The status of two Monte Carlo generators, HELAC-PHEGAS, a program for
multi-jet processes and VBFNLO, a parton level program for vector boson fusion
processes at NLO QCD, is briefly presented. The aim of these tools is the
simulation of events within the Standard Model at current and future high
energy experiments, in particular the LHC. Some results related to the
production of multi-jet final states at the LHC are also shown.Comment: 8 pages, 8 figures. Presented at the XXXI International Conference of
  Theoretical Physics, Matter To The Deepest: Recent Developments In Physics of
  Fundamental Interactions, Ustron, 5-11 September 2007, Polan

Worek, Malgorzata

Acta Physica Polonica B

English

arXiv

The status of two Monte Carlo generators, Helac-Phegas, a program for multi-jet processes and Vbfnlo, a parton level programfor vector boson fusion processes at NLO QCD, is briefly presented. The aim of these tools
is the simulation of events within the Standard Model at current and future high energy experiments, in particular the LHC. Some results related to the production of multi-jet final states at the LHC are also shown

Worek, Małgorzata

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Monte Carlo generators for the LHC  Author: Małgorzata Worek  Citation style: Worek Małgorzata. (2007). Monte Carlo generators for the LHC. "Acta Physica Polonica B" (Vol. 38, no. 11 (2007), s. 3399-3406).   Vol. 38 (2007) ACTA PHYSICA POLONICA B No 11MONTE CARLO GENERATORS FOR THE LHC∗Małgorzata Worek†Institute for Theoretical Physics (ITP)Karlsruhe University, 76-128 Karlsruhe, GermanyandInstitute of Physics, University of SilesiaUniwersytecka 4, 40-007 Katowice, Polandworek@particle.uni-karlsruhe.de(Received October 16, 2007)The status of two Monte Carlo generators, Helac-Phegas, a programfor multi-jet processes andVbfnlo, a parton level program for vector bosonfusion processes at NLO QCD, is briefly presented. The aim of these toolsis the simulation of events within the Standard Model at current and futurehigh energy experiments, in particular the LHC. Some results related to theproduction of multi-jet final states at the LHC are also shown.PACS numbers: 12.38.Bx, 13.85.Dz, 13.85.LgThe main aim of the Large Hadron Collider (LHC), which is expectedto start in 2008, is the discovery of the last missing particle predicted bythe Standard Model (SM), the Higgs boson. Almost as high on the agenda,however, is the search for signals of new physics beyond the SM. Backgroundprocesses to these searches are mostly due to QCD interactions which aresometimes accompanied by electroweak vector bosons. The final states arecharacterized by a high number of jets and/or identified particles. Theoret-ical predictions in such cases require the computation of scattering ampli-tudes with a large number of external particles. The complexity of calcula-tions grows with the number of external legs. For example, the numbers ofFeynman diagrams which are needed for the computation of the gg → 8gand qq¯ → 8g amplitudes, are 10, 525, 900 and 4, 016, 775, respectively.In general the number of Feynman diagrams grows asymptotically factori-ally with the number of particles. Moreover, for a given jet configuration∗ Presented at the XXXI International Conference of Theoretical Physics, “Matter tothe Deepest”, Ustroń, Poland, September 5–11, 2007.† Report number: KA-TP-23-2007.(3399)3400 M. Worekthere are usually many contributing subprocesses, e.g. for the calculationof pp → e+νe + 6 jets, 2476 subprocesses have to be taken into account. Inaddition, neither the color nor the spin of the partons are observed. Thus,for an amplitude with p quarks and q gluons (2× 3)p(2× 8)q configurationshave to be considered in principle for every phase space point. Both, theusual techniques of evaluating Feynman diagrams and straightforward sum-mation over color and helicity configurations are in practice almost unusable.The next challenge is the phase space integration. Each amplitude peaks ina complicated way inside the momentum phase space. Direct integration is,therefore, impractical and one has to search for efficient mappings to do im-portance sampling in a multi-particle phase space. Clearly, new alternativetechniques and automatization of calculations for multileg LHC processes isa timely task.Over the last years new algorithms along with their implementations forcomputing tree-order scattering amplitudes have been proposed [1–7]. Theyreorganize various off-shell subamplitudes in a systematic way so that aslittle of the computation is repeated as possible. A scattering amplitudeis computed through a set of recursive equations derived from the effectiveaction as a function of the classical fields. These equations represent nothingelse but the tree order Dyson–Schwinger (DS) equations and give recursivelythe n-point Green’s functions in terms of the 1-, 2-, . . . , (n− 1)-point func-tions. They hold all the information about the fields and their interactionsfor any number of external legs and to all orders in perturbation theory. Forexample in QED these equations can be written as follows:= +bµ(P ) =n∑i=1δP=pibµ(pi)∑P=P1+P2(ig)Πµν (P2)γνψ(P1)ε(P1, P2) , (1)wherebµ(P ) = ψ(P ) = ψ¯(P ) =describes a generic n-point Green’s function with, respectively, one outgoingphoton, fermion or antifermion leg carrying momentum P . Πµν stands forthe boson propagator and ε takes into account the sign due to fermionantisymmetrization. In the same way recursive equations for other particlesin the SM can be derived.Monte Carlo Generators for the LHC 3401Helac [7] is the only existing implementation of the algorithm basedon DS equations. It is able to calculate iteratively matrix elements for anarbitrary multi-particle and multi-jet process within the SM in leptonic andhadronic collisions. For multi-jet states all elementary parton level subpro-cesses are taken into account. All electroweak vertices in both Feynman andunitary gauges have been included, whereas unstable particles are treatedin a fully consistent way, by using either a fixed width or a complex massscheme [8–10]. Spin and color correlations are taken into account natu-rally and there is no approximation involved. A substantial speed up hasbeen obtained with Monte Carlo (MC) techniques to perform the sum overhelicity and color configurations [5, 6]. The computational cost of Helacgrows like ∼ 4n (3n), which essentially counts the steps used to solve therecursive equations1. The program incorporates the possibility to use ex-tended numerical precision by exploiting the virtues of Fortran90. Thedσ/dE ⊥1 (pb/GeV) (a) AlpgenAriadneHelacMadEventSherpa10-210-1100101102E⊥1 (GeV)-1-0.5 0 0.5 1 0  50  100 150 200 250 300 350 400 450 500dσ/dE ⊥2 (pb/GeV) (b)10-210-1100101102E⊥2 (GeV)-1-0.5 0 0.5 1 0  50  100  150  200  250  300  350  400dσ/dE ⊥3 (pb/GeV) (c)10-310-210-1100101E⊥3 (GeV)-1-0.5 0 0.5 1 0  50  100  150  200  250  300dσ/dE ⊥4 (pb/GeV) (d)10-310-210-1100101E⊥4 (GeV)-1-0.5 0 0.5 1 0  50  100  150  200Fig. 1. Inclusive E⊥ spectra of the leading 4 jets at the LHC (pb/GeV). In all casesthe full line gives the Alpgen results, the dashed line gives the Ariadne resultsand the “+”, “x” and “o” points give the Helac, Madevent and Sherpa results,respectively.1 To reduce the computational complexity down to an asymptotic 3n each 4-bosonvertex must be replaced with a 3-boson vertex e.g. by introducing an auxiliary fieldrepresented by the antisymmetric tensor Hµν , see [5,6] for details.3402 M. Worekuser can easily switch to quadruple precision or to an even higher, user-defined precision by using the multi-precision library [11]. Finally, the peak-ing structure of the amplitude is dealt with by the phase space generatingalgorithm Phegas [12]. Phegas is the first implementation of a completelyautomated algorithm of multi-channel phase space mappings for an arbi-trary number of external particles. It uses the information generated byHelac and automatically performs a multi-channel phase space generation,utilizing “scalarized” Feynman graphs. In the case of pp and pp¯ collisionsthe cross section is also convoluted with parton distribution functions. Inthat case the integration is optimized by using the Parni algorithm [13].The program makes use of the Les Houches Accord PDF Interface library(LHAPDF) [14]. It also generates a Les Houches Accord (LHA) file [15, 16]with all the necessary information needed to interface to the Pythia [17]parton shower and hadronization program. In fact, the problem of doublecounting of jets may arise when interfacing fixed order tree level matrix ele-ments to parton showers. In order to deal with it, a matching algorithm hasto be applied, which provides a smooth transition between the part of thephase space covered by parton showers and the one described by matrix el-ements. We have used the so-called MLM matching algorithm, see e.g. [18].Let us note that a comparative study [19] of matching algorithms imple-mented in different MC codes namely Helac, Alpgen [20], Ariadne [21],MadEvent [22, 23] and Sherpa [24, 25] has recently been published forthe W + n jets production with kinematics corresponding to the TeVatronand the LHC. As an example in Fig. 1, inclusive E⊥ spectra of the leading4 jets at the LHC (pb/GeV) for Alpgen, Ariadne Helac, Madeventand Sherpa are given. Fig. 2 shows graphically the cross-section systematic 0 0.5 1 1.5 2 2.5 3≥ 0 ≥ 1 ≥ 2 ≥ 3 ≥ 4σ(W++≥ N jets) / <σ>AlpgenAriadneHelacMadEventSherpaFig. 2. Range of variation for the LHC cross-section rates of the five codes, normal-ized to the average value of the default settings for all codes in eachmultiplicity bin.Monte Carlo Generators for the LHC 3403error ranges. For each multiplicity, the rates are normalized to the averageof the default values of all the codes. The complete information on the sim-ulation details can be found in Ref. [19]. The Helac-Phegas package [7]is now publicly available2, see also [26–30].As we have seen, if one is content with the tree level calculations only,it is possible to go to high orders with up to 8–10 partons in the final state.Of course, they have to be kept well separated to avoid the phase spaceregions where divergencies become troublesome. Soft and collinear regionscan then be covered by the parton shower. However, to resolve the large scaledependence inherent in leading order calculations it is necessary to includeNLO corrections. The complexity of a calculation increases with the order inperturbation theory. Currently available NLO calculations are restricted tothe 2–4 final state particles only3. More importantly, only one MC library,MC@NLO [32], incorporates NLO QCD matrix elements consistently intoa parton shower framework. A general purpose NLO MC library does notexist yet. However, there are a few MC programs for specialized processes.In particular, Vbfnlo belongs to this category4 when various VectorBoson Fusion (VBF) processes are concerned. For example, the q¯Q→ q¯QHVBF process can be visualized as the elastic scattering of two quarks me-diated by the t-channel W or Z exchange with the Higgs boson radiatedoff the weak boson propagator, see Fig. 3. It is expected to provide a co-pious source of Higgs bosons in pp collisions at the LHC and together withgluon fusion, it represents the most promising production process for Higgsboson discovery. Once the Higgs boson has been found and its mass deter-mined, the measurement of its couplings to gauge bosons and fermions will(a) (b)gQVVHQ QHQq q q qFig. 3. Feynman graphs contributing to q¯Q → q¯QH at (a) tree level and (b)including virtual corrections to the upper quark line.2 http://helac-phegas.web.cern.ch/helac-phegas/3 There are no NLO programs for the LHC with more than 3 hard particles in the finalstate. NLO programs with four particles in the final state are available only for e+e−annihilation. See e.g. [31] for a recent review on this subject.4 http://www-itp.particle.uni-karlsruhe.de/∼vbfnloweb/3404 M. Worekbe of main interest. Here VBF will be of the central importance since itallows for independent observation in the H → γγ, H → bb¯, H → τ+τ−,H → W+W− and H → invisible channels. This multitude of channels iscrucial for separating the effects of different Higgs boson couplings. VBFmeasurements can be performed at the LHC with statistical accuracies oncross sections times decay branching ratios, σ×B reaching (5–10)% [33,34].Theoretical predictions of the SM production cross section with error wellbelow 10% are required. This clearly entails knowledge of the NLO QCDcorrections. In order to distinguish the VBF Higgs boson signal from back-grounds, stringent cuts are required on the Higgs boson decay products, aswell as on the two forward quark jets which are characteristic for VBF. Thiscan be best addressed with Vbfnlo which contains, among others, Higgsboson production in the narrow resonance approximation [35]. In addition,anomalous couplings have been added for the Higgs boson [36]. The pro-duction of W → lνl and Z → l+l− [37] bosons in association with two jets isalso included in the program since it is an important background. Moreover,W+W− [38] and ZZ [39] production via vector-boson fusion with subse-quent leptonic decay of the W s and Zs with all resonant and non-resonantFeynman diagrams and spin correlations of the final-state leptons have beenimplemented. Let us note that in all these cases any identical fermion effects,i.e. s-channel exchange and interference effects of t-channel and u-channeldiagrams are systematically neglected. In the phase space region whereVBF can be observed experimentally, with widely-separated quark jets ofvery large invariant mass, the neglected terms are strongly suppressed bythe large momentum transfer in one or more weak-boson propagators. Forthe evaluation of partonic matrix elements, amplitude techniques of [40, 41]have been employed. The calculation of NLO QCD corrections is basedon the dipole subtraction formalism, in the version proposed by Catani andSeymour [42]. Radiative corrections to a single quark line have only been cal-culated, since any interference between subamplitudes with gluons attachedto both the upper and the lower quark lines vanishes identically at order αs,because of the color singlet nature of the exchanged weak boson. The virtualcontributions, obtained from the interference of one-loop diagrams with theBorn amplitude, include self-energy, triangle, box and pentagon corrections.A Passarino–Veltman reduction of tensor integrals [43], which is stable inthe phase space regions covered by VBF-type reactions is implemented upto box-type virtual corrections. For pentagon contributions, however, thistechnique gives rise to numerical instabilities, if kinematical invariants, suchas the Gram determinants, become small. Therefore, the reduction schemeproposed by Denner and Dittmaier for the tensor reduction of pentagon in-tegrals [44, 45] has been used. In all cases the QCD corrections are modest,changing total cross sections by less than 10%. Remaining scale uncertain-Monte Carlo Generators for the LHC 3405ties are at the few percent level. Modest corrections are also present indistributions. Let us note that Vbfnlo is a fully flexible MC program. Ar-bitrary cuts can be implemented and independent scales can be fixed for theradiative correction on the upper and lower quark lines. Moreover, variousscale choices and PDF sets are available in the later case also through theLHAPDF library. Finally, the program generates an LHA file.Work supported in part by the RTN European Programme MRTN-CT-2006-035505 HEPTOOLS — Tools and Precision Calculations for physicsDiscoveries at Colliders, as well as by BMBF grant 05 HT6VKC. We wouldalso like to thank the Galileo Galilei Institute for Theoretical Physics for thehospitality and the INFN for partial support during the completion of thiswork.REFERENCES[1] F. Caravaglios, M.Moretti, Phys. Lett. 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Monte Carlo Generators for the LHC

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Repozytorium Uniwersytetu Śląskiego RE-BUŚ