In this talk, we report on a recent next-to-leading order QCD calculation of
the production of a W boson in association with three jets at hadron colliders.
The computation is performed by combining two programs, BlackHat for the
computation of the virtual one-loop matrix elements and Sherpa for the real
emission part.Comment: 4 pages, contribution to the proceedings of the XLIIIth Rencontres de
  Moriond (QCD

Berger, C. F.

Bern, Z.

Cordero, F. Febres

Dixon, L. J.

Forde, D.

Gleisberg, T.

Ita, H.

Kosower, D. A.

Maitre, D.

English

arXiv

In this talk, we report on a recent next-to-leading order QCD calculation of the production of a W boson in association with three jets at hadron colliders. The computation is performed by combining two programs, BlackHat for the computation of the virtual one-loop matrix elements and Sherpa for the real emission part. The addition of NLO corrections greatly reduces the factorization and renormalization scale dependence of the theory prediction for this process. This result demonstrates the applicability of unitarity-based methods for hadron collider physics

Berger, C.F.

Dixon, L.J.

Cordero, F.Febres

Kosower, D.A.

UNT Digital Library

Work supported in part by US Department of Energy contract DE-AC02-76SF00515IPPP/09/39MIT-CTP 4038Saclay-IPhT-T09/059SLAC–PUB–13630UCLA/09/TEP/48Multi-jet cross sections at NLO with BlackHat and SherpaC. F. Bergera, Z. Bernb, L. J. Dixonc, F. Febres Corderob, D. Fordec, T. Gleisbergc, H. Itab,D. A. Kosowerd and D. MâıtreeaCenter for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USAbDepartment of Physics and Astronomy, UCLA, Los Angeles, CA 90095-1547, USAcSLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94309, USAdInstitut de Physique Théorique, CEA–Saclay, F–91191 Gif-sur-Yvette cedex, FranceeDepartment of Physics, University of Durham, DH1 3LE, UKIn this talk, we report on a recent next-to-leading order QCD calculation of the production ofa W boson in association with three jets at hadron colliders. The computation is performedby combining two programs, BlackHat for the computation of the virtual one-loop matrixelements and Sherpa for the real emission part. The addition of NLO corrections greatlyreduces the factorization and renormalization scale dependence of the theory prediction forthis process. This result demonstrates the applicability of unitarity-based methods for hadroncollider physics.1 IntroductionThe production of a vector boson in association with jets is an important process at the LHC.Apart from its interest as a test of QCD, it contributes significantly to the background of manyStandard Model processes (tt̄ production, single top production, and Higgs decay to two vectorbosons) and new physics processes. Successful measurements of these processes require a reliabletheoretical description of the vector boson+ jets processes.Leading-order QCD predictions for processes with jets suffer from a large dependence on therenormalization and factorization scales. This problem can be tamed by adding next-to-leadingorder (NLO) corrections. Such corrections are composed of two parts. The real corrections toan n-parton process arise when an additional parton is emitted, in an (n + 1)-parton process.One-loop n-parton amplitudes generate the virtual part of the NLO correction.BlackHat 1 is a numerical implementation in C++ of so-called on-shell methods for comput-ing one-loop amplitudes. The starting point for a one-loop amplitude A with massless propaga-tors is its general decomposition in terms of scalar integrals,A =∑ici4Ii4 +∑ici3Ii3 +∑ici2Ii2 + R , (1)where Ii2, Ii3, Ii4 are scalar bubble, triangle and box integrals. The ‘rational term’ R is a rationalfunction of spinor products and does not contain any logarithms. The objective of on-shellmethods is to determine the coefficients cin of the integrals and R without using Feynmandiagrams. We refer the reader to the literature 2 for more details on these methods.In our numerical implementation, the coefficients of the integrals are determined using theanalytic approach of Forde 3, which is related to other recent methods 4. The rational term isMay 2009Invited talk presented at the Rencontres de Moriond:  QCD and High Energy Interactions (2009), 3/14/2009 -- 3/21/2009, La Thuile, Italy40 80 120 160 200 240 280 320 36010-410-310-210-1100dσ / dET    [ pb / GeV ]LONLOCDF data40 80 120 160 200 240 280 320 360Jet ET   [ GeV ]0.511.5LC NLO / NLOLO / NLOCDF / NLONLO scale dependenceW  +  jetBlackHat+SherpaLO scale dependence20 40 60 80 100 120 140 160 180 20010-410-310-210-1100dσ / dET    [ pb / GeV ]LONLOCDF data20 40 60 80 100 120 140 160 180 200Second Jet ET   [ GeV ]0.511.52LC NLO / NLOLO / NLOCDF / NLONLO scale dependenceW + 2 jetsBlackHat+SherpaLO scale dependenceFigure 1: NLO Differential cross section dσ(W → eν+ ≥ n − jets)/dEnth−jetTfor n = 1, 2 compared with themeasured cross section. The upper panels contain the LO and NLO parton level predictions and the CDF datapoints with their statistical and total uncertainties represented by the inner and outer error bars respectively.The distributions normalized by the NLO prediction are shown in the lower panels. The scale uncertainty of thedifferent predictions is represented by the shaded grey (NLO) and orange (LO) bands. The dotted black linerepresents our leading color approximation.number of jets CDF LC NLO NLO1 53.5 ± 5.6 58.3+4.6−4.6 57.8+4.4−4.02 6.8 ± 1.1 7.81+0.54−0.91 7.62+0.62−0.863 0.84 ± 0.24 0.908+0.044−0.142 —Table 1: Comparison of the total cross sections in pb for W +n jets with Enth-jetT> 25 GeV from CDF toNLO QCD. For 1 and 2 jets the cross sections with and without LC approximation are displayed to show thequality of the approximation. For the three jets result, only the LC NLO result is currently available, but weexpect a similarly small deviation for the full NLO result. The experimental statistical, systematic and luminosityuncertainties have been combined for the CDF results.computed using on-shell recursion relations for one-loop amplitudes 5. Numerical stability of theimplementation is achieved by using high-precision libraries 6 when (and only when) necessary.This stability has been demonstrated elsewhere 7.Sherpa 8 is a C++ Monte Carlo event generator. It can compute the real part of the NLOcorrections in an automated way 9 using Catani and Seymour’s dipole subtraction method 10.In addition, the subtraction term integrated over the unresolved phase space is provided. Theresults presented below have been integrated over the relevant phase space using Sherpa.For the W + 3 jets virtual cross section we used a leading-color (LC) approximation for thefinite part of the virtual amplitude. This approximation amounts to neglecting the terms in theratio of the virtual terms to the tree cross section that are suppressed by factors of 1/N2C (colorsuppressed) or Nf/Nc (virtual quark loop). This approximation has been shown to be very goodin the following section for W + 1,2 jets 11, so we expect it to be valid for W + 3 jets. A related,but different, approximation that includes only a subset of partonic subprocesses has been usedin another computation12 of W + 3 jets. The benefit of our approximation is that the number of(color ordered) primitive amplitudes to evaluate is significantly reduced. We checked agreementbetween the primitive amplitudes we used here and those found in a different calculation 13.2 W+3 jets at the TevatronWe compare the NLO prediction for W + 1,2,3 jets with data from the CDF experiment 14 atthe Tevatron. For the analysis we have used the same cuts as in the CDF analysis with the20 30 40 50 60 70 80 9010-310-210-1dσ / dET    [ pb / GeV ]LONLOCDF data20 30 40 50 60 70 80 90Third Jet ET   [ GeV ]0.511.52 LO / NLOCDF / NLONLO scale dependenceW + 3 jetsBlackHat+SherpaLO scale dependence-2-1012345σ  [ pb ]LONLO1/4 1/2 1 2 4µ / µ000.511.5k-factorµ0 = MW =  80.419 GeVBlackHat+SherpaW+3 jets @ TevatronFigure 2: The left panel shows the NLO Differential cross section dσ(W → eν+ ≥ 3 − jets)/dE3rd−jetTcomparedwith the measured cross section. Its upper part shows the LO and NLO parton level predictions (within theLC approximation for the virtual part) and the CDF data points with their statistical and total uncertaintiesrepresented by the inner and outer error bars respectively. The normalized distributions are shown in the lowerpart of the left panel. The scale uncertainties are represented by the shaded grey (NLO) and orange (LO) bands.The right panel shows the scale dependence of the total cross section on the renormalization and factorizationscale µ, taken equal and varied between 1/4 and 4 times the mass of the W boson.SISCone 15 jet algorithm instead of the JETCLU 16 cone algorithm used by CDF, as the latteris not infrared safe. We set an event-by-event renormalization and factorization scale accordingto µ =√m2W + P2T (W ).In Figure 1 we present the transverse energy distribution of the n-th jet for W + 1,2 jetsjets production. The NLO result agrees with the previously available results from MCFM 17.The lower part of these plots shows the reduced scale dependence of the NLO prediction. Thedotted black line demonstrates the validity of our LC approximation across the whole ET range.The plot in Figure 2 shows a good agreement between the NLO prediction (within our LCapproximation) for the ET distribution of the third jet and the experimental data. The secondplot of Figure 2 displays the improvement of the scale dependence of the cross section whenNLO corrections are added. More details on the setup of our analysis can be found elsewhere 11.3 W+3 jets at the LHCWe repeated the same analysis for the LHC with a center-of-mass energy of 14 TeV. For thisanalysis, we chose cuts suggested by the ATLAS and CMS technical design reports: EeT > 20GeV, |ηe| < 2.5, 6ET > 30 GeV, MWT > 20 GeV, and EjetT > 30 GeV. Here the EiT s aretransverse energies, 6ET is the missing transverse energy, MWT the transverse mass of the eνpair, and η the pseudorapidity. The ET -ordered jets are required to have a rapidity in the range|η| < 3. We used SISCone 15 with R = 0.4. Figure 3 shows the distributions in the scalartransverse energy sum HT and in the three-jet mass Mjjj =√(kj1 + kj2 + kj3)2 for W− + 3 jetsat the LHC.AcknowledgmentsThis research was supported by the US Department of Energy under contracts DE–FG03–91ER40662, DE–AC02–76SF00515 and DE–FC02–94ER40818. DAK’s research is supported bythe Agence Nationale de la Recherche of France under grant ANR–05–BLAN–0073–01, and bythe European Research Council under Advanced Investigator Grant ERC–AdG–228301. Thisresearch used resources of Academic Technology Services at UCLA and of the National Energy200 400 600 800 1000 1200 140010-310-210-1dσ / dHT    [ pb / GeV ]LONLO200 400 600 800 1000 1200 1400HT   [ GeV ]0.511.522.533.54LO / NLOW- + 3 jetsBlackHat+SherpaNLO scale dependenceLO scale dependence100 200 300 400 500 600 70010-210-1dσ / dMjjj    [ pb / GeV ]LONLO100 200 300 400 500 600 700Mjjj   [ GeV ]0.511.522.5 LO / NLO NLO scale dependenceW- + 3 jetsBlackHat+SherpaLO scale dependenceFigure 3: The NLO prediction for the scalar transverse energy sum HT (left panel) and the three-jet mass Mjjj(right panel) compared to the LO prediction. The LC approximation has been used for the virtual contributionto the NLO result. The scale uncertainties are represented by the bands in the lower parts of the plots.Research Scientific Computing Center, which is supported by the Office of Science of the U.S.Department of Energy under Contract No. DE-AC02-05CH11231.References1. C. F. Berger et al., Phys. Rev. D 78, 036003 (2008) [0803.4180 [hep-ph]].2. Z. Bern, L. J. Dixon and D. A. Kosower, Annals Phys. 322, 1587 (2007) [0704.2798 [hep-ph]].3. D. Forde, Phys. Rev. D 75, 125019 (2007) [0704.1835 [hep-ph]].4. G. Ossola, C. G. Papadopoulos and R. Pittau, Nucl. Phys. B 763, 147 (2007) [hep-ph/0609007]; R. K. Ellis, W. T. Giele and Z. Kunszt, JHEP 0803, 003 (2008) [0708.2398[hep-ph]].5. Z. Bern, L. J. Dixon and D. A. Kosower, Phys. Rev. D 71, 105013 (2005) [hep-th/0501240];Phys. Rev. D 72, 125003 (2005) [hep-ph/0505055]; Phys. Rev. D 73, 065013 (2006) [hep-ph/0507005]; C. F. Berger, Z. Bern, L. J. Dixon, D. Forde and D. A. Kosower, Phys. Rev.D 74, 036009 (2006) [hep-ph/0604195].6. Y. Hida, X. S. Li and D. H. Bailey, http://crd.lbl.gov/˜dhbailey/mpdist, report LBNL-46996.7. C. F. Berger et al., 0808.0941 [hep-ph].8. T. Gleisberg et al., JHEP 0902, 007 (2009) [0811.4622 [hep-ph]].9. T. Gleisberg and F. Krauss, Eur. Phys. J. C 53, 501 (2008) [0709.2881 [hep-ph]].10. S. Catani and M. H. Seymour, Nucl. Phys. B 485, 291 (1997) [Erratum-ibid. B 510, 503(1998)] [hep-ph/9605323].11. C. F. Berger et al., 0902.2760 [hep-ph], to appear in Phys. Rev. Lett.12. R. K. Ellis, K. Melnikov and G. Zanderighi, 0901.4101 [hep-ph].13. R. K. Ellis, W. T. Giele, Z. Kunszt, K. Melnikov and G. Zanderighi, JHEP 0901, 012(2009) [0810.2762 [hep-ph]].14. T. Aaltonen et al. [CDF Collaboration], Phys. Rev. D 77, 011108 (2008) [0711.4044 [hep-ex]].15. G. P. Salam and G. Soyez, JHEP 0705, 086 (2007) [0704.0292 [hep-ph]].16. F. Abe et al. [CDF Collaboration], Phys. Rev. D 45, 1448 (1992).17. J. M. Campbell and R. K. Ellis, Phys. Rev. D 65, 113007 (2002) [hep-ph/0202176].

Multi-jet Cross Sections at NLO with BlackHat and Sherpa

Multi-jet cross sections at NLO with BlackHat and Sherpa

Multi-jet cross sections at NLO with BlackHat and Sherpa

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