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Journal of High Energy Physics

, 2012:61 | Cite as

Merging meets matching in MC@NLO

  • Rikkert Frederix
  • Stefano FrixioneEmail author
Open Access
Article

Abstract

The next-to-leading order accuracy for MC@NLO results exclusive in J light jets is achieved if the computation is based on matrix elements that feature J and J + 1 QCD partons. The simultaneous prediction of observables which are exclusive in different light-jet multiplicities cannot simply be obtained by summing the above results over the relevant range in J; rather, a suitable merging procedure must be defined. We address the problem of such a merging, and propose a solution that can be easily incorporated into existing MC@NLO implementations. We use the automated aMC@NLO framework to illustrate how the method works in practice, by considering the production at the 8 TeV LHC of a Standard Model Higgs in association with up to J = 2 jets, and of an e + ν e pair or a \( t\overline{t} \) pair in association with up to J = 1 jet.

Keywords

Monte Carlo Simulations NLO Computations 

References

  1. [1]
    M.H. Seymour, A simple prescription for first order corrections to quark scattering and annihilation processes, Nucl. Phys. B 436 (1995) 443 [hep-ph/9410244] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    M.H. Seymour, Matrix element corrections to parton shower algorithms, Comput. Phys. Commun. 90 (1995) 95 [hep-ph/9410414] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M. Bengtsson and T. Sjöstrand, Coherent parton showers versus matrix elements: implications of PETRA-PEP data, Phys. Lett. B 185 (1987) 435 [INSPIRE].ADSGoogle Scholar
  4. [4]
    G. Gustafson and U. Pettersson, Dipole formulation of QCD cascades, Nucl. Phys. B 306 (1988) 746 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    G. Miu and T. Sjöstrand, W production in an improved parton shower approach, Phys. Lett. B 449 (1999) 313 [hep-ph/9812455] [INSPIRE].ADSGoogle Scholar
  6. [6]
    S. Catani, F. Krauss, R. Kuhn and B.R. Webber, QCD matrix elements + parton showers, JHEP 11 (2001) 063 [hep-ph/0109231] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    F. Krauss, Matrix elements and parton showers in hadronic interactions, JHEP 08 (2002) 015 [hep-ph/0205283] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    L. Lönnblad, Correcting the color dipole cascade model with fixed order matrix elements, JHEP 05 (2002) 046 [hep-ph/0112284] [INSPIRE].CrossRefGoogle Scholar
  9. [9]
    N. Lavesson and L. Lönnblad, W+ jets matrix elements and the dipole cascade, JHEP 07 (2005) 054 [hep-ph/0503293] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    S. Hoeche, F. Krauss, S. Schumann and F. Siegert, QCD matrix elements and truncated showers, JHEP 05 (2009) 053 [arXiv:0903.1219] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    K. Hamilton, P. Richardson and J. Tully, A modified CKKW matrix element merging approach to angular-ordered parton showers, JHEP 11 (2009) 038 [arXiv:0905.3072] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    L. Lönnblad and S. Prestel, Matching tree-level matrix elements with interleaved showers, JHEP 03 (2012) 019 [arXiv:1109.4829] [INSPIRE].CrossRefGoogle Scholar
  13. [13]
    J. Alwall et al., Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions, Eur. Phys. J. C 53 (2008) 473 [arXiv:0706.2569] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    M. Dobbs, Incorporating next-to-leading order matrix elements for hadronic diboson production in showering event generators, Phys. Rev. D 64 (2001) 034016 [hep-ph/0103174] [INSPIRE].ADSGoogle Scholar
  15. [15]
    S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    Y.-j. Chen, J. Collins and X.-m. Zu, NLO corrections in MC event generator for angular distribution of Drell-Yan lepton pair production, JHEP 04 (2002) 041 [hep-ph/0110257] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    Y. Kurihara et al., QCD event generators with next-to-leading order matrix elements and parton showers, Nucl. Phys. B 654 (2003) 301 [hep-ph/0212216] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    Z. Nagy and D.E. Soper, Matching parton showers to NLO computations, JHEP 10 (2005) 024 [hep-ph/0503053] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    C.W. Bauer and M.D. Schwartz, Event generation from effective field theory, Phys. Rev. D 76 (2007) 074004 [hep-ph/0607296] [INSPIRE].ADSGoogle Scholar
  21. [21]
    Z. Nagy and D.E. Soper, Parton showers with quantum interference, JHEP 09 (2007) 114 [arXiv:0706.0017] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    W.T. Giele, D.A. Kosower and P.Z. Skands, A simple shower and matching algorithm, Phys. Rev. D 78 (2008) 014026 [arXiv:0707.3652] [INSPIRE].ADSGoogle Scholar
  23. [23]
    C.W. Bauer, F.J. Tackmann and J. Thaler, GenEvA. I. A new framework for event generation, JHEP 12 (2008) 010 [arXiv:0801.4026] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    N. Lavesson and L. Lönnblad, Extending CKKW-merging to one-loop matrix elements, JHEP 12 (2008) 070 [arXiv:0811.2912] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    S. Hoche, F. Krauss, M. Schonherr and F. Siegert, Automating the POWHEG method in Sherpa, JHEP 04 (2011) 024 [arXiv:1008.5399] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    S. Hoeche, F. Krauss, M. Schonherr and F. Siegert, A critical appraisal of NLO+PS matching methods, JHEP 09 (2012) 049 [arXiv:1111.1220] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    R. Frederix et al., aMC@NLO predictions for Wjj production at the Tevatron, JHEP 02 (2012) 048 [arXiv:1110.5502] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    K. Hamilton and P. Nason, Improving NLO-parton shower matched simulations with higher order matrix elements, JHEP 06 (2010) 039 [arXiv:1004.1764] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    S. Hoche, F. Krauss, M. Schonherr and F. Siegert, NLO matrix elements and truncated showers, JHEP 08 (2011) 123 [arXiv:1009.1127] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    W.T. Giele, D.A. Kosower and P.Z. Skands, Higher-order corrections to timelike jets, Phys. Rev. D 84 (2011) 054003 [arXiv:1102.2126] [INSPIRE].ADSGoogle Scholar
  31. [31]
    S. Alioli, K. Hamilton and E. Re, Practical improvements and merging of POWHEG simulations for vector boson production, JHEP 09 (2011) 104 [arXiv:1108.0909] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    S. Hoeche, F. Krauss, M. Schonherr and F. Siegert, QCD matrix elements + parton showers: the NLO case, arXiv:1207.5030 [INSPIRE].
  33. [33]
    T. Gehrmann, S. Hoche, F. Krauss, M. Schonherr and F. Siegert, NLO QCD matrix elements + parton showers in e + e hadrons, arXiv:1207.5031 [INSPIRE].
  34. [34]
    A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    C. Berger et al., An automated implementation of on-shell methods for one-loop amplitudes, Phys. Rev. D 78 (2008) 036003 [arXiv:0803.4180] [INSPIRE].ADSGoogle Scholar
  36. [36]
    R.K. Ellis, W.T. Giele, Z. Kunszt and K. Melnikov, Masses, fermions and generalized D-dimensional unitarity, Nucl. Phys. B 822 (2009) 270 [arXiv:0806.3467] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    V. Hirschi et al., Automation of one-loop QCD corrections, JHEP 05 (2011) 044 [arXiv:1103.0621] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    G. Bevilacqua et al., HELAC-NLO, arXiv:1110.1499 [INSPIRE].
  39. [39]
    S. Becker, D. Goetz, C. Reuschle, C. Schwan and S. Weinzierl, NLO results for five, six and seven jets in electron-positron annihilation, Phys. Rev. Lett. 108 (2012) 032005 [arXiv:1111.1733] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    G. Cullen et al., Automated one-loop calculations with GoSam, Eur. Phys. J. C 72 (2012) 1889 [arXiv:1111.2034] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    F. Cascioli, P. Maierhofer and S. Pozzorini, Scattering amplitudes with open loops, Phys. Rev. Lett. 108 (2012) 111601 [arXiv:1111.5206] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    S. Agrawal, T. Hahn and E. Mirabella, FormCalc 7, J. Phys. Conf. Ser. 368 (2012) 012054 [arXiv:1112.0124] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    Z. Bern et al., Four-jet production at the Large Hadron Collider at next-to-leading order in QCD, Phys. Rev. Lett. 109 (2012) 042001 [arXiv:1112.3940] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    S. Badger, B. Biedermann, P. Uwer and V. Yundin, Numerical evaluation of virtual corrections to multi-jet production in massless QCD, arXiv:1209.0100 [INSPIRE].
  45. [45]
    T. Gleisberg and F. Krauss, Automating dipole subtraction for QCD NLO calculations, Eur. Phys. J. C 53 (2008) 501 [arXiv:0709.2881] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    R. Frederix, T. Gehrmann and N. Greiner, Automation of the dipole subtraction method in MadGraph/MadEvent, JHEP 09 (2008) 122 [arXiv:0808.2128] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    M. Czakon, C.G. Papadopoulos and M. Worek, Polarizing the dipoles, JHEP 08 (2009) 085 [arXiv:0905.0883] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    R. Frederix, S. Frixione, F. Maltoni and T. Stelzer, Automation of next-to-leading order computations in QCD: the FKS subtraction, JHEP 10 (2009) 003 [arXiv:0908.4272] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    K. Hasegawa, S. Moch and P. Uwer, AutoDipole: automated generation of dipole subtraction terms, Comput. Phys. Commun. 181 (2010) 1802 [arXiv:0911.4371] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  50. [50]
    R. Frederix, T. Gehrmann and N. Greiner, Integrated dipoles with MadDipole in the MadGraph framework, JHEP 06 (2010) 086 [arXiv:1004.2905] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    T. Stelzer and W.F. Long, Automatic generation of tree level helicity amplitudes, Comput. Phys. Commun. 81 (1994) 357 [hep-ph/9401258] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    F. Caravaglios and M. Moretti, An algorithm to compute Born scattering amplitudes without Feynman graphs, Phys. Lett. B 358 (1995) 332 [hep-ph/9507237] [INSPIRE].ADSGoogle Scholar
  53. [53]
    F. Yuasa et al., Automatic computation of cross-sections in HEP: status of GRACE system, Prog. Theor. Phys. Suppl. 138 (2000) 18 [hep-ph/0007053] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    A. Kanaki and C.G. Papadopoulos, HELAC: a package to compute electroweak helicity amplitudes, Comput. Phys. Commun. 132 (2000) 306 [hep-ph/0002082] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  55. [55]
    M. Moretti, T. Ohl and J. Reuter, OMega: an optimizing matrix element generator, in 2nd ECFA/DESY study 19982001, pp. 1981–2009 [hep-ph/0102195] [INSPIRE].
  56. [56]
    F. Krauss, R. Kuhn and G. Soff, AMEGIC++ 1.0: A Matrix Element Generator In C++, JHEP 02 (2002) 044 [hep-ph/0109036] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    M.L. Mangano, M. Moretti, F. Piccinini, R. Pittau and A.D. Polosa, ALPGEN, a generator for hard multiparton processes in hadronic collisions, JHEP 07 (2003) 001 [hep-ph/0206293] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    J. Fujimoto et al., GRACE/SUSY automatic generation of tree amplitudes in the minimal supersymmetric standard model, Comput. Phys. Commun. 153 (2003) 106 [hep-ph/0208036] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    A. Cafarella, C.G. Papadopoulos and M. Worek, Helac-Phegas: a generator for all parton level processes, Comput. Phys. Commun. 180 (2009) 1941 [arXiv:0710.2427] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    E. Boos et al., CompHEP 4.5 status report, PoS(ACAT08)008 [arXiv:0901.4757] [INSPIRE].
  61. [61]
    J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, MadGraph 5: going beyond, JHEP 06 (2011) 128 [arXiv:1106.0522] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    R. Frederix et al., Four-lepton production at hadron colliders: aMC@NLO predictions with theoretical uncertainties, JHEP 02 (2012) 099 [arXiv:1110.4738] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    S. Frixione, P. Nason and B.R. Webber, Matching NLO QCD and parton showers in heavy flavor production, JHEP 08 (2003) 007 [hep-ph/0305252] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    S. Catani, Y.L. Dokshitzer, M.H. Seymour and B.R. Webber, Longitudinally invariant k T clustering algorithms for hadron hadron collisions, Nucl. Phys. B 406 (1993) 187 [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    E. Boos et al., Generic user process interface for event generators, hep-ph/0109068 [INSPIRE].
  66. [66]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    K. Hamilton, P. Nason and G. Zanderighi, MINLO: Multi-scale Improved NLO, JHEP 10 (2012) 155 [arXiv:1206.3572] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    S. Mrenna and P. Richardson, Matching matrix elements and parton showers with HERWIG and PYTHIA, JHEP 05 (2004) 040 [hep-ph/0312274] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    J. Alwall, S. de Visscher and F. Maltoni, QCD radiation in the production of heavy colored particles at the LHC, JHEP 02 (2009) 017 [arXiv:0810.5350] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    G. Corcella et al., HERWIG 6: an event generator for hadron emission reactions with interfering gluons (including supersymmetric processes), JHEP 01 (2001) 010 [hep-ph/0011363] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    M. Bahr et al., HERWIG++ physics and manual, Eur. Phys. J. C 58 (2008) 639 [arXiv:0803.0883] [INSPIRE].ADSCrossRefGoogle Scholar
  72. [72]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  73. [73]
    M. Cacciari, G.P. Salam and G. Soyez, The anti-k T jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    M. Wobisch and T. Wengler, Hadronization corrections to jet cross-sections in deep inelastic scattering, in Proceedings of the Workshop on Monte Carlo Generators for HERA Physics, Hamburg Germany, 27–30 Apr 1998, pp. 270–279 [hep-ph/9907280] [INSPIRE].
  75. [75]
    Y.L. Dokshitzer, G.D. Leder, S. Moretti and B.R. Webber, Better jet clustering algorithms, JHEP 08 (1997) 001 [hep-ph/9707323] [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    M. Cacciari and G.P. Salam, Dispelling the N 3 myth for the k T jet-finder, Phys. Lett. B 641 (2006) 57 [hep-ph/0512210] [INSPIRE].ADSGoogle Scholar
  77. [77]
    A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) 189 [arXiv:0901.0002] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    J.M. Campbell, R.K. Ellis and C. Williams, Hadronic production of a Higgs boson and two jets at next-to-leading order, Phys. Rev. D 81 (2010) 074023 [arXiv:1001.4495] [INSPIRE].ADSGoogle Scholar
  79. [79]
    J.M. Campbell et al., NLO Higgs boson production plus one and two jets using the POWHEG BOX, MadGraph4 and MCFM, JHEP 07 (2012) 092 [arXiv:1202.5475] [INSPIRE].ADSCrossRefGoogle Scholar
  80. [80]
    M.L. Mangano, M. Moretti, F. Piccinini and M. Treccani, Matching matrix elements and shower evolution for top-quark production in hadronic collisions, JHEP 01 (2007) 013 [hep-ph/0611129] [INSPIRE].ADSCrossRefGoogle Scholar
  81. [81]
    P. Torrielli and S. Frixione, Matching NLO QCD computations with PYTHIA using MC@NLO, JHEP 04 (2010) 110 [arXiv:1002.4293] [INSPIRE].ADSCrossRefGoogle Scholar
  82. [82]
    P. Nason, S. Dawson and R.K. Ellis, The total cross-section for the production of heavy quarks in hadronic collisions, Nucl. Phys. B 303 (1988) 607 [INSPIRE].ADSCrossRefGoogle Scholar
  83. [83]
    S. Dittmaier, P. Uwer and S. Weinzierl, NLO QCD corrections to \( t\overline{t} \) + jet production at hadron colliders, Phys. Rev. Lett. 98 (2007) 262002 [hep-ph/0703120] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA 2012

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität ZürichZürichSwitzerland
  2. 2.PH Department, TH UnitCERNGeneva 23Switzerland
  3. 3.ITPP, EPFLLausanneSwitzerland

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