In this talk we summarize some recent developments in perturbative QCD and
their application to particle physics phenomenology.Comment: 7 pages, 6 figures. Contribution to the proceedings of the
  international symposium on Physics in Collision 2013 (PIC 2013

/SLAC

Hoeche, Stefan

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 In this paper we summarize some recent developments in perturbative QCD and their application to particle physics phenomenology. </jats:p

Stefan Höche

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International Journal of Modern Physics A

Applications of higher-order QCD

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Applications of higher order QCDStefan HöcheSLAC National Accelerator Laboratory, Menlo Park, CA 94025, USAshoeche@slac.stanford.eduSLAC-PUB-15867In this talk we summarize some recent developments in perturbative QCD and theirapplication to particle physics phenomenology.1. IntroductionWith the discovery of a new boson at the Large Hadron Collider (LHC), particlephysics has entered a new era. Since this discovery, the field has quickly movedtowards precision measurements on the new particle. In order to further improvethese measurements and to find possible small deviations that may hint towardsnew physics, improved theoretical predictions, including higher-order perturbativeQCD corrections for production rates and kinematics are urgently needed. The sameis true for other reactions of interest at the LHC, like top quark production andW/Z production. The toolkit used to this end ranges from fixed order calculationsat the parton-level over resummation to parton showers and particle-level eventgenerators. Tremendous progress has been made in the field during the past year.Some of the recent developments will be briefly summarized in this talk.2. Higher-order calculationsFixed-order calculations are available for a large variety of processes. At the treelevel, they have long been performed completely automatically using programs likeALPGEN [1], Amegic++ [2], Comix [3], CompHEP [4], HELAC [5], MadGraph [6]and Whizard [7]. At the next-to-leading order (NLO), automation required two mainingredients: The implementation of known generic methods to perform the subtrac-tion of infrared singularities [8–10], and the automated computation of one-loop am-plitudes. As infrared subtraction terms consist of tree-level matrix elements joinedby splitting operators, existing programs for leading order calculations are ideallysuited to compute them. Correspondingly, Catani-Seymour dipole subtraction hasbeen implemented in the existing generators Amegic++ [11], Comix, HELAC [12]and MadGraph [13,14]. FKS subtraction is realized in MadGraph only [15].The automated computation of virtual corrections has received a boost fromgeneralized unitarity [18–20], which can be used to determine one-loop amplitudesWork supported by US Department of Energy under contract DE-AC02-76SF00515 and HEP.Presented at The Physics in Collision 2013IHEP, Beijing, September 3-7 20132 S. Höche100 200 300 400 500 600 700 80010-410-3dσ / dHTjets     [ pb / GeV ]LONLO100 200 300 400 500 600 700 800HTjets    [ GeV ]0.511.522.533.5LO / NLO NLO scale dependenceW- + 5 jets + XBlackHat+SherpaLO scale dependencepTjet  >  25 GeV,  | ηjet |  <  3 ETe  >  20 GeV,   | ηe |   <  2.5ETν > 20 GeV,   MTW  > 20 GeVR   =   0.5   [anti-kT]√s   =  7 TeVµR  =  µF  =  HT^ ’  / 2Fig. 1. Distribution of the visible energy inW + 5 jet events. Figure taken from [16].102103104105106σ(pb)NJet + Sherpapp→ jets at 7 TeVLONLOATLAS dataCERN-PH-EP-2011-0982 3 4 5 6Inclusive Jet Multiplicity12Theory/dataFig. 2. Jet multiplicity distribution in purejet events (right). Figure taken from [17].by decomposing them into known scalar one-loop integrals and rational coefficientsdetermined from tree amplitudes, plus a rational piece [21–25]. Programs like Black-Hat [26], Gosam [27], HELACNLO [28], MadLoop [29], NJet [30], OpenLoops [31]and Rocket [32, 33] implement these techniques and supplement established pro-grams like MCFM [34,35] and dedicated codes based on improved tensor reductionapproaches [36, 37]. New techniques have also been proposed to accelerate the nu-merical calculation of the integrand of one-loop amplitudes, independent of thereduction scheme [31]. Figures 1 and 2 show examples from recent NLO calcula-tions for W+5 jet production [16] and 5 jets production [17], both performed usingunitarity based techniques. Other recently completed calculations include Higgs bo-son plus 3 jet production [38] and di-photon plus 2 jet production [39]. The rapidprogress in this field is reflected by the fact that all calculations from the experi-menter’s wishlist for the LHC have now been tackled [40]. Most of the programsused to perform the calculations, or their results, are publicly available.Driven by the need for higher precision in some selected Standard-Model reac-tions, the field of next-to-next-to leading order (NNLO) calculations has significantlyadvanced in the past years. One of the most challenging problems is the regulariza-tion of infrared divergences at NNLO. Sector decomposition [41–43] has been used inthe past to perform several 2 → 1 calculations [44,45]. Antenna subtraction [46,47]was worked out and implemented for e+e− → 3 jets [48, 49]. qT subtraction [50]was employed in several calculations, including Higgs production [51], W/Z pro-duction [52], associated Higgs production [53] and di-photon production [54]. Morerecently sector-improved subtraction methods were introduced [55, 56]. They havebeen used to compute cross sections for pp→ tt̄ [57,58] and pp→ H+jet [59]. At thesame time, antenna subtraction was extended to initial states [60–63] and employedto compute pp → di-jets fully differentially at NNLO [64]. Figures 3 and 4 showApplications of higher order QCD 3 50 100 150 200 250 300 350 6.5  7  7.5  8  8.5σtot [pb]√s [TeV]Indep. µF,R variationPP → tt+X; mtop=173.3 GeVMSTW2008(68c.l.) LO; NLO; NNLONNLO (scales)NLO (scales)LO (scales)CMS, 7TeVATLAS+CMS, 7TeVATLAS, 7TeVCMS, 8TeVFig. 3. Energy dependence of the pp→ tt̄ to-tal cross. Figure taken from [58].T1/pµ1 (pb)T/dpσd2030405060708090310×LONLONNLO=8 TeVs R=0.7Tanti-kMSTW2008nnloµ= Fµ= Rµ < 97 GeVT80 GeV < pFig. 4. Scale dependence of the pp →di-jetcross section. Figure taken from [64].results from some of these calculations. The calculation of pp → tt̄ has also beencombined with higher logarithmic resummation [65–67]. Its theoretical uncertaintyis such that uncertainties from scale choices, PDF, strong coupling measurementsand top-quark mass measurements are all of the same order [68].3. Resummation of jet vetoesThe analysis of the Higgs-like particle discovered at the LHC places new demandson resummed calculations. Many of the Higgs analysis channels, most notably H →WW ∗ → `+`−νν̄, veto on the transverse momentum of final state jets to distinguishdifferent Standard Model backgrounds and separate them from the signal. Theleading systematic uncertainty is the theoretical uncertainty on the signal crosssection in the jet bins. This uncertainty can be reduced by a proper resummation ofthe logarithms associated with the jet veto. Various groups have investigated thisproblem, in most cases up to next-to-next-to leading logarithmic accuracy matchedto NNLO fixed order, relying either on more traditional resummation methods [69,70], or on Soft Collinear Effective Theory [71–75]. Higgs plus one jet productionwas studied at next-to-leading logarithmic order (NLL) and matched to NLO fixedorder using SCET [76].4. Parton showers and matching to NLO calculationsThe interest in parton showers as a means to produce particle-level predictionsfully differentially in the phase space of multi-jet events has increased significantlyin recent years. New concepts for the construction of parton showers have beenproposed, which are based on antenna subtraction [77, 78] and/or sectorizing thephase space [79, 80]. Efforts were made to include subleading color corrections intoshowers as a means to improve their logarithmic accuracy [81, 82]. However, thecrucial development was the proposal of a method to match parton showers toNLO calculations [83], later extended to eliminate negative weights [84, 85]. This4 S. Höche     -60     -40     -20     0     20     40     60 20  40  60  80  100  120  140  160  180  200Deviation [%]p! 1  [GeV]POWHEG H+jettMS=15...45 GeV,    lltMS=15...45 GeV,  cctMS=15...45 GeV, hh1.0"10-121.0"10-111.0"10-10d#/d p! 1  [mb/GeV] Pythia8UNLOPS (no K-factor) tMS=15 GeV, ccUNLOPS (no K-factor) tMS=30 GeV, ccUNLOPS (no K-factor) tMS=45 GeV, ccFig. 5. Transverse momentum of first jet inHiggs plus jets events. Figure taken from [91].pjet⊥ > 30GeVpjet⊥ > 20GeV(×10)bbbbbbbbbbbb ATLAS dataMePs@NloMePs@Nlo µ/2 . . . 2µMEnloPSMEnloPS µ/2 . . . 2µMc@Nlo0 1 2 3 4 510 110 210 310 4Inclusive Jet MultiplicityNjetσ(W+≥Njetjets)[pb]Fig. 6. Jet multiplicity distribution in W+jetsevents. Figure taken from [92].matching has been partially or fully automated in several projects [86–90], suchthat particle-level predictions at NLO accuracy are now widely available.The description of multi-jet final states with parton showers can be improvedusing so-called ME+PS merging methods [93–97], which, in contrast to matchingmethods, allow to correct the parton shower for an arbitrary number of emissionswith higher-order tree-level calculations. These methods were recently refined andextended, leading to algorithms which can combine multiple NLO calculations ofvarying multiplicity (like W + 0 jet, W + 1 jet, W + 2 jet, etc.) into a single,inclusive simulation (e.g. of W+jets production) [91, 92, 98–100]. Figures 5 and 6show examples for the application of ME+PS merging to Higgs boson plus jetsproduction and to W+jets production. A particular scale choice is required for theevaluation of the strong coupling in ME+PS merging, which has also been adoptedfor the matching to higher-multiplicity NLO calculations on its own in the so-calledMINLO approach [101].The MINLO method accounts for Sudakov suppression effects in higher-multiplicity final states and allows to extrapolate NLO calculations to zero jettransverse momentum, thus offering the opportunity to match to NNLO calcu-lations for a limited class of processes and observables [102]. A different proposalfor a matching to NNLO parton-level calculations was made in [91, 98], which isbased on a subtraction method similar to the one used in ME+PS merging at NLO.Both techniques are promising candidates to further increase the precision of eventgenerators for collider physics.Applications of higher order QCD 55. SummaryWe have presented some of the recent developments in perturbative QCD and ap-plications to particle physics phenomenology. 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Applications of Higher Order QCD

 In this talk we summarize some recent developments in perturbative QCD and their application to particle physics phenomenology. </jats:p

Applications of higher order QCD

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