Table Of ContentQCD and Collider Processes
GiuliaZanderighi
UniversityofOxfordandSTFC,Theoretical Physics,1KebleRoad,OX13PNOxford,UK
Abstract
I review the status of today’s theoretical description of Standard Model pro-
cesses relevant for Tevatron and LHC analyses, and of the tools that are used
in phenomenological studies. I will also discuss a few recent ideas to further
refineourabilities toperform technically challenging calculations.
2 1 Introduction
1
0 Today we face many fundamental questions, some of which are driven by experimental data, such as
2 the question about the mechanism of electroweak (EW) symmetry breaking, the nature of dark matter,
n and the physics associated with the vacuum energy, as well as questions that are driven by theoretical
a
curiosity and ambition, which are in essence propelled by our hope that there is an elegant structure
J
behind what weobserve in nature. Questions of the latter type include why there are three generations,
4
2 what causes the hierarchy of fermion masses and mixing, and how the strong CP problem is resolved.
Whilequestionsofthefirsttypedohaveadefiniteanswer,thisisnotnecessarilythecaseforthequestions
]
h of the second type. From this point of view, some of these questions might not even be the right ones
p
to ask. With the start of the LHC we feel that we are at a verge of big changes, the depth of which we
-
p can not assess yet. Indeed, the LHC marks the start of a long research program and experiments at the
e
LHC are expected to revolutionize our understanding of the fundamental forces and matter. The LHC
h
[ will definitely explore the origin of mass and the associated nature of EW symmetry breaking. In the
courseofthis,itmightalsoshedlightonthenatureofdarkmatterandtheoriginofthematter-antimatter
2
v asymmetry. Itmayalsoexplorethephysicsthatunderlies theevolution oftheearlyuniverse. Whileitis
5
clearthattheLHCwillnotanswerallthefundamentalquestions thatwehave,thequestionsweasknow
0
will most likely change after the LHCera. It is therefore really a great and unique time to be a particle
9
3 physicist.
.
1 Sincethebeginningofitsrunin2010,theLHChasbeenremarkablesuccessful. ATLASandCMS
0
collected around 45pb−1 in2010, morethan1fb−1 bythetimeofsummerconferences, andmorethan
2
1 5fb−1 bytheendoftheyear. Attheendofthe2011run, almosteveryweekhassetanewrecord inin-
: stantaneous luminosity. Withthe2010andearly2011data,remarkably, allmajorStandardModel(SM)
v
i processes have already been re-established, including single-top and di-boson production, challenging
X
measurements (because of the small/large cross-sections/backgrounds) that have been performed at the
r
a Tevatron only inrecent years. Bynow, wehave entered anew territory inthe search of physics beyond
theSM(BSM)withsensitivities already wellexceeding thoseofLEPandtheTevatron.
One important question then concerns the role of QCD for LHC measurements and new-physics
searches. Understanding how QCD works is essential in order to make accurate predictions for both
the signal and background processes. This typically requires complex calculations to higher orders in
the perturbative expansion of the coupling constant. Understanding QCD dynamics can however also
help reduce backgrounds and sharpen the structure of the signal. This can for instance be achieved by
designing better observables, by employing appropriate jet algorithms, by using jet-substructure, or by
exploiting properties of boosted kinematics. Finally, once discovery is made, QCD will be crucial to
extract the properties (masses, spins, andcouplings) ofthe newstates found. Therefore, atthe LHC,no
matterwhatphysicsyoudo,QCDwillbepartofyourlife.
Itisinteresting tofirstrecallarecentmeasurementthatwastheoriginofconsiderable excitement.
In April 2011, CDF reported the observation of a peak in the m distribution in W + dijet events [1],
jj
22)eV/c)eV/c 770000 CCWWDDWWFF++ ddWWaaZZttaa 44((..4455..%%33 ffbb--11)) 2)eV/c 116800 BBkkgg SSuubb DDaattaa ((44..33 ffbb--11))
8 G8 G 660000 WW++JJeettss 8800..22%% 8 G 140 GGaauussssiiaann
s/(s/( TToopp 66..55%% s/( 120 WWWW++WWZZ ((aallll bbkkgg ssyysstt..))
ntnt 550000 ZZ++jjeettss 22..88%% nt
ee e 100 (d)
vv QQCCDD 55..33%% v
EE 440000 E 80
(a) 60
330000
40
220000 20
0
110000
-20
00 -40
110000 220000 100 200
MM [[GGeeVV//cc22]] M [GeV/c2]
jjjj jj
Fig.1: ThedijetinvariantmassdistributionforW plusdijeteventsasmeasuredbyCDF.Theleftpaneshowsthe
fits for knownprocessesonly. Therightpane shows, by subtraction, the resonantcontributionto m including
jj
WW andWZ productionandahypothesizednarrowGaussiancontribution.Figurestakenfrom[1].
see Fig 1. The first measurement had a 3.2σ significance, and was based on 4.3 fb−1. Subsequently,
moredata(7.3fb−1)hasbeenanalyzed,leadingtoasignificanceofmorethan4σ[2]. Sincethen,alarge
number of tentative new-physics explanations appeared on the arXiv, along with a few SM analyses
that address the question of whether this effect can be attributed to a mismodelling of one of the SM
backgrounds(inparticularsingletop)[3–5]. Theexcitementwascurbedfewmonthsafterwards,whenin
June,D0announcedthatitdidnotconfirmtheexcessseenbyCDF[6]. Itisyetunclearwhatthereasons
for the discrepancy between CDF and D0 findings are, if any. However, this example demonstrates
that even in the case where one identifies a mass peak in the tail of a distribution (a scenario that was
considered “an easy discovery”) a robust control of SM backgrounds remains mandatory, in particular
when the shape of the backgrounds is one of the issues. Currently we have a number of other recent
measurements atcollider experiments thatreport afew sigmadeviations from the SMpredictions. This
isforinstance thecaseforthetopforward-backward asymmetrymeasuredbybothCDF[7]andD0[8],
forthedimuonchargeasymmetrymeasuredbyD0[9],forW +bmeasuredbyD0[10],CPviolation in
time-integrated D0 decays[11],andafewmore.
The important question becomes then what the tools at our disposal are to make precise predic-
tions, andwhether wehave the solid control ofsignal and background processes that isneeded in order
to claim discoveries. In this write-up I will discuss the status of our theoretical knowledge of most
important SM processes, the tools at our disposal to describe these processes, and the impact of QCD
higherordersinviewofrecentTevatron/LHCresults. Finally,Iwilldiscussafewrecentideastofurther
improveonthewayweperform technically challenging calculations.
2 Perturbative tools
The range of physics analyses that one can do at the LHC is very broad. It includes pure instrumental
QCD studies, such as measurements of parton densities and inclusive jet cross-section measurements,
precision EWmeasurements, Higgssearches, directandindirectBSMsearches, B physics, topphysics,
diffractive studies and forward physics, and heavy ion physics. Each of these topics includes a vast
numberofmeasurementsandstudies. Yet,therearethreethingsthateverybody involved inanyofthese
analyses cannotlivewithout. TheseareMonteCarlos(MCs),partondistribution functions (PDFs),and
jets.
2
vents111110000077777 (cid:242) L dt ~ 1.34 fb-1 DToattaal 2S0M1 1P (r edsi c=t i7o nTeV)
E111110000066666 ATLAS AAllppggeenn Wttfifi mq l,nll
111110000055555 Alpgen Zfi (eem,mt,t)
Alpgen Wfi (e,t)n
111110000044444 SUSY Point (1220,180)
111110000033333 W Control Region
111110000022222 pT > 55 GeV jets
1111100000
11111
1111100000-----11111
DATA / PredictionDATA / Prediction0101....22555511 11111 22222 33333 44444 55555 66666 77777 88888 99999 1111100000
00 11 22 33 44 55 66 77 88 99 1100
NNuummbbeerr ooff JJeettss
Fig.2: Themultiplicityofjetswithp >55GeVforeventsinaW enrichedcontrolregionattheLHC(7TeV).
T
Figuretakenfrom[18].
2.1 MonteCarlosandleadingordermatrixelements
The first thing one can not live without at the LHC are MC generators. Apart from very few excep-
tions, every analysis at the LHC uses a MC program for the simulation of the signal process, for the
backgrounds, for subtracting the underlying event and the non-perturbative contributions, and/or for ef-
ficiency studies and modeling of the detector response. The current level of sophistication is such that
essentially not asingle study relies on Pythia/Herwig alone. It is well understood that in multi-parton
processesitisimportanttodescribethemultiplehardQCDradiationatleastusingexactmatrixelements,
employing forinstance Alpgen[12],Madgraph[13],orSherpa[14].
Since experimental studies rely heavily on all these leading-order (LO)tools, there is continuous
progress intheirdevelopment, andtheHerwig/Pythiacodesthatwehavetodaybearlittleresemblance
to their original version of the ’80s. In particular, in Pythia 8.1 [15] (a C++ code) there is a new
fullyinterleaved p -ordered multi-parton interaction (MPI),initial-andfinalstateevolution (theoriginal
t
mass-ordered evolution is not supported any longer), a richer mix of underlying event processes (γ,
J/Ψ, DY), the possibility to select two hard interactions in the same event, an x-dependent proton size
intheMPIframework, thefullhadron–hadron machinery fordiffractive systems, several newprocesses
in and beyond the SM, and various other new features. Herwig++ [16] (the current version is 2.5.2)
has new next-to-leading order (NLO) matrix elements, including weak boson pair production, a colour
reconnection model,diffractive processes, additional modelsofBSMphysics, andnewLOelementsfor
hadron-hadron, lepton-lepton collisions, andphoton-initiated processes. Sherpa[14](version1.3.1)has
improved integration routines in Comix, a simplified kinematics reconstruction algorithm of the parton
shower(PS),leadingtonumericallymorestablesimulations,HepMCoutputforNLOeventsandvarious
other improvements/bug-fixes. Madgraph [13] (version 5) has a completely new diagram generation
algorithm, which makes optimal use of model-independent information, has an efficient decay-chain
package,andanewlibraryforthecolourcalculations. SomeapplicationsfromALOHA[17],anautomatic
library of helicity amplitudes for Feynamn diagram computations are also implemented. Altogether,
there is continuous, fast progress in various directions. Sofar, it is amazing how well these tools work,
once thenormalization isfixedusing data. Averyrecent comparison ofdatawithAlpgenuptosixjets
(a control region for BSM searches) is shown as an illustration in Fig. 2 [18]. Yet, the devil is often in
the detail (i.e. inthe 20 30% effects that areopposite toexpectations). Forinstance ingeneral one
∼ −
expectsmatrix-element basedMCstoworkbetterthanpurePSs,butthisisnotalwaysthecase(seee.g.
[19]). Altogether, theseLOprogramswillundergo arealstresstestinthecomingyears.
3
2.2 TheNLOrevolution
TheoristsliketoadvertiseNLOcomputations byusingthereductionofscaleuncertainties inthepredic-
tions as an argument, which is meant to reflect the reduction in the theoretical perturbative uncertainty.
However, the strongest argument in support of NLO calculations is their past success in accurately de-
scribing LEPandTevatrondata. Becauseoftheimportance ofNLOcorrections, anindustrial efforthas
been devoted in the last years to these computations [20]. Recent revolutionary ideas in the way NLO
computations are performed include sewing together tree-level amplitudes to compute loop amplitudes
(usingon-shellintermediatestates,cuts,unitarityideas,...)[21],theOPPalgorithm,analgebraicwayto
extractcoefficientsofmasterintegralsbyevaluatingtheamplitudesatspecificvaluesoftheloopmomen-
tum [22], and D-dimensional unitarity, a practical numerical tool to evaluate full amplitudes, including
therationalpart,withunitarityideas[23]. Forapedagogicalreviewonunitaritymethodssee[24]. These
methodsledinthepast2to3yearstoanumberof2 4calculationsathadroncolliders. Theseinclude
W +3jets[25,26],Z+3jets[27],tt¯b¯b[28],tt¯ W→+W−b¯b[29],W+W+ +2jets[30],W+W− +2
jets[31],b¯bb¯b[32],tt¯+2jets[33],fourjetprodu→ction [34],andafewotherones.
Feynman diagram methods have also been applied successfully to 2 4 calculations, this is for
instance thecaseforquark-induced b¯bb¯b[35],tt¯b¯b[36],W+W−b¯b[37]pro→duction, Wγγ+jet[38],and
anumber ofvector boson fusioon (VBF)processes which areavailable inthepublic code VBFNLO[39].
VBFprocesses haveneverbeenmeasured attheTevatron. Firstmeasurements ofVBFW orZ produc-
tion at the LHC are therefore of particular interest. They also pave the way to measurements of VBF
Higgs production. Note that only a few years ago, performing this type of calculation with Feynman
diagramswasconsidered animpossible task.
A novel approach to NLO calculations, based on the results of [40], promotes traditional tree
algorithms togenerators ofloop-momentum polynomials, thatarecalledopenloops[41]. Theexcellent
performance of the method has been demonstrated, open loops have therefore a potential to address a
numberofmulti-particleprocessesathadroncolliders. Anotherrecentapproachevaluatesone-loopQCD
amplitudespurelynumerically[42]. Thealgorithmconsistsofsubtractionterms,approximatingthesoft,
collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the integration
contour for the loop integration into the complex space. The algorithm is formulated at the amplitude
level and does not rely on Feynman graphs. The power of this method has been demonstrated recently
withtheleading colorNLOcalculation ofuptosevenjetsine+e− collisions [43].
Given that both Feynman diagram and unitarity based methods allowed us to compute 2 4
→
processes at NLO in QCD, it might be unclear where the revolution advocated in the heading of the
subsection liesin. Therevolution, Ibelieve, isnotyetintheapplications thatweseetoday, ratherinthe
prospectforlow-costfullycomputer-automated NLOcalculationsevenbeyond2 4inthenearfuture.
→
Indeed, two 2 5 processes have already been computed at NLO, namely W + 4 jets [44] and Z + 4
→
jets[45].1 Fig.3illustratesinthecaseofW−+4jetsthetypicaleffectofincludingNLOcorrections: one
obtains aconsiderable reduction ofthescaleuncertainty, and,forsomedistributions, achange inshape.
Asfarasthefullautomationisconcerned,letmehighlightthreeinterestingapproaches. Thefirstone[46]
is a method based on Feynman diagrams, it uses the OPP procedure for the virtual calculation, and the
FKS subtraction of divergences, together with clever and efficient procedures to deal with instabilities.
Moreimprovementsandrefinementsaretobeexpectedsoon. Atpresentthereisnopubliccode,instead
the idea is to provide N-tuples. The second approach, HELAC-1LOOP [47], is a program that evaluates
numericallyQCDvirtualcorrectionstoscatteringamplitudesusingtheOPPmethod. Thepublicprogram
is part of the HELAC-NLO framework that allows for a complete evaluation of QCD NLO corrections.
GoSam[48]isathirdapproachwhichaimsatthefullautomatedcalculationofNLOcorrectionsformulti-
particle processes. The one-loop amplitudes are generated using Feynman diagrams and are reduced
using D-dimensional unitarity, a refined Passarino-Veltman style tensor reduction, or a combination of
1Inbothcasestheleadingcolourapproximationhasbeenused. Thisapproximationisexpectedtogiverisetoverysmall
(percent)correctionsonly.
4
50 100 150 50 100 150 50 100 150 50 100 150
100 100
-
W + 4 jets + X (cid:214) (cid:190)s = 7 TeV LO
10-1 NLO 10-1
V ]
Ge
pb / 10-2 10-2
p [ T
sd / d 10-3 pETjeet >> 2250 GGeeVV,, | |h hjeet || << 32 .5 10-3
T
m = m = H^’ / 2 ETn > 20 GeV, MTW > 20 GeV
10-4 R F T R = 0.5 [anti-kT] 10-4
LO / NLO NLO scale dependence LO scale dependence BlackHat+Sherpa
2 2
1.5 1.5
1 1
0.5 0.5
50 100 150 50 100 150 50 100 150 50 100 150
First Jet p [ GeV ] Second Jet p [ GeV ] Third Jet p [ GeV ] Fourth Jet p [ GeV ]
T T T T
Fig.3:ThetransversemomentumdistributionoftheleadingfourjetsinW−+4-jetproductionattheLHC(7TeV)
at LO and NLO. Thelower panelsshow the LO and NLO scale-dependencebands(Hˆ′/4 µ = µ Hˆ′ )
≤ R F ≤ T
normalizedtothecentralNLOprediction(µ =µ =Hˆ′ /2).Figuretakenfrom[44].
R F T
both. GoSam can be used to calculate one-loop corrections to both QCD and electroweak theory, and
model files for BSM theories can be also linked. An interface to programs calculating real radiation is
includedtoo. TheflexibilityofGoSamhasbeendemonstratedexplicitlybyconsideringvariousexamples.
2.3 MergingNLOandPartonShowers
WhileNLOpredictionsproviderelativelyaccurateresultsforinclusivecross-sections,theydonotfurnish
an exclusive description of the final state that can be compared with actual particles in the detectors, as
MC programs do. It is therefore useful to combine the best features of both approaches. Two public
frameworksexistforthispurpose,namelyMC@NLO[49]andPOWHEG[50]. Thesetoolsarealmost10years
oldnow,andsincetheirconceptionalonglistofprocesseshasbeenimplementedinbothframeworks. In
particular, recently the POWHEG BOXwas released [51], which is a general framework for implementing
NLO calculations in shower MC programs according to the POWHEG method. The user only needs to
provide a simple set of routines (Born, colour-correlated Born, virtual, real, and phase space) that are
partofanyNLOcalculation.
Similarly,[email protected]@NLOhasbeen
used recently for the calculation of W/Zb¯b [52] and W+dijet production [53]. Fig. 4 (left) shows an
applicationtoHiggssearchesoftheW/Zb¯bcalculation: theinvariantmassofthepairofthetwoleading
b-jets, for the processes Wbb, Zbb, WH, and ZH. The figure illustrates a case where signals and
irreducible backgrounds arecomputedwiththesameaccuracy. TheprocessWb¯bhasbeenimplemented
shortlybeforealsointhePOWHEG BOX[54].
Fig. 4 (right) illustrates predictions from aMC@NLO for the invariant mass for the dijet system in
Wjj (the observable mentioned in the introduction where CDF observed a large deviation from the
SM). CDF and D0 estimate the Wjj using a leading order Monte Carlo (LO+PS) re-weighted to the
NLO cross-section or to data. With aMC@NLO instead it is possible to compute directly the Wjj cross-
sectionattheNLO+PSlevel. Itwasthereforeparticularlyinterestingtocheckwhetherthereisanyshape
differencebetweenLO+PSandNLO+PSintheM distribution. Thestudyofref.[53]showsthatthere
jj
isnosizableshapedifference. Anotherinteresting application ofaMCNLOisthecalculation ofscalarand
pseudo-scalar Higgsproduction inassociation withatt¯pair[55].
5
Fig.4: Left:Invariantmassofthepairofthetwoleadingb-jetsforWb¯b,Zb¯b,WH( ℓνb¯b),ZH( ℓ+ℓ−b¯b)at
→ →
theLHC(7TeV),thelattertwoarerescaledbyafactoroften. Figuretakenfrom[52]. Right: Invariantmassof
thepairofthetwohardestjetsinW+jeteventswithCDF/D0inclusivecuts. Figuretakenfromref.[53].
1e-2 1e-2
V] POWHEG+PYTHIA V] POWHEG+PYTHIA
e e
G NLO G NLO
b/ b/
[fOT 1e-3 [fOT 1e-3 First 3 jets only
T T
T, T,
H H
d 1e-4 d 1e-4
/ /
sd sd
NLO 1.5 NLO 1.5
yt)/ 1.0 yt)/ 1.0
P P
+ +
hg 0.5 hg 0.5
(P 0 500 1000 1500 2000 (P 0 500 1000 1500 2000
H [GeV] H [GeV]
T,TOT T,TOT
Fig.5: ComparisonofNLOandPOWHEG+PYTHIAresultsfortheH distributionintheprocessW+W++2
T,TOT
jetsattheLHC(7TeV),whenalljetsareincludedinthedefinitionofH (leftpane),andwhenonlythethree
T,TOT
hardestjetsareincluded(rightpane).Figuretakenfromref.[56].
A lot of effort has been devoted recently also to the implementation of higher multiplicity pro-
cesses in the POWHEG BOX and in aMC@NLO. The first 2 4 process that has been implemented in the
→
POWHEG BOX is pp W+W++ 2 jets including both the QCD induced part [56] as well as the VBF
→
contributions [57]. This is a relatively simple 2 4 process since the cross-section is finite without
→
any cut on the jets. As expected, for inclusive observables there are only minor differences between
pure NLO and POWHEG+PS, but for exclusive observables, depending on the details of the observable
definition, there can be important differences. This is shown in Fig. 5 for two different definitions of
H = p , the transverse energy of the event. From the figure it is clear that if only the three
T,TOT j t,j
P
hardest jets are included in the definition of H , the corrections from the PS are very moderate (right
T
pane), but if all soft jets present in the event are included, then additional radiation from the PS can
alter the distribution substantially (left pane). The POWHEG method has been used recently also for the
description of other important processes, e.g. for the calculation of Z boson in association with a top
anti-top pairatNLOaccuracyincluding PSeffects[58].
2.4 MENLOPSandLoopSim
InNLO+PSapproaches only contributions withoneadditional jet, relative totheBorncontribution, are
computed accurately, while all other emissions are described only in the shower approximation. There
6
4
10
LO LO LO
3 NLO NLO NLO
V] 10
e
G
0 102
0
1
b /
V [f 10
d
/
pp, 14 TeV
sd 1
anti-k, R=0.7
t
pt,j1 > 200 GeV, Z fi e+e- MCFM 5.7, CTEQ6M
-1
10
250 500 750 1000 250 500 750 1000 250 500 750 1000
V = p [GeV] V = p [GeV] V = H [GeV]
t,Z t,j1 T,jets
Fig.6: The LO andNLO distributionsfor threeobservablesin Z+jetproductionthatare identicalat LO:the Z
transversemomentum(left),thep ofthehardestjet(middle),andthescalarsumofthetransversemomentaofall
t
thejets,H (right). Thebandscorrespondtotheuncertaintyfromasimultaneousvariationofµ = µ = µ
T,jets R F
byafactoroftwoaroundthedefaultµ=√p2 +m2. Figuretakenfrom[61].
t,j1 Z
are however situations in which one has important contributions from higher multiplicity final states
(e.g. because of new channels that open up that are enhanced by kinematical factors, gluon PDFsetc.).
MENLOPS[59,60]isamethodtofurtherimproveonNLO+PSpredictionswithmatrixelementsinvolving
more partons inthe final state. Forexample, forW production it includes, asin MC@NLOor POWHEG,W
productionatNLO,thePS,butalsoW +1,2,3,...jetsusingexactmatrixelements. Roughlyspeaking,
it uses a jet-algorithm to define two different regimes, and then corrects the 1-jet fraction using exact
matrixelements andthe2-jetfractionusingtheNLOK-factor. ThisachievesNLOquality accuracy for
inclusivequantities butanimprovedsensitivity tohardradiation andmulti-parton kinematicfeatures.
Afurther recent theoretical development isLoopSim. Ifoneconsiders the process W +1jet, the
three observables p , p , and H = p are identical at LO.However, as illustrated in Fig. 6,
t,Z t,j T,jets j t,j
P
at NLO p has a moderate K-factor (/ 2), p has a large K-factor ( 5) and H has a giant
t,Z t,j T,jets
∼
K-factor ( 50). The very large K-factors in the last two observables are due to the fact that the NLO
∼
result is dominated by configurations where there are two hard jets and a soft W (these are enhanced
byEWlogarithms),additionally thereisanimportantenhancement comingfromincomingqq channels.
LoopSim [61] is a procedure that uses a sequential algorithm, close to the Cambridge/Aachen one, to
determine the branching history, “loops” over soft particles (i.e. they are removed from the event and
the residual event is adjusted), and it uses aunitary operator to cancel divergences. In essence, this is a
way to extend a calculation that is exact at a given order in perturbation theory, in an approximate way
to higher orders. The procedure is expected to be more accurate the larger the corresponding K-factor
is. Onemightexpect other extensions oftheMLM/CKKWmatching procedure along thesamelines as
MENLOPSandLoopSiminthenearfuture.
3 Top-quark production
Thetopisthemostinteresting SMquark. ItslargemassimpliesalargeYukawacoupling, whichcauses
thetoptobeaprominentdecayproductinmanyBSMmodels. LHCdatahavealreadybeensuccessfully
compared to approximate next-to-next-to-leading order (NNLO) predictions [62,63], however various
approximate NNLO predictions, based on a threshold resummation, do not fully agree within quoted
uncertainties [64–68]. Significant improvements in the tt¯cross-sections can be expected only upon in-
clusionofthecompleteNNLOcorrections. Abetterperturbativecontrolofthetop-quarkpairproduction
cross-section isalsoimportanttofurtherconstrain gluonPDFs,tohaveanaccurateextraction ofthetop
7
massfromthecross-section,andtoimproveourperturbativecontroloverthett¯forward-backwardasym-
metry. Infact,analmost3σ deviationfromtheSMisobservedbyCDF,whichbecomesa4.2σ effectin
the high-mass region, Mtt¯> 450 GeV [7]. Thelarge inclusive asymmetry has been seen both by CDF
andD0[8],whiletheriseinthespectrumoftheasymmetryisnotconfirmedbyD0. Onehashoweverto
bearinmindthattt¯productionisadifficultmeasurementgiventhepresenceofneutrinosinthefinalstate,
the combinatorics in the reconstruction of the tops, and the limited statistics at the Tevatron. Neverthe-
less,varioussuggestionshavebeenmaderecentlytoexplaintheasymmetryintermsofBSMphysics,but
all proposals face the problem that they have to preserve the good agreement withthe symmetric tt¯ob-
servables,respectdijetboundsand/ormustevadethestringentlimitsonlike-signtopproduction. Fervid
activity is therefore currently devoted towards a complete NNLO calculation of tt¯production (see [69]
and references therein). Recently, the program Top++ was released that evaluates numerically the total
inclusive cross-section for producing top quark pairs at hadron colliders. It calculates the cross-section
at fixed order through approximate NNLO and it includes a soft-gluon resummation in Mellin space at
next-to-next-to-leading logarithmic accuracy [70]. The program Hathor [71] also calculates the total
cross-section fortop-quark pairproduction inhadronic collisions. Itincludes approximate next-to-next-
to-leading order perturbative QCD corrections. It also offers the possibility to obtain the cross-section
asafunction oftherunning top-quark mass. Adirectcomparison betweenthetwoprograms ishowever
notpossible astheyuseadifferentsubleading termsinthethreshold expansion.
Besides the inclusive cross-section, top pair production in association with light jets, heavy par-
tons, photons or heavy vector bosons is also interesting. We know now at NLO tt¯ + 2 jets [33],
tt¯b¯b [28,36], tt¯Z [72], tt¯+ γ [73], and for tt¯+ 1 jet including hard jet radiation by the top quark
decay products [74]. Amatching to parton shower has been recently achieved also to tt¯+1jet produc-
tion[75,76].
The NLOcalculation ofsingle top in the s and t channel [77,78]and in the Wtchannel [79,80]
have also been matched to parton showers. Fora discussion of recent theoretical progress in single-top
physicsathadroncolliders, andofaspectsofsingle-top production inbeyondStandardModelscenarios
Ireferthereadertoref.[81].
4 A few theoretical issues inHiggsproduction
Possibly the most awaited result during the firstyear of running of the LHCconcerned Higgs searches.
Currently, both ATLASand CMS reached the expected sensitivity, around or better than the SM cross-
section. ATLASrestrictedthemostlikelymassrangeat95%confidencelevel(CL)totheregion115.5
−
131GeV.Theyobserve anexcess around 126 GeV,withalocal significance of3.6σ,withcontributions
from the main channels H ττ, H ZZ 4l, H WW 2l2ν. The global significance
→ → → → →
taking intoaccount thelook-elsewhere-effect is2.3σ. CMSexcludes theregion 127 600GeVat95%
−
CL (while their expected exclusion is 117 543 GeV). They could not exclude the region below 127
−
GeVsincedatahasamodestexcessofeventsbetween115and127GeVthatappears,quiteconsistently,
in five independent channels. The excess is compatible with a SM Higgs hypothesis in the vicinity of
124GeVorslightlybelow,butthestatisticalsignificance, 2.6σ localand1.9σ globalaftercorrecting for
the look-elsewhere-effect in the low mass region, is not large enough to say anything conclusive. For
bothexperiments, whatisobserved nowisconsistent eitherwithabackground fluctuation orwithaSM
Higgsboson. Morerefinedanalyses andadditional datain2012willdefinitelygiveananswer.
At the LHC, the Higgs is mainly produced via an intermediate top loop in gluon-gluon fusion.
Theurge tounderstand the EWsymmetry breaking led inthe past years to thecomputation ofthe most
advanced theoretical predictions forthisprocess. Forinstance wenowknow themaingg H produc-
→
tion mechanism including NLO corrections with exact top and bottom quarks in the loop [82], NNLO
corrections in the large m limit [83–85], EW corrections [86], mixed QCD-EW corrections [87], and
t
resummation of large logarithms possibly withN3LOsoft effects [88–93]. Threshold corrections tothe
boson rapidity distribution are also known [94], these higher order corrections stabilise the theoretical
8
predictions under scale variations. Furthermore, the most advanced codes [95,96] allow for fully ex-
clusive decays of the Higgs to γγ, W+W− e+νe−ν¯, and ZZ 4l. A similar accuracy has been
→ →
reached recently also in associated VH production where, because this process is an important one if
the Higgs is light, the decay of the Higgs into b¯b has been considered [97]. NLO EW corrections to
WH/ZH production including thevector-boson decaysarealsoknown[98]. Asexpected, theEWcor-
rections, which are at the level of (5-10)% for total cross sections, increase with increasing transverse
momentum cuts. For instance, for p > 200 GeV, which is an interesting range at the LHC, the EW
T,H
corrections toWH production areoftheorderof-15%forM = 120GeV.
H
ThefullydifferentialdecayofalightHiggsbosontobottomquarksatNNLOinperturbativeQCD
hasbeencomputedrecentlyin[99]. Fromatechnicalpointofview,itisinterestingtonotethatthiswork
constitutes the first physical application of a novel method of non-linear mappings for the treatment of
singularities in the radiative processes which contribute to the decay width. The program iHixs [102]
hasalsobeenrecentlyreleased,itcomputestheinclusiveHiggsbosoncross-section, includingQCDcor-
rections through NNLO,EWcorrections, mixedQCD-electroweak corrections [87],quark-mass effects
throughNLOinQCD,andfinitewidtheffectsfortheHiggsbosonandtheheavyquarks. Furthermore,it
allowsthe evaluation ofthecross-section inmodified Higgsboson sectors withanomalous Yukawaand
EWinteractions asappearing insomeextensions oftheSM[101,102].
Giventhehighaccuracywithwhichgluon-gluon-fusion hasbeencomputed,itisinterestingtoask
whatistheactualtheoretical uncertainty onthisprocess. Unfortunately, thereistodaynofullconsensus
onthisquestion. Somemoreconservative estimates quoteerrorsoftheorderof40%[103](attheTeva-
tron)andsimilaruncertaintiesattheLHC,whileotherstudiessuggestthattheperturbativeuncertaintyis
considerably smaller. Assigningacorrecttheoreticalerrorisveryimportantwhenclaiminganexclusion
or an excess, and, at a later stage, when making measurements of the Higgs-boson couplings, which is
theonlywaytoidentifytheprecisenatureoftheHiggsbosonandEWsymmetrybreaking. Yet,evenfor
themainHiggs-production channel there arestill somecontroversies andsubtleties. Mostcontroversies
havetodowithhowdifferent sourcesoferrors shouldbecombined, othersconcern thequestion ofhow
toassign/interpret theperturbative uncertainties. Iwillillustrateherejusttwooftheseissues.
The soft logarithms appearing in cross-sections can be resummed using an effective theory ap-
proach. Performing such a calculation requires an introduction of a matching scale, where the full and
effectivetheoryamplitudesmustagree. Itiswell-knownthatchoosingatime-like(i.e. complex)match-
ingscaleeffectivelyresumsπ2 enhancedterms. In[104]itissuggestedthatthisprocedure improvesthe
convergence of the perturbative expansion significantly, and reduces the uncertainty of the perturbative
(NNLO) prediction. This approach is criticized in [105] with the arguments that π2 are just numbers,
sothatthereisnoformallimitinwhichtheydominate, andthatonlyoneclassofπ2 termsisresummed
(thosethatarisefromthegluonformfactor), butnotallofthem. Inthiscontext,onehastomentionthat
perturbativeQCDisoftenaboutpushingapproximations beyondtheirformallimitofvalidity,andthata
givenapproach shouldbejudgedbyseeinghowwellitfaresinpractice.
The second issue I would like to mention here has to do with a jet-veto in Higgs searches. As
can be seen from Fig. 7, in Higgs searches one needs to impose a jet-veto to suppress the large top
background. Higgs production is then studied in 0-, 1-, 2-jet bins separately in order to maximize the
sensitivity. Currently, ATLAS uses p = 25 GeV, while CMS employs p = 30 GeV in their
t,veto t,veto
Higgssearches.
In [107] the inclusive, NNLOHiggs production cross-section at the Tevatron is split into 0-,1-jet
exclusive, and2-jetinclusive components
dσ
tot = 66.5%+5%(0 jet)+28.6%+24%(1 jet)+4.9%+78%( 2 jets) = [ 14.3%+14.0%]. (1)
σ −9% − −22% − −41% ≥ − −
tot
Theerrorsdenotethescaleuncertainty thatisobtainedbyvaryingtherenormalization andthefactoriza-
tionscaletogetheraroundacentralvaluem = 160GeVbyafactoroftwo. InanNNLOcalculation of
H
9
s 2000
e ATLASPreliminary Data SM (sys ¯ stat)
ntri 1800 s = 7 TeV, (cid:242) L dt = 1.70 fb-1 WW WZ/ZZ/Wg
E 1600 tt Single Top
Hfi WWfi ln ln Z+jets W+jets (data driven)
1400 H [150 GeV]
1200
1000
800
600
400
200
C 2
M
a / 1.5
Dat 1
0.5
0 2 4 6 8 10
N
jets
Fig.7:Multiplicityofjetswithp >25GeVafterbasicHiggssearchcuts.Thelowerpartshowstheratiobetween
T
thedataandthebackgroundexpectationfromMC,withtheyellowbandindicatingthetotalsystematicuncertainty
in the normalization (but not the shape) of the various components. The signal is shown for m = 150 GeV.
H
Figuretakenfrom[106].
inclusiveHiggsproduction,onlythe0-jetbinisknownatNNLO,whilethe1-jetbinisknowatNLOand
the 2-jet bin is computed at LOonly. Therefore is itnot surprising that the relative errors increase with
the number of jets. In [107] one can also find a detailed discussion of why it is not appropriate to use
the standard scale variation as an estimate of the perturbative uncertainty for the 0-jet bin cross-section
(Fig.1of[108]alsoshowsthatforaparticularchoiceofp oneobtainsavanishingscaleuncertainty
T,veto
band in the 0-jet bin). The numbers in eq. (1) were updated by Campbell et al. in [109] who evaluated
the2-jetbincontribution atNLO.Theeffectofthisadditionwasaslightchangeinallrelativenumbers,
and,mainly,adecrease intheperturbative uncertainty ofthe2-jetbin,
dσ
tot = 60%+5%(0 jet)+29%+24%(1 jet)+11%+35%( 2jets) = [ 15.5%+13.8%]. (2)
σ −9% − −23% − −31% ≥ −
tot
Fromeq.(2),itisevidentthatthescaleuncertainty issmallerfortheexclusivemeasurement with0-jets,
than the one of the fully inclusive measurement. To explain this feature, Stewart and Tackmann recall
that there are two mechanisms at work in the 0-jet cross-section [110]: there is a large K-factor from
perturbative higher orders, as well as large negative logarithms α C /πln2M /p that become
s A H t,veto
−
more important the smaller p is. They therefore suggest that the error on the 0-jet bin should be
t,veto
computed taking into account a full correlation between jet-bins, i.e. the error from the 0-jet cross-
sectioniscomputedfromtherelationσ = σ σ . Oneobtainsthensimply∆2σ = ∆2σ +
0 incl ≥1−jet 0 incl
−
∆2σ . Theeffectofthisisillustrated inFig.8. Whilethisprocedureiscertainlymoreconservative
≥1−jet
thanaconventionalscalevariation,itisclearthattoreducetheuncertaintyonthejet-vetocross-section,a
resummationoflargelogarithmsinvolvingtheratiop /M isrequired. Currently,onlyresummation
t,veto H
for quantities related to the jet-veto exist, e.g. for p [111] or for the beam-thrust [112]. Both
T,Higgs
observables are however not the ones used in current Higgs searches. Furthermore the beam thrust has
thedrawback that itreceives very large non-perturbative corrections, ascan beeasily seen byrunning a
PSprogram onceatpartonandonceathadronlevel.
10
