The MC@NLO method as implemented in the Sherpa MC generator is presented
using the production of W-bosons in conjunction with up to three jets as an
example. Corresponding results computed at next-to leading order in QCD and
including parton shower corrections are compared to recent experimental data
from the Large Hadron Collider.Comment: 4 pages, 2 figures. To appear in the proceedings of DIS 201

Hoeche, Stefan

Krauss, Frank

Schonherr, Marek

Siegert, Frank

English

arXiv

The MC@NLO method as implemented in the Sherpa MC generator is presented using the production of W-bosons in conjunction with up to three jets as an example. Corresponding results computed at next-to leading order in QCD and including parton shower corrections are compared to recent experimental data from the Large Hadron Collider

DESY

W+n-jet predictions at NLO matched with a parton shower

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UNT Digital Library

SLAC-PUB-15097W+n-jet predictions at NLO matched with a par-ton showerFrank Siegert1, Stefan Höche2, Frank Krauss3, Marek Schönherr31Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany2SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA3Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, UKDOI: will be assignedThe MC@NLO method as implemented in the Sherpa MC generator is presented using theproduction of W-bosons in conjunction with up to three jets as an example. Correspondingresults computed at next-to leading order in QCD and including parton shower correctionsare compared to recent experimental data from the Large Hadron Collider.1 IntroductionTo make the LHC a discovery machine we have to acknowledge the fact that it is a QCDmachine. Many signals suffer from large backgrounds largely due to QCD multi-jet productionwhich have to be under good theoretical control to interpret the measurements.There are mainly two approaches to include higher-order QCD corrections in theoreticalcalculations of scattering matrix elements (ME):Fixed-order ME calculations put an emphasis on the exact evaluation of a finite numberof terms in the perturbation series. Apart from being exact to the given order this also has thebenefit of including all interference terms from different diagrams and working with a numberof colours NC = 3. Last, but not least, it becomes possible to include also the exact finite partof virtual contributions in a fixed-order calculation.Their disadvantages appear when an observable becomes sensitive to logarithmically en-hanced regions. It is not sufficient to truncate the perturbation series at a fixed order anymore,if the perturbative nature of the coupling constant αs is countered by large logarithms whichappear when partons become soft or collinear to each other. This problem is solved in the par-ton shower approach (PS), where the logarithmically enhanced contributions are resummedto all orders, albeit only in an approximation valid in the collinear limit of the matrix elementand in the large NC limit. This allows to generate events with partons at the hadronisationscale and thus enables exclusive hadron-level event generation.It is thus a worthwhile goal to combine the two approaches and keep the advantages: Includethe virtual contributions and first hard emission from the exact next-to-leading order matrixelement, and add further parton evolution using a parton shower approach.DIS 2012 1arXiv:hep-ph/1206.4873v1Presented at XX Int’l Workshop on Deep Inelastic Scattering and Related SubjectsBonn, Germany,  October 13-18, 2012Work supported in part by US Department of Energy contract DE-AC02-76SF00515.2 Recap: Resummation and NLO calculationsThe basic property of QCD allowing a parton shower resummation is the universal factorisationof real emission matrix elements in the collinear limit:R ij collinear−→ D(PS)ij = B ×(12pipj8παs Kij(pi, pj))(1)With the approximation that multiple emissions happen independently of each other (thusyielding Poisson statistics) the corresponding branching probability can be exponentiated togive the total no-branching probability down to an evolution scale t:∆(PS)(t) =∏ı̃exp− ∑fi=q,g∫dΦijR|B Θ(t(ΦijR|B)− t) D(PS)ijB (2)To understand the implications of the no-branching probability ∆, let us look at the expec-tation value of an observable O taking into account up to one emission from the parton showeron top of a Born-level event:〈O〉(PS) =∫dΦB B[∆(PS)(t0)O(ΦB)︸ ︷︷ ︸unresolved+∑ı̃∑fi∫ µ2Ft0dΦijR|BD(PS)ijB ∆(PS)(t)O (rı̃(ΦB))︸ ︷︷ ︸resolved](3)The “unresolved” contribution corresponds to the event generation case where no emissionabove the parton shower cut-off scale t0 has been generated and is thus proportional to theno-branching probability ∆(t0). The “resolved” contribution on the other hand represents theintegration over events which had an emission with evolution scale t > t0.As a reminder and to fix some notation, the contributions of an NLO calculation for theexpectation value of O are briefly recalled:〈O〉(NLO) =∑~fB∫dΦBB(ΦB) + Ṽ(ΦB) + ∑ı̃I(S)ı̃ (ΦB) O(ΦB)+∑~fR∫dΦRR(ΦR)O(ΦR)−∑{ij}D(S)ij (ΦR)O(bij(ΦR)) (4)Here, the Born (B), virtual (V) and real emission (R) pieces are denoted accordingly. SinceV and R are oppositely divergent in separate phase space integrations, one needs to employa subtraction procedure: The real subtraction terms D are linked to their integrated form Iby a phase space integration over the 1-emission phase space and can be calculated e.g. in thescheme of [1].3 Combining NLO and PSApplying PS resummation on top of such NLO events is not straightforward: The observablehas to be evaluated at different kinematics in the R and D terms. But if that is taken into2 DIS 2012account, and they are thus showered separately, one generates an additional term at O(αs) [2]which is not present in the NLO calculation (“double counting”). To counter that term asolution was proposed in [2] introducing an additional set of “modified” subtraction termsD(A). When generating events according to that modified NLO cross section, they will haveeither ΦR kinematics (resolved, non-singular term) and are kept as they are or ΦB kinematics.In the latter case, they are processed through a one-step PS with ∆(A), i.e. using the modifiedsubtraction terms as PS kernels, either generating an emission (resolved, singular) or no emission(unresolved, singular) above t0. The result of this procedure,〈O〉(NLO+PS) =∑~fB∫dΦBB̄(A)(ΦB) ∆(A)(t0)︸ ︷︷ ︸unresolvedO(ΦB) +∑{ı̃,fi}∫t0dΦijR|BD(A)ij (rı̃(ΦB))B(ΦB)∆(A)(t)︸ ︷︷ ︸resolved, singularO(rı̃(ΦB))+∑~fR∫dΦR[R(ΦR)−∑ijD(A)ij (ΦR)]︸ ︷︷ ︸resolved, non-singularO(ΦR),with B̄(A)(ΦB) defined asB̄(A)(ΦB) = B(ΦB)+Ṽ(ΦB)+∑{ı̃}I(S)ı̃ (ΦB)+∑{ı̃}∑fi=q,g∫dΦijR|B[D(A)ij (rı̃(ΦB))−D(S)ij (rı̃(ΦB))]can be shown to reproduce 〈O〉(NLO) to O(αs).This procedure still leaves the freedom of choosing ∆(A). The original approach [2] uses theparton shower splitting kernels as additional subtraction terms, D(A)ij → D(PS)ij . This optionhas the advantage that the exponentiation in the “resolved, singular” contribution is naturallybounded by the factorisation scale µF . Problems appear though with soft divergences in the“resolved, non-singular” integration, since the parton shower splitting kernels do not cover softdivergences.An alternative approach was suggested in [3] and implemented in SHERPA [4], where the fullCatani-Seymour dipoles are used D(A)ij → D(S)ij . With this, B̄(A) simplifies significantly, but at acost: D(S) can become negative, resulting in ∆ > 1. This is generated in SHERPA by a weightedNC = 3 one-step PS based on the subtraction terms D(S). With this approach, exact NLOaccuracy also for sub-leading colour configurations is achieved. The phase space boundary forthe exponentiation though has to be imposed “artificially” by cuts in the dipole phase space.4 ResultsResults for W + n-jet production at the LHC are presented here in comparison to ATLASdata [5]. Events are simulated using SHERPA’s MC@NLO for W +0, W +1, W +2 and W +3-jetproduction with virtual corrections from BLACKHAT [6] including a leading-colour approxima-tion for the W + 3-jet virtual ME. For n > 0 events are generated requiring kT jets withp⊥ > 10 GeV, and the exponentiation region was restricted using an α = 0.01-cut in the dipoleterms [7]. The comparison comprises of three levels of event simulation: “NLO” as fixed-ordercalculation, “MC@NLO 1em” as MC@NLO including the hardest emission only and “MC@NLOPL” as MC@NLO including the full PS. All distributions are simulated at NLO accuracy andthe theoretical predictions describe data very well.DIS 2012 3bbbbbbbbbbbbbbbbbbbbbbbp⊥(first jet)p⊥(second jet)p⊥(third jet)Sherpa+BlackHatW+1,2,3 jets ATLAS databNLOMC@NLO 1emMC@NLO PL50 100 150 200 250 30010−210−1110 1Jet transverse momentap⊥ [GeV]dσ/dp⊥[pb/GeV]b b b b b b b b b b0.511.5MC/datab b b b b b b0.511.5MC/datab b b b b b50 100 150 200 250 3000.511.5p⊥ [GeV]MC/dataFig. 1: Transverse momentum of the first, sec-ond and third jet (from top to bottom).b b b bbb bbbbb bbb bb b bb bbbbb bbbb b bSherpa+BlackHatW+2 jetsATLAS databNLOMC@NLO 1emMC@NLO PL0510152025303540Rapidity Distance of Leading Jetsdσ/d∆y[pb]b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b-6 -4 -2 0 2 4 60.511.5∆y(First Jet, Second Jet)MC/datab bb bb b bbbbbbbbbbSherpa+BlackHatW+2 jetsATLAS databNLOMC@NLO 1emMC@NLO PL050100150Azimuthal Distance of Leading Jetsdσ/d∆φ[pb]b b b b b b b b b b b b b b b b0 0.5 1 1.5 2 2.5 30.511.5∆φ(First Jet, Second Jet)MC/dataFig. 2: Angular correlations of the two leadingjets in W±+ ≥ 2 jet production.5 Conclusions and outlookThe concept of NLO+PS matching was presented in a common formalism, and MC@NLO wasdeveloped as a special case. It was emphasised that an exact treatment of sub-leading colourconfigurations can be achieved by exponentiating Catani-Seymour subtraction terms. The firstNLO+PS predictions for W+3 jets were presented and showed good agreement with exper-imental data from ATLAS. With this method at hand, it becomes now possible to generateexclusive hadron-level event samples at NLO accuracy.In the future, an improved functional form of the phase-space cut α will allow for a betterlimitation of the exponentiation region. Also, by merging NLO+PS with higher-multiplicitytree-level MEs one can already provide an improved description of multi-jet final states in theMENLOPS approach [8]. Ultimately, it remains a goal to achieve the merging of NLO+PSpredictions at different multiplicities into one inclusive sample.References[1] S. Catani and M. H. Seymour. Nucl. Phys. B485 (1997) 291–419, arXiv:hep-ph/9605323.[2] S. Frixione and B. R. Webber. JHEP 06 (2002) 029, hep-ph/0204244.[3] S. Höche, F. Krauss, M. Schönherr, and F. Siegert. arXiv:1111.1220 [hep-ph].[4] T. Gleisberg et al. JHEP 02 (2009) 007, arXiv:0811.4622 [hep-ph].[5] G. Aad et al. arXiv:1201.1276 [hep-ex].[6] C. F. Berger et al. Phys. Rev. D78 (2008) 036003, arXiv:0803.4180 [hep-ph].[7] Z. Nagy. Phys. Rev. D68 (2003) 094002, arXiv:hep-ph/0307268.[8] S. Höche, F. Krauss, M. Schönherr, and F. Siegert. JHEP 08 (2011) 123, arXiv:1009.1127 [hep-ph].4 DIS 2012

W+n-jet Predictions at NLO Matched with a Parton Shower

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W+n-jet predictions at NLO matched with a parton shower

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