Weak Bosons and Jets at the LHC

0.14 MB·English

by  Tom Melia

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Weak Bosons and Jets at the LHC
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] TomMelia †
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p UniversityofOxfordTheoreticalPhysics
- E-mail: [email protected]
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[ In this talk, I outline theoreticalpredictionsforweak bosonpair productionin association with

1 two jets at the LHC. I will discuss the next-to-leadingorder QCD correctionsto the processes
v pp W+W+jj and pp W+W jj, and the interfacing of pp W+W+jj with a parton
5 → → − →
0 showerusingthePOWHEG BOXframework.
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10thInternationalSymposiumonRadiativeCorrections(ApplicationsofQuantumFieldTheoryto
Phenomenology)-Radcor2011
September26-30,2011
Mamallapuram,India
Speaker.
∗
†BasedonworkdoneincollaborationwithKirillMelnikov,PaoloNason,RaoulRöntsch,andGiuliaZanderighi-
seeRefs.[1,2,3].
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
WeakBosonsandJetsattheLHC TomMelia
Figure1:TypesofFeynmangraphsencounteredinatree-levelcalculationofweakbosonpairproductionin
associationwithtwojets.Wavylinesdepictweakbosonsandspiralledlinesaregluons.Quarkflavourlabels
andweakbosonlabels(W+/W /Z0)havebeendeliberatelysuppressedtohighlightthegeneraltopologyof
−
thegraphswhichmaycontributetodifferentprocesses.
1. Introduction andMotivation
Precision calculations of standard model processes are essential for interpreting the signals
measured at the Large Hadron Collider (LHC) and for fully realising the discovery potential of
this experiment. Next-to-leading order (NLO)calculations in perturbative QCDhave proved very
successful whenused inTevatron analyses, and areagood waytoreduce theoretical uncertainties
in a description of a given process. On top of this, merging an NLO calculation with a parton
shower provides arealistic hadron-level prediction foran event whilst maintaining NLOaccuracy
forinclusive observables.
In this talk I shall discuss the production of a pair of weak bosons in association with jets –
specifically the two processes pp W+W+jj and pp W+W jj. I will describe the compu-
−
→ →
tation of the NLO QCD corrections to both processes, as well as the merging of pp W+W+jj
→
withapartonshower,doneintheframeworkofthePOWHEG BOX[4].
Figure 1 depicts the structure of some of the types of Feynman graphs one encounters in a
tree-level calculation of weak boson pair production along with two jets. All of these types of
graphcontribute towardstheprocess pp W+W jj,butonlygraphsofthetypeshowninthefar
−
→
right ofthefigurecontribute towards pp W+W+jj. Here,charge conservation requires thetwo
→
W+bosonstobeemittedfromseparatequarklinesandthisleadstoanunusualtheoreticalproperty
–thecrosssectionforthisprocessremainsfiniteeveniftherequirement thattwojetsareobserved
is lifted. This will be investigated later on, and I will present results for W+W++n jets, where
n=0,1,2. Thecalculation of pp W+W+jjcanbeseenasasteppingstonetothecalculationof
→
pp W+W jj,sinceitinvolves asmallsubsetoftheFeynmangraphsneededforthelatter.
−
→
Bothprocesses are2 4 processes, and to calculate the QCDcorrections tothem one needs
→
to dealwithone-loop, six-point tensor integrals ofrelatively high rank. There isthus atheoretical
incentive in performing these calculations and much progress has been made over the past few
years in the methods used to compute them – this will be discussed in the following section. But
beforethis,Iwillgoontodiscussthestudyofbothprocesses attheLHCinabitmoredetail.
1.1 W+W+jjattheLHC
At√s=14TeV,thecross-sectionforthisprocessisabout1pb(40%ofthisforW W jj)and
− −
istherefore accessible. Inthe following wetake theW+ bosons toboth decay leptonically, giving
risetoanearlybackground-free signaturewhichinvolves same-signleptons. Thisisaninteresting
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WeakBosonsandJetsattheLHC TomMelia
process tostudyinitsownright, butthereareotherreasons tostudyit: pp W+W+jjisaback-
→
ground to physics both within and beyond the standard model. For example, it is possible to use
same-sign lepton pairstostudydouble partonscattering attheLHC[5],towhich pp W+W+jj
→
is a background. Beyond the standard model, resonant slepton production in R-parity violating
SUSYmodels[6],diquark production [7],anddoublycharged Higgsbosonproduction [8]areex-
amples of processes which also lead to a signature of two same-sign leptons, missing energy, and
jets.
1.2 W+W jjattheLHC
−
The production of a W+W boson pair in association with zero, one or two jets is an im-
−
portant background toHiggsbosonproduction, especially whenthedecayH W+W opensup.
−
→
AlthoughmostofthesensitivityinHiggsbosonsearchescomesfromthezerojetprocesses, which
have thelargest cross-section, theproduction ofaHiggs boson inassociation with twojetsis also
relevant – about 10% of Higgs events at the LHC involve two jets [9, 10]. The production of a
Higgsbosonviaweakbosonfusion (WBF)alsohasasizeable cross-section. Thesignature ofthis
processincludestwoforwardtaggingjetsand pp W+W jjisanirreduciblebackgroundtothis.
−
→
As we did forW+W+jj, in the following we will take bothW bosons to decay leptonically. The
resulting signature oftwoopposite-sign leptons, jetsandmissing energy isalso abackground toa
classic beyondthestandard modelphysicssearch.
2. Method ofcalculation
2.1 TheNLOQCDcorrections
NLO QCD calculations of processes involving more than five particles is difficult. For the
virtual amplitude, thenumberofFeynmandiagrams needing evaluation growsfactorially withthe
number ofparticles in theprocess. In addition tothis, the one-loop tensor integrals whichneed to
be computed become more involved. However, a refinement of traditional computation methods,
as well as the development of new techniques based on unitarity and on-shell methods, have seen
asignificant growth inthe number of 2 4processes (and even a2 5process) known atNLO
→ →
inthepastfewyears(see[11]forarecentreview). Platformsfortheautomation ofNLO-accurate
processes arecurrently beingdeveloped (seee.g. [12,13,14,15]).
Asdescribed indetail inthepapers[1,3],thetechnique ofD-dimensional generalised unitar-
ity[16]wasusedtoobtainthevirtualpartoftheamplitudefortheQCDprocesses pp W+W+jj
→
and pp W+W jj. It is worth pointing out that, as currently formulated, on-shell methods re-
−
→
quireworkingwithanorderingofexternallines–thesearecolourorderedorprimitiveamplitudes.
Itisonlycolour-charged particleswhichareorderedinprimitiveamplitudesandsoallpossiblein-
sertions ofthecolourless weakbosons mustbeconsidered foranytree-level orone-loop primitive
amplitude. The D-dimensional unitarity cuts reduce one-loop primitive amplitudes to products of
tree-levelhelicityamplitudes,andacertainamountofdifficultyexistsinensuringnoover-counting
takes place whencombining the cuts of different parent diagrams. Nevertheless, this isjust book-
keeping and these two calculations demonstrated that unitarity methods can deal with more com-
plicated, colourless finalstates. Thetree-level helicity amplitudes themselves arecalculated using
Berend-Giele recursion relations [17].
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WeakBosonsandJetsattheLHC TomMelia
3.5 2-jetinclusive NLLOO 3 2-jetexclusive NLLOO 00..6605 1-jetexclusive NLLOO 0.10 0-jetexclusive NLLOO
0.09
@Dfb3.0 @Dfb2 @Dfb00..5505 @Dfb0.08
Σ2.5 Σ1 Σ Σ
0.45 0.07
2.0 0 0.40 0.06
0.35
50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400
Μ@GeVD Μ@GeVD Μ@GeVD Μ@GeVD
Figure 2: The dependence on factorisation and renormalisation scales of cross-sections for
pp e+m +n en m +njets, n = 0,1,2 at leading and next-to-leading order in perturbative QCD. Here
→
m =m =m .
F R
2.2 Mergingwithapartonshower
Methods which include both the benefits of an NLO calculation and a parton shower model
(NLO+PSgenerators) havebecomeavailable inrecentyears-twoframeworksarecurrently being
used for collider physics: MC@NLO [18] and POWHEG [19]. A general computer framework for
building a POWHEG implementation of an arbitrary NLO process exists - the POWHEG BOX [4].
Here, one needs only to supply a few ingredients: phase-space and flavour information, the Born
andrealmatrixelementsandthevirtualmatrixelementsforagivenNLOprocess. Theimplemen-
tation of pp W+W+jj in the POWHEG BOXis reported in [2]. This was the first time a 2 4
→ →
process wasimplementedinaNLO+PSgenerator.
Since all of the ingredients needed by the POWHEG BOX were already known from [1], the
POWHEG implementation of this process did not present any special problem, except for a non-
trivial issue of high computational demands coming from the virtual corrections. The technical
details of how this problem was dealt with are described in detail in [2]. The resulting code is
publicandisavailable atthewebsite[20].
3. Results
3.1 Selectedresultsfor pp W+W+jjattheLHC
→
First I will present results from the NLO calculation of pp W+W+jj, taken from [1]. We
→
consider proton-proton collisions at a center-of-mass energy √s=14 TeV. We require leptonic
decays of theW-bosons and consider the final state e+m +n en m . TheW-bosons are on the mass-
shellandweneglectquarkflavourmixing. Weimposestandardcutsonleptontransversemomenta
p >20GeV,missingtransversemomentum p >30GeVandchargedleptonrapidity h <
,l ,miss l
⊥ ⊥ | |
2.4. We define jets using anti-k algorithm, with R=0.4 and with a transverse momentum cut
⊥
p = 30 GeV on the two jets. The mass of the W-boson is taken to be m = 80.419 GeV,
,j W
th⊥e width G =2.140 GeV.W couplings to fermions are obtained from a (m )=1/128.802
W QED Z
and sin2q =0.2222. We use MSTW08LO parton distribution functions for leading order and
W
MSTW08NLO for next-to-leading order computations, corresponding to a (M )=0.13939 and
s Z
a (M ) = 0.12018 respectively. We do not impose lepton isolation cuts. All results discussed
s Z
below apply to theQCDproduction pp W+W+jj; the electroweak contribution to this process
→
isignored.
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WeakBosonsandJetsattheLHC TomMelia
eV] 1e-1 POWHEG+PYTNHLIOA
G
b/
p [ft,j3 1e-2
d
/ 1e-3
sd
NLO1e1-.54
yt)/ 1.0
P
+
hg 0.5
P 0 50 100 150 200
(
p [GeV]
t,j3
Figure 3: The kinematic distribution for the transverse momentum of the third hardest jet in the QCD
productionof pp e+m +n en m +2 jets. The pureNLO result and the resultwith POWHEG+PYTHIAare
→
bothshown.
Figure2showsthedependence oftheproduction cross-sections for pp e+m +n en m +njets
→
on the renormalisation and factorisation scales, which we set equal to each other. Considering
the range of scales 50 GeV m 400 GeV, we find the two-jet inclusive cross-section to be
≤ ≤
s LO=2.7 1.0fbatleading orderands NLO=2.44 0.18fbatnext-to-leading order. Theforty
± ±
percent scale uncertainty at leading order is reduced to less than ten percent at NLO.We observe
similarstabilizationofthescaledependenceforthe0-and1-jetexclusivemultiplicities. Combining
these cross-sections we obtain a total NLO cross-section of about 2.90 fb for pp e+m +n en m
→
inclusive production. This implies about 60 e+m ++e+e++m +m + events per year at the LHC
with 10 fb 1 annual luminosity. While this is not a gigantic number, such events will have a very
−
distinct signature, sotheywilldefinitelybeseenanditwillbepossible tostudythem.
Thedramaticchangeinthetwo-jetexclusivecross-section apparentfromfigure2isdiscussed
and investigated in [1]. We find that the feature observed here, that the two-jet exclusive is sig-
nificantly smaller than the two-jet inclusive, remains present when we increase the jet cut and so
allow for greater perturbative convergence of the exclusive cross section. This smallness implies
that quite a large fraction of events in pp e+m +n en m + 2 jets have a relatively hard third jet.
→ ≥
Thisfeaturemaybeusefulforrejectingcontributionsof pp W+W+jjwhenlookingformultiple
→
partonscattering.
Next I present results from the POWHEG implementation of pp W+W+jj, taken from the
→
paper[2]. Heretheset-upisasdescribed above,butweconsider ppcollisions atadifferentcentre
of mass energy: √s=7 TeV. A dynamic scale is used for the renormalisation and factorisation
scales:
m =m =(p +p +E +E )/2, E = m2 +p2 ,
R F ,1 ,2 ,W1 ,W2 ,W q W ,W
⊥ ⊥ ⊥ ⊥ ⊥ ⊥
where p , p , p and p are the transverse momenta of the twoWsand the twoemitted
,W1 ,W2 ,1 ,2
⊥ ⊥ ⊥ ⊥
partons intheunderlying Bornconfiguration.
Withnojetcuts,butwiththeleptoniccutsdescribedabove,wefindthecross-section fortobe
1.11 0.01 fb for the pure NLO result, and a slightly lower cross-section of 1.06 0.01 fb when
± ±
events are generated by POWHEG and are subsequently showered with PYTHIA. A comparison
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WeakBosonsandJetsattheLHC TomMelia
LHC, s=7TeV LO 200
55 NLO LO
Μ=MW
NLO
50
150
Db Db Μ=2MW
@f 45 @f
Σ Σ 100
40 Μ=4MW
35 50
100 150 200 250 300 7 8 9 10 11 12 13 14
Μ @GeVD s @TeVD
Figure4:Leftpane:theproductioncross-sectionoftheprocesspp (W+ n ee+)(W− m −n¯m )jjatthe
→ → →
7TeVLHCindependenceonthefactorisationandrenormalisationscalesm =m =m atbothLOandNLO
F R
inperturbativeQCD.Rightpane:thedependenceofthecross-sectiononcentreofmassenergy√swithLO
resultsindashedblueandNLOresultsinsolidred. Threechoicesofm areshown: m =m ,2m ,4m .
W w W
of kinematic distributions was carried out in [2] and for the most part, there was good agreement
between the NLO and the POWHEG+PYTHIA results. However, there were some distributions
which showed expected and marked changes, one of which I shall highlight in this talk. Figure 3
showsthe transverse momentum ofthe third-hardest jet. SinceatNLOitisonly therealradiation
which contributes to this distribution, wesee a divergence for small p in the pure NLOresult.
,j3
⊥
In contrast one can see the Sudakov peak inthe POWHEG + PYTHIAresult, and the distribution
goestozeroas p 0.
⊥,j3 →
3.2 Selectedresultsfor pp W+W jjattheLHC
−
→
Here I will present selected results from the calculation of pp W+W jj, taken from the
−
→
paper [3]. HeretheW bosons decayleptonically: W+W−jj e+m −n en¯m jj. Thefullresults with
→
genericopposite-signleptonscanbeobtainedfromthesebymultiplyingbyafactoroffour. Weuse
thesameleptonic cutsandelectroweak inputparameters asweredescribed inthe pp W+W+jj
→
results section above. However, here of course a jet cut must be applied and two jets observed in
ordertoobtainafinitecross-section: wetake p >30GeVand h <3.2.
,j j
⊥ | |
Figure 4 shows the dependence of the production cross-section on renormalisation and fac-
torisation scales, which are again set equal to each other, at a centre of mass energy √s=7 TeV.
The dependence of the cross-section on centre of mass energy is also shown in figure 4. One ob-
serves a dramatic reduction in scale dependence in going from leading order to next-to-leading
order. Considering a range of scales m < m <4m we obtain a cross section at leading order
W W
s =46 13fbandatNLOs =42 1fb. Assuming fiftypercent efficiency, with5fb 1 of
LO NLO −
± ±
data at the 7TeV run of the LHC,weexpect about 400 dilepton events e+m ,e+e ,m +e ,m +m .
− − − −
It is interesting that at NLO, the dependence of the cross-section on centre of mass energy √s is
almost linear. If one defines an ‘optimal’ scale choice to be the choice of scale for which NLO
corrections aresmallestthenthis‘optimal’scaleshiftsfrom2m at7TeVto4m at14TeV.
W W
Finally I present two kinematic distributions for this process which are relevant for a Higgs
boson search at the LHC. The left pane of figure 5 plots the relative azimuthal angle between the
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WeakBosonsandJetsattheLHC TomMelia
14
25 LO 12 LO
NLO NLO
DV 10
Db 20 Ge
@f (cid:144)b 8
Μ+ @f
dΦe- Ηj1,j2 6
(cid:144)Σ 15 dD
d (cid:144)Σ 4
d
2
10
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 -6 -4 -2 0 2 4 6
Φ DΗ
e-Μ+ j1,j2
Figure 5: Distributions of lepton opening angle and jet pseudorapidity difference for the process
pp (W+ n ee+)(W− m −n¯m )jj at the 7 TeV LHC. LO results are shown in blue, NLO results in
→ → →
red. Theuncertaintybandsareforscalem <m <4m andthesolidlinesshowtheresultsatm =2m .
W W W
leptons which peaks at f e m + = p . This is in contrast to leptons produced via the mechanism
−
H WW e+m nn wherethis angle tends tobesmall. Thepseudorapidity difference between
−
→ →
the two leading jets, D h =h h , is plotted in the right pane of figure 5. This is a useful
j1j2 j1 j2
−
distribution for studying Higgs boson production via WBF - this mechanism leads to jets which
tend to have a large D h . For a Higgs produced via gluon fusion and, as we see here for
j1j2
| |
pp W+W jj, this distribution is peaked around D h =0. The significant reduction in the-
− j1j2
→ | |
oretical scale uncertainties can also be seen in these distributions, and there is no observed shape
change in going from LO to NLO. These observations were typical of all kinematic distributions
considered in[3].
4. Conclusion
In this talk I have presented the NLO QCD corrections for the process pp W+W+jj and
→
theprocess pp W+W jjwhichwerecomputedusingthemethodofD-dimensionalgeneralised
−
→
unitarity. A significant reduction inthe theoretical uncertainties ofanLHCprediction isobserved
for both processes. The process pp W+W+jj has been implemented in the POWHEG BOX
→
which matches the NLO result with a parton shower. I look forward to measurements of pairs of
weakbosonsandjetsattheLHC.
Acknowledgements
Iwishtothanktheorganisers ofRADCOR2011forareallyfantasticconference andforproviding
financial support. This talk is based on work done in collaboration with Kirill Melnikov, Paolo
Nason, Raoul Röntsch, and Giulia Zanderighi and draws on the papers [1, 2, 3]. This research is
supported bytheBritishScienceandTechnology FacilitiesCouncil.
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WeakBosonsandJetsattheLHC TomMelia
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