Table Of ContentMPP-2010-3
0
1
gg
0 Radiative corrections to W production at the LHC
2
n
a
J
5
1
] Uli Baur,DoreenWackeroth
h
p DepartmentofPhysics,StateUniversityofNewYork,Buffalo,NY14260,USA
- E-mail: [email protected],
p
e [email protected]
h
[ MarcusM.Weber
∗
1 Max-Planck-InstitutfürPhysik,FöhringerRing6,80805Munich,Germany
v E-mail: [email protected]
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RadiativeWproductionathadroncollidersisanimportanttestinggroundfortheStandardModel.
2
. WeconsiderWgg productionwhichissensitivetothequarticWWgg coupling. Furthermorethe
1
0 StandardModelamplitudeforthisprocesscontainsaradiationzero. Wepresentacalculationof
0 theNLOQCDcorrectionsforWgg productionattheLHC.
1
:
v
i
X
r
a
RADCOR2009-9thInternationalSymposiumonRadiativeCorrections(ApplicationsofQuantumField
TheorytoPhenomenology)
October25-302009
Ascona,Switzerland
Speaker.
∗
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
RadiativecorrectionstoWgg productionattheLHC MarcusM.Weber
1. Introduction
With the startup of the LHC the mechanism of electroweak symmetry breaking is accessible
to direct experimental investigation. In the Standard Model electroweak symmetry breaking is
realized bytheHiggsmechanism leading toasingle scalar physical state, theHiggsboson. Ifthis
description is correct the LHC will be able to discover the Higgs boson and measure some of its
properties. It is also possible that the LHCwill uncover evidence of physics beyond the Standard
Model either by the direct production of new states or by deviations of the couplings of known
particles fromtheirStandardModelvalues.
Anomalous interactions oftheknowngauge bosons areoneinteresting possibility andcanbe
studied in gauge-boson production processes. While double gauge-boson production gives access
to thetriple gauge couplings, triple gauge-boson production processes allow to investigate quartic
gauge couplings. The QCD corrections to the production of three heavy gauge bosons have been
calculated [1], in some cases including the leptonic decays, and turn out to be fairly large. The
corrections toWWg and ZZg production at the LHC have also become available recently [2] and
aresizeable.
Another interesting process isWgg production which is sensitive to both the tripleWgg and
the quarticWWgg coupling [3, 4]. As already the case forWg production this process exhibits a
radiation zero, i.e. the leading order amplitude vanishes exactly for some momentum configura-
tions. TheradiationzerointheamplitudeappearsataspecificpolarangleoftheW withrespectto
theincomingquarkdirectioninthepartoniccentre-of-massframeifthephotonsarecollinear. This
zero willbe washed out in practice by the the difficulty in reconstructing the partonic c.m. frame,
the unknown incoming quark direction and finite detector resolution effects. Furthermore itcould
befilledbyradiativecorrections.
Inviewofthelargeradiative corrections forsimilarprocesses afullNLOQCDcalculation is
needed for reliable theoretical predictions. Wepresent the QCDcorrections toWgg production at
theLHCtreatingtheW asstable,i.e. withoutincluding decaysoftheW. Ourcalculation hasbeen
implemented inaflexible MonteCarlocomputer code allowingtocalculate arbitrary distributions
fromasetofweightedevents.
2. Calculation
Since we are interested in the anomalous quartic gauge coupling and the radiation zero we
focus on the production oftwo isolated photons accompanying theW. Producing both photons in
thehardinteractiongivesrisetothedirectcontributionto pp Wgg . Thesamefinalstatecanalso
→
be reached by producing Wqg in the hard interaction followed by a non-perturbative splitting of
the quark into a photon. This is described by a fragmentation function Dg/q(z) which is formally
of O(a ). Both the direct and the fragmentation contribution are therefore formally of the same
a
s
order in the couplings. In fact only the sum of direct and fragmentation contributions is physi-
callymeaningful. Inthefragmentation contribution thephotonwillbeaccompanied byacollinear
hadronic remnant. This contribution can therefore be suppressed by requiring the photons to be
isolated whichwillnotaffectthedirectcontribution.
2
RadiativecorrectionstoWgg productionattheLHC MarcusM.Weber
s (pp W+gg )[fb]
→
standard withisolation iso&jetveto
LOdirect 7.253(5) 7.253(5) 7.253(5)
LOfrag 24.30(2) 1.505(1) 1.501(1)
LOtotal 31.55 8.758 8.754
NLO 39.33(6) 25.62(4) 11.83(4)
Kfactor 1.25 2.93 1.35
Table 1: Total cross sections for pp W+gg at LHC for √s = 14TeV with standard cuts only, with
→
additional photon isolation cuts and with photon isolation and jet veto cuts. Shown are the leading-order
directand fragmentationcontributions,the total leading-ordercrosssection, the completeNLO resultand
theK-factor.
At NLO both the corrections to the direct and the fragmentation contributions are needed in
principle. Thefragmentationcontribution willproduceafragmentationcountertermwhichcancels
the QEDsingularity from the q qg splitting in the real radiation process qg Wqg . TheQED
→ →
singularity is therefore absorbed into a redefinition of the fragmentation function at NLO. Due to
the effective suppression of the fragmentation contribution using photon isolation cuts the NLO
corrections tothefragmentation process contribute onlylittle. Wetherefore takeintoaccount only
the NLO corrections to the direct contribution. The fragmentation contribution is calculated only
atLObutwiththeNLOfragmentation functions ofRef.[5], i.e. thefragmentation counterterm is
included.
The calculation itself has been performed in a diagrammatic approach mostly using standard
techniques and tools. Forthe virtual corrections the generation and simplification ofthe diagrams
has been performed using FEYNARTS [6] and FORMCALC [7]. The analytical results of FORM-
CALC havethenbeentranslated toC++code. Fortherealamplitudes MADGRAPH hasbeenused
[8]. In order to extract the soft and collinear singularities from the real corrections and combine
them with the virtual contribution we have implemented both a two cutoff phase-space slicing
methodaccording to[9]andthedipolesubtraction formalism[10].
The tensor 1-loop integrals appearing in the virtual amplitudes are evaluated using a tensor
reduction approach. The5-point integrals arereduced toscalar 4-point functions inanumerically
stable way using Ref. [11]. For the 3- and 4-point tensor integrals we employ Passarino-Veltman
reduction [12]. Inregionsofphasespacewherethisbecomesunstablewestillusethesamereduc-
tion butswitchtohigh-precision arithmetic using the QD library [13]. Sinceonlyasmallfraction
ofthepointsareunstabletheadditionaltimeneededbythehigh-precision evaluationsismoderate.
3. Numerical Results
Wenow turn to the study of some results forW+gg production at the LHCfor √s=14TeV.
Toobtainawell-definedcrosssectionweimposethefollowingstandard cuts
pT,g >30GeV h g <2.5 D Rgg >0.4 D R=pD f 2+D h 2
| |
onthetransversemomenta,thepseudorapiditiesandtheseparationofthephotons. Thecorrespond-
ingcrosssectionandtheassociated K-factorareshowninTab.1. Forthesecutsthefragmentation
3
RadiativecorrectionstoWgg productionattheLHC MarcusM.Weber
σ[fb]
pp W+γγ
→
35
LOdirect
NLOren
NLOfact
30
√s=14TeV
25
20
15
10
5
10 100 1000
Q[GeV]
Figure1: Scaledependenceofthedirectleading-orderandthefullNLOcrosssectionsusingthestandard
andphotonisolationcuts. Nojetvetoisapplied. Therenormalizationandfactorizationscaledependencies
oftheNLOresultareshownseparately.
contribution is by far dominant. The NLO corrections are only moderate when compared to the
combined LO result. However no corrections to the fragmentation contribution have been taken
intoaccountinourcalculation.
In order to isolate the direct contribution we impose an additional photon isolation criterion.
This is implemented by requiring the hadronic transverse energy inside a cone around the photon
tobelimited
ET,had <e ET,g insidecone D R(g ,had)<Rcone.
We use the energy fraction e =0.15 and a cone size of R =0.7. As Tab. 1 shows this sup-
cone
pressesthefragmentationcontributionbymorethananorderofmagnitudewhileleavingthedirect
contribution unchanged. The NLO corrections are very large with a K-factor of 2.93. At NLO
quark-gluon and antiquark-gluon induced partonic channels open up in the real corrections which
mightberesponsible forthelargecorrections.
In order to verify if the large corrections are caused by the real corrections we impose a jet
vetoinaddition tothestandard andisolationcuts. Weremovealleventswiththejetsfulfilling
p >50GeV and h <3.
Tj j
| |
ThisleavestheleadingorderunchangedwhilegreatlyreducingtheQCDcorrectionsascanbeseen
from Tab.1. Thecorrections arenowonly 35%andthelarge corrections seenwithoutjetvetoare
therefore indeedcausedbyrealradiation.
The scale dependence at leading and next-to-leading order is shown in Fig. 1. Since the LO
amplitude does not contain a the renormalization scale dependence is increased at NLO. The
s
factorization scaledependence isstabilized however.
InFig.2distributionsintheinvariantmassMgg ofthephotonsandthetransverseW momentum
p areshown. Thecorrections showashapedependence inbothcases. Thisisespecially strong
T,W
inthe p distributionwithaK-factorofabout2.5at p =20GeVandabout10at p =500GeV.
T,W T T
The effect of the jet veto is to remove the positive corrections at high invariant masses and p
T
completely while not affecting the lower regions as much. Regardless of the use of a jet veto the
4
RadiativecorrectionstoWgg productionattheLHC MarcusM.Weber
dMdσγγ[fb] pp W+γγ dpdTσ,W [fb] pp W+γγ
→ →
1 1
√s=14TeV tree √s=14TeV tree
NLO NLO
NLOveto NLOveto
0.1 0.1
0.01 0.01
0.001 0.001
0.0001 0.0001
0 100 200 300 400 500 600 700 800 900 1000 0 100 200 300 400 500
Mγγ[GeV] pT,W[GeV]
Figure 2: Distributions in gg invariantmass andW transverse momentum at leading and next-to-leading
orderusingstandardandphotonisolationcuts. AlsoshownistheNLOresultusinganadditionaljetveto.
dηγγd−σηW[fb] pp W+γγ dηγγd−σηW[fb] pp W+γγ
→ →
1.4 1.4
√s=14TeV cosθγγ>0 √s=14TeV cosθγγ>0
1.2 leadingorder cosθγγ<0 1.2 NLO cosθγγ<0
1 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
5 4 3 2 1 0 1 2 3 4 5 5 4 3 2 1 0 1 2 3 4 5
− − − − − − − − − −
ηγγ−ηW ηγγ−ηW
Figure 3: Distributions in pseudorapidity separation between the W and the two-photon system for the
photons in the same and in opposite hemispheres at leading order (l.h.s) and NLO (r.h.s). Both photon
isolationandjetvetocutshavebeenimposed.
NLO corrections show a strong shape dependence and can therefore not be described by a global
K-factor.
ToinvestigatetheimpactoftheNLOcorrections ontheradiationzeroweshowtheseparation
in pseudorapidity between the gg system and the W in Fig. 3. To show the radiation zero most
clearlynotonlyphotonisolationbutalsojetvetocutsareused. Thevariableusedhereissimilarto
that used for the Tevatron analysis of the radiation zero in Ref. [3]. Atleading order a dip at zero
pseudorapidity can be seen which is stronger for photons in the same hemisphere since the exact
amplitude zero only occurs for collinear photons. The NLO corrections have the effect of almost
filling the dip, similar to what has been observed for Wg production at the LHC [14]. This will
makeitverychallenging todetectthisfeatureoftheamplitudeattheLHC.
4. Conclusions
WehavecalculatedtheNLOQCDcorrectionstoWgg productionattheLHC.Thisprocesscan
be used to constrain the anomalous quarticWWgg gauge couplings and is therefore an important
5
RadiativecorrectionstoWgg productionattheLHC MarcusM.Weber
testing ground of the Standard Model. We have also included the single fragmentation contribu-
tion to this process at leading order. The fragmentation contribution can however be effectively
suppressed usingphotonisolation cuts.
Wefind large radiative corrections of about +200% which reduce to about +35% when using
an additional jet veto. Thesize ofthe corrections is similar to what has been found inWg and Zg
production. AsexpectedthetotalscaledependenceisincreasedatNLOwhilethepurefactorization
scale dependence is stabilized. The corrections induce strong shape distortions in several key
distributions. Theyalsotendtofillthedipcaused bytheradiation zerooftheamplitude making it
very hard toexperimentally verify this feature atthe LHC.Thecalculation has been implemented
inaflexibleMonteCarlocodewhichallowstostudyanydistribution usingarbitrarycuts.
Acknowledgments
ThisworkissupportedinpartbytheNationalScienceFoundationundergrantno. NSF-PHY-
0547564 andNSF-PHY-0757691.
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