttheorydevelopmentsfortoppairproduction,generatorsandshowering EmanueleRe
to NLO in QCD. A remarkable result was recently obtained in ref. [24], where the same effects
werealsocomputedatNLOfortheprocess pp W+W bb¯+1jet.
−
→
Itisworthstressingthattwooftheaforementionedcomputations(namely[22]and[23])were
performedinthe“4-flavor”scheme, i.e. thebquarksareconsideredmassive, henceresultsarefi-
nitealsointhelimitofvanishing p forone(orboth)bquarks(aswellasforunresolvedb-tagged
T
jets). Thereforethesecomputationsallowacleancomparisonamongtheorypredictions(atNLO)
anddatafortheexperimentalsignaturetraditionallycalled“single-topWt”production: sincearbi-
trarycutscanbesafelyplacedonbjets, consistentresultscanbeobtainedforthesamefinalstate
detected experimentally (2 b-tagged jets vs. e.g. 1 b-tag and 1 b-veto), thereby avoiding the am-
biguities intrinsically present when a separation between top-pair andWt production is attempted
theoretically. Anexperimentalanalysisdedicatedtoa comparisonamongthesecomputationsand
datawouldcertainlybeveryvaluable.
3. Recentimprovementsineventgenerators
Fully exclusive Monte Carlo event generators based on parton-shower algorithms are used
ubiquitously in experimental searches, hence their importance for LHC phenomenology doesn’t
need to be stressed in this short review. A substantial step to improve the accuracy of these
simulation tools has been made more than a decade ago, when methods to consistently match
NLO QCD computations with parton showers algorithms were devised (NLO+PS). Since then,
an enormous progress took place in this field: all important processes of the type pp tt¯+X
→
can be simulated at NLO+PS, thanks to the developments of fully- or partially-automated frame-
works [25, 26, 27, 28, 29]. Among them, MadGraph5_aMC@NLO [26] deserves to be specially
mentioned, being it the only one which is currently fully automated in the strictest sense. For
otherframeworks,ifaspecificprocessofinterestisnotpubliclyavailable,itsNLO+PSsimulation
can be obtained with minor efforts, by linking against external codes (typically, to obtain 1-loop
amplitudes with large multiplicity). Nowadays this can be done straightforwardly, using standard
interfacesdevelopedspecificallyforthispurpose[30,31].
There are currently two very active research topics in the community of Monte Carlo de-
velopers that are relevant for top pair production at hadron colliders: the consistent inclusion of
offshellnesseffectsinpresenceofintermediateresonancesdecayingintocoloredparticles,andthe
merging of NLO+PS simulations for different jet multiplicities. I will review them in turn, with
particularemphasisontheformer.
3.1 Simulationof pp W+W bb¯ atNLO+PSaccuracy
−
→
Beforeturningtotheexplanationofthetheoreticalissuespresentlyaddressedbythecommu-
nity, I want to recall that a major application where a NLO+PS simulation of of pp W+W bb¯
−
→
can have an impact is in the determination of the top mass, at least for the techniques where the
kinematicsofvisibleparticlesfromtop-decayisusedforthispurpose(see[32]forarecentreview).
TheproblemwiththesimulationofW+W bb¯ productioncanbestatedasfollows: unlessspe-
−
cial care is taken, when NLO correction to the decay are included in NLO+PS tools, the interme-
diate top-quark virtuality is not preserved. If this happens, non-physical distortion can potentially
4
Latesttheorydevelopmentsfortoppairproduction,generatorsandshowering EmanueleRe
show up in kinematic distributions. Although there are issues also with the MC@NLO method (see
forinstance[33]),fromthispointonwardI’llfocusonthePOWHEGapproach.
Before entering into details, a remark is due: it is legitimate to ask whether the issues dis-
cussedbelowarereallyrelevantforpracticalpurposes,especiallybecauseNLO+PSresultsforthe
W+W bb¯ final state (with offshellness and interference effects) were obtained with PowHel in
−
ref. [34], and no particular problems were noticed by the authors. The definitive answer can only
be given by developing more refined tools and performing careful comparisons among them and
againstolderapproaches.
ThePOWHEG“masterformula”togeneratearesolvedemissionreads
R(Φ ,Φ ) (cid:20) (cid:90) R(Φ ,Φ ) (cid:21)
dσ =dΦ dΦ B¯(Φ ) B rad exp B rad dΦ . (3.1)
B rad B rad
B(Φ ) − B(Φ )
B B
The concept of “underlying Born” phase space (Φ ) is central in POWHEG, and we assume the
B
reader to be familiar with it: once a point in Φ is picked, according to the weight B¯, the hardest
B
emission (a point in (Φ ,Φ )) is generated according to the POWHEG Sudakov. The mapping
B rad
Φ (Φ ,Φ )isthesameastheoneusedtoperformthesubtractionofsingularitiespresentin
B B rad
→
theRtermcontainedwithintheB¯function,anditdependsonthesingularregionathand[35]. Two
problemsarepresent:3
1. In the standard POWHEG BOX algorithm, the phase space region associated to final-state
gluon emission off the b-quark would be handled by a mapping that, in general, does not
preserve the virtuality of the intermediate resonance, i.e. m2 (Φ )=m2 (Φ ,Φ ). The
Wb B (cid:54) Wbg B rad
problem is manifest: unless m2 Γ E , R and B will not be on the resonance peak at the
bg (cid:28) t bg
same time, hence the ratio R/B can become large when R is on peak and B is not, yielding
a“Sudakovsuppression”thatisspurious,sincethe(Φ ,Φ )kinematicswouldbefarfrom
B rad
the true QCD singularity. Quantitatively, one expects the mass profile of the b-jet to be
distortedwhenm2 E Γ .
jet b t
∼
2. Afurtherproblemcanariseduringtheparton-showeringstage: fromthesecondemissionon-
ward,theshowershouldbeinstructedtopreservethemassoftheresonances. Thiscouldbe
doneeasilyiftherewasanuniquemechanismto“assign”theradiationtoagivenresonance.
Forprocesseswhereinterferenceispresent,noobviouschoiceispossible.
An intermediate solution to the previous issues was presented in ref. [36], where a fully con-
sistentNLO+PSsimulationforW+W bb¯ productioninthenarrow-widthlimitwasobtained. Off-
−
shellenssandinterferenceeffectswereimplementedinanapproximateway,asfollows:
a. Byusingmatrixelementsinthenarrow-widthlimit,realandvirtualcorrectionsforproduc-
tion and decay can be clearly separated, i.e. no interference arises. This also allows for a
non-ambiguous“resonanceassignment”forfinal-stateradiation.
b. For radiation in the decay, Φ is generated by first boosting momenta in the resonance
rad
rest-frame. Inthisway,theintermediatevirtualityisthesameforΦ and(Φ ,Φ ).
rad B rad
3Extendedexplanationscanbefoundinrefs.[36,37].
5
Latesttheorydevelopmentsfortoppairproduction,generatorsandshowering EmanueleRe
c. Thephasespaceintegration, andtheeventgeneration, spans also overtheoff-shellregions.
Aprojectionontoanon-shellkinematics,testedextensively,allowstousetheNLOon-shell
amplitudes(computedinrefs.[38,39]).
d. From the off-shell phase space, a reweighting of the B¯ function is performed using the LO
exactresults(wherefinitewidthandnon-double-resonantdiagramsarefullyincluded).
The above expedients allow the construction of
a NLO+PS generator where the theoretical problems V] 10−1 prod+decay
e prodonly
G
mentioned above are solved, and offshellness effects b/ 10−2
p
[
adrreesisnecdl:udbeyddeafpapurlotxiinmPaOteWlyH.EGAofnulrythtehreihssaurdeewstaesmaids-- md+ljB 10−3
/
sion is generated. However, for the tt¯ process, emis- σd 10−4
1.1
sions from decay are rarely the hardest, hence they
o
would be dealt with by the shower most of the time, rati 1
0.9
despite the previous improvements. In ref. [36] a pro- 0 20 40 60 80 100 120 140 160
ceduretokeep,atthesametime,theinitialstateradia- ml+jB [GeV]
tionaswellasthosefromdecayingresonanceswasim- Figure 2: Invariant mass distribution of
plemented, to alleviate the aforementioned issue. An the charged lepton and b-flavored jet at
NLO+PS including correction for produc-
exampleoftheresultsisillustratedinfig.2,wherethe
tion only or for production and decay
impact of the new POWHEG BOX generator is shown
(LHC, √S=8 TeV), with the method de-
on an “endpoint” observable typically used to extract
scribed in ref. [36]. Figure adapted from
m .
t ref.[36].
Finally, I want to mention that, shortly after the
conference,furthersubstantialprogresswaspresentedinref.[37]. Amethodtohandleexactlythe
completematrixelementsalsoatNLOwasdeveloped,bypartiallyusingsomeoftheimprovements
inref.[36]butalsogeneralizingsubstantiallythepartitionofphasespaceintosingularregionsand
theassociatedsubtractionscheme. Althoughresultswerepublishedonlyforsingle-top,themethod
isfullygeneral,anditsapplicationtoW+W bb¯ isinprogress[40].
−
3.2 MultijetmergingatNLO
At large collision energies, a significant fraction of tt¯events is produced in association with
one or more jets. At times a tool describing several jet multiplicities in a single event sample is
needed. Atypicalexampleiswhen“H ”variablesareused,asisoftenthecaseinBSMsearches.
T
The CKKW-L and MLM-merging methods succesfully address this issue at LO. Since this
accuracywillbecomealimitingfactorforprecisionstudies,itisdesirabletoextendthesemethods
to NLO (“NLOPS multijet merging”). Reaching such accuracy is a non-trivial theoretical chal-
lenge, since it requires a detailed understanding of the interplay among resummation and fixed
ordereffectsinNLO+PSsimulations. Severalapproacheswereproposedintheliteratureoverthe
lastthreeyears. Inthecontextoftop-pairproduction,sofarresultswerepublishedonlyusingthe
MEPS@NLO[41]andFxFx[42]mergingmethods.4 ThemeasurementofQCDactivityintt¯events
4Phenomenological studies performed by the original authors can also be found in refs. [43, 44] and ref. [26].
Moreoverathoroughcomparisonwhereotherapproachesarealsoincludedwillbepresentedintheproceedingsofthe
2015“PhysicsatTeVColliders”workshop[45].
6
Latesttheorydevelopmentsfortoppairproduction,generatorsandshowering EmanueleRe
will allow to test these tools against data in “SM dominated” regions, thereby providing a robust
assessmentoftheaccuracythatcanbeassumedwhentheyareusedforBSMsearches.
References
[1] M.Czakon,P.FiedlerandA.Mitov,Phys.Rev.Lett.110,252004(2013)
[2] M.Czakon,Phys.Lett.B693,259(2010)
[3] M.Czakon,P.FiedlerandA.Mitov,Phys.Rev.Lett.115,no.5,052001(2015)
[4] M.Czakon,D.HeymesandA.Mitov,arXiv:1511.00549[hep-ph].
[5] J.Gao,C.S.LiandH.X.Zhu,Phys.Rev.Lett.110,no.4,042001(2013)
[6] M.Brucherseifer,F.CaolaandK.Melnikov,JHEP1304,059(2013)
[7] G.Abelof,A.Gehrmann-DeRidderandI.Majer,JHEP1512,074(2015)
[8] R.Bonciani,S.Catani,M.Grazzini,H.SargsyanandA.Torre,Eur.Phys.J.C75,no.12,581(2015)
[9] H.T.Li,C.S.Li,D.Y.Shao,L.L.YangandH.X.Zhu,Phys.Rev.D88,074004(2013)
[10] S.Catani,M.GrazziniandA.Torre,Nucl.Phys.B890,518(2014)
[11] M.Czakon,A.MitovandG.F.Sterman,Phys.Rev.D80,074017(2009)
[12] N.Kidonakis,Phys.Rev.D82,114030(2010)
[13] V.Ahrens,A.Ferroglia,M.Neubert,B.D.PecjakandL.L.Yang,JHEP1009,097(2010)
[14] M.Beneke,P.Falgari,S.KleinandC.Schwinn,Nucl.Phys.B855,695(2012)
[15] M.Cacciari,M.Czakon,M.Mangano,A.MitovandP.Nason,Phys.Lett.B710,612(2012)
[16] M.Beneke,P.Falgari,S.Klein,J.Piclum,C.Schwinn,M.UbialiandF.Yan,JHEP1207,194(2012)
[17] N.Kidonakis,Phys.Rev.D90,no.1,014006(2014)
[18] C.Muselli,M.Bonvini,S.Forte,S.MarzaniandG.Ridolfi,JHEP1508,076(2015)
[19] A.Denner,S.Dittmaier,S.KallweitandS.Pozzorini,JHEP1210,110(2012)
[20] G.Bevilacqua,M.Czakon,A.vanHameren,C.G.PapadopoulosandM.Worek,JHEP1102,083
(2011)
[21] G.Heinrich,A.Maier,R.Nisius,J.SchlenkandJ.Winter,JHEP1406,158(2014)
[22] R.Frederix,Phys.Rev.Lett.112,no.8,082002(2014)
[23] F.Cascioli,S.Kallweit,P.MaierhöferandS.Pozzorini,Eur.Phys.J.C74,no.3,2783(2014)
[24] G.Bevilacqua,H.B.Hartanto,M.KrausandM.Worek,arXiv:1509.09242[hep-ph].
[25] S.Alioli,P.Nason,C.OleariandE.Re,JHEP1006,043(2010)
[26] J.Alwalletal.,JHEP1407,079(2014)
[27] S.Hoeche,F.Krauss,M.SchonherrandF.Siegert,JHEP1209,049(2012)
[28] S.PlatzerandS.Gieseke,Eur.Phys.J.C72,2187(2012)
[29] A.Kardos,C.PapadopoulosandZ.Trocsanyi,Phys.Lett.B705,76(2011)
7
Latesttheorydevelopmentsfortoppairproduction,generatorsandshowering EmanueleRe
[30] T.Binothetal.,Comput.Phys.Commun.181,1612(2010)
[31] S.Aliolietal.,Comput.Phys.Commun.185,560(2014)
[32] G.Corcella,arXiv:1511.08429[hep-ph].
[33] A.Papanastasiou,theseproceedings.
[34] M.V.Garzelli,A.KardosandZ.Trocsanyi,JHEP1408,069(2014)
[35] S.Frixione,P.NasonandC.Oleari,JHEP0711,070(2007)
[36] J.M.Campbell,R.K.Ellis,P.NasonandE.Re,JHEP1504,114(2015)
[37] T.JežoandP.Nason,JHEP1512,065(2015)
[38] J.M.CampbellandR.K.Ellis,J.Phys.G42,no.1,015005(2015)
[39] S.Badger,R.SattlerandV.Yundin,Phys.Rev.D83,074020(2011)
[40] T.Ježo,J.Lindert,P.Nason,C.OleariandS.Pozzorini,inprogress.
[41] S.Hoeche,F.Krauss,M.SchonherrandF.Siegert,JHEP1304,027(2013)
[42] R.FrederixandS.Frixione,JHEP1212,061(2012)
[43] S.Hoeche,J.Huang,G.Luisoni,M.SchoenherrandJ.Winter,Phys.Rev.D88,014040(2013)
[44] S.Hoeche,F.Krauss,P.Maierhoefer,S.Pozzorini,M.SchonherrandF.Siegert,Phys.Lett.B748,74
(2015)
[45] https://phystev.cnrs.fr/
8