Merging multi-leg NLO matrix elements with parton showers



We discuss extensions of multi-jet matrix element and parton shower merging approaches, to also include next-to-leading order accuracy. Specifically, we generalise the so-called CKKW-L prescription and the recently developed unitarised matrix element + parton shower (UMEPS) scheme. Endowing tree-level merging methods with NLO corrections greatly enhances the perturbative accuracy of parton shower Monte Carlo programs.

To generalise the CKKW-L approach, we augment the Nils-Lavesson-Leif-Lönnblad (NL3) scheme, which was previously developed for e+e-annihilation, with a careful treatment of parton densities. This makes the application of the NL3 method to hadronic collisions possible. NL3 is further updated to use for more readily accessible next-to-leading order input calculations.

We also extend the UMEPS scheme to NLO accuracy. The resulting approach, dubbed unitarised next-to-leading order + parton shower (UNLOPS) merging, does not inherit problematic unitarity-breaking features of CKKW-L, and thus allows for a theoretically more appealing definition of NLO order merging.

Both schemes have been implemented in PYTHIA8. We present results for the merging of W- and Higgs-production events, where the zero- and one-jet contribution are corrected to next-to-leading order simultaneously, and higher jet multiplicities are described by tree-level matrix elements. We find that NL3 and UNLOPS yield a very similar description for W production. For Higgs production however, UNLOPS produces more stable results.

The implementation of the NLO merging procedures is completely general and can be used for higher jet multiplicities and other processes, subject to the availability of programs able to correctly generate the corresponding partonic states to leading and next-to-leading order accuracy.


Monte Carlo Simulations NLO Computations 


  1. [1]
    S. Catani, F. Krauss, R. Kuhn and B. Webber, QCD matrix elements + parton showers, JHEP 11 (2001) 063 [hep-ph/0109231] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    L. Lönnblad, Correcting the color dipole cascade model with fixed order matrix elements, JHEP 05 (2002) 046 [hep-ph/0112284] [INSPIRE].CrossRefGoogle Scholar
  3. [3]
    N. Lavesson and L. Lönnblad, W + jets matrix elements and the dipole cascade, JHEP 07 (2005) 054 [hep-ph/0503293] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    S. Höche, F. Krauss, S. Schumann and F. Siegert, QCD matrix elements and truncated showers, JHEP 05 (2009) 053 [arXiv:0903.1219] [INSPIRE].CrossRefGoogle Scholar
  5. [5]
    L. Lönnblad and S. Prestel, Matching Tree-Level Matrix Elements with Interleaved Showers, JHEP 03 (2012) 019 [arXiv:1109.4829] [INSPIRE].CrossRefGoogle Scholar
  6. [6]
    L. Lönnblad and S. Prestel, Unitarising Matrix Element + Parton Shower merging, JHEP 02 (2013) 094 [arXiv:1211.4827] [INSPIRE].CrossRefGoogle Scholar
  7. [7]
    Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    G. Ossola, C.G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys. B 763 (2007) 147 [hep-ph/0609007] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    R.K. Ellis, W. Giele and Z. Kunszt, A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes, JHEP 03 (2008) 003 [arXiv:0708.2398] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    G. Ossola, C.G. Papadopoulos and R. Pittau, On the Rational Terms of the one-loop amplitudes, JHEP 05 (2008) 004 [arXiv:0802.1876] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    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
  14. [14]
    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
  15. [15]
    S. Becker, C. Reuschle and S. Weinzierl, Numerical NLO QCD calculations, JHEP 12 (2010) 013 [arXiv:1010.4187] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    F. Cascioli, P. Maierhofer and S. Pozzorini, Scattering Amplitudes with Open Loops, Phys. Rev. Lett. 108 (2012) 111601 [arXiv:1111.5206] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    P. Nason, A New method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with Parton Shower simulations: the POWHEG method, JHEP 11 (2007) 070 [arXiv:0709.2092] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 06 (2010) 043 [arXiv:1002.2581] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    S. Platzer and S. Gieseke, Dipole Showers and Automated NLO Matching in HERWIG++, Eur. Phys. J. C 72 (2012) 2187 [arXiv:1109.6256] [INSPIRE].ADSGoogle Scholar
  21. [21]
    S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    S. Höche, F. Krauss, M. Schönherr and F. Siegert, A critical appraisal of NLO+PS matching methods, JHEP 09 (2012) 049 [arXiv:1111.1220] [INSPIRE].CrossRefGoogle Scholar
  23. [23]
    S. Höche, F. Krauss, M. Schönherr and F. Siegert, W+n-jet predictions at the Large Hadron Collider at next-to-leading order matched with a parton shower, Phys. Rev. Lett. 110 (2013) 052001 [arXiv:1201.5882] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    V. Hirschi et al., Automation of one-loop QCD corrections, JHEP 05 (2011) 044 [arXiv:1103.0621] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    N. Lavesson and L. Lönnblad, Extending CKKW-merging to One-Loop Matrix Elements, JHEP 12 (2008) 070 [arXiv:0811.2912] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    T. Gehrmann, S. Hoöche, F. Krauss, M. Schönherr and F. Siegert, NLO QCD matrix elements + parton showers in e + e hadrons, JHEP 01 (2013) 144 [arXiv:1207.5031] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    S. Höche, F. Krauss, M. Schönherr and F. Siegert, QCD matrix elements + parton showers: the NLO case, arXiv:1207.5030 [INSPIRE].
  28. [28]
    R. Frederix and S. Frixione, Merging meets matching in MC@NLO, JHEP 12 (2012) 061 [arXiv:1209.6215] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    Z. Nagy and D.E. Soper, Matching parton showers to NLO computations, JHEP 10 (2005) 024 [hep-ph/0503053] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    K. Hamilton, P. Nason and G. Zanderighi, MINLO: multi-Scale Improved NLO, JHEP 10 (2012) 155 [arXiv:1206.3572] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    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].ADSMATHCrossRefGoogle Scholar
  32. [32]
    S. Plätzer, Controlling inclusive cross sections in parton shower + matrix element merging, arXiv:1211.5467 [INSPIRE].
  33. [33]
    J. Alwall et al., A Standard format for Les Houches event files, Comput. Phys. Commun. 176 (2007) 300 [hep-ph/0609017] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    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
  35. [35]
    C.W. Bauer, F.J. Tackmann and J. Thaler, GenEvA. II. A Phase space generator from a reweighted parton shower, JHEP 12 (2008) 011 [arXiv:0801.4028] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    S. Alioli et al., Combining Higher-Order Resummation with Multiple NLO Calculations and Parton Showers in GENEVA, arXiv:1211.7049 [INSPIRE].
  37. [37]
    M. Rubin, G.P. Salam and S. Sapeta, Giant QCD K-factors beyond NLO, JHEP 09 (2010) 084 [arXiv:1006.2144] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    F. Campanario and S. Sapeta, WZ production beyond NLO for high-pT observables, Phys. Lett. B 718 (2012) 100 [arXiv:1209.4595] [INSPIRE].ADSGoogle Scholar
  39. [39]
    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
  40. [40]
    S. Höche, F. Krauss, M. Schönherr and F. Siegert, NLO matrix elements and truncated showers, JHEP 08 (2011) 123 [arXiv:1009.1127] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    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
  42. [42]
    S. Alioli, P. Nason, C. Oleari and E. Re, NLO vector-boson production matched with shower in POWHEG, JHEP 07 (2008) 060 [arXiv:0805.4802] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    S. Alioli, P. Nason, C. Oleari and E. Re, Vector boson plus one jet production in POWHEG, JHEP 01 (2011) 095 [arXiv:1009.5594] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    S. Alioli, P. Nason, C. Oleari and E. Re, NLO Higgs boson production via gluon fusion matched with shower in POWHEG, JHEP 04 (2009) 002 [arXiv:0812.0578] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    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
  46. [46]
    M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    ATLAS collaboration, Study of jets produced in association with a W boson in pp collisions at \( \sqrt{s}=7 \) TeV with the ATLAS detector, Phys. Rev. D 85 (2012) 092002 [arXiv:1201.1276] [INSPIRE].ADSGoogle Scholar
  48. [48]
    T. Sjöstrand and P.Z. Skands, Transverse-momentum-ordered showers and interleaved multiple interactions, Eur. Phys. J. C 39 (2005) 129 [hep-ph/0408302] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    R.K. Ellis, W.J. Stirling and B. Webber, QCD and collider physics, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 8 (1996) 1.Google Scholar
  50. [50]
    Axial Field Spectrometer collaboration, T. Akesson et al., Double parton scattering in pp collisions at \( \sqrt{s}=63 \) GeV, Z. Phys. C 34 (1987) 163 [INSPIRE].ADSGoogle Scholar
  51. [51]
    CDF collaboration, F. Abe et al., Measurement of double parton scattering in pp collisions at \( \sqrt{s}=1.8 \) TeV, Phys. Rev. Lett. 79 (1997) 584 [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    ATLAS collaboration, Measurement of underlying event characteristics using charged particles in pp collisions at \( \sqrt{s}=900 \) GeV and 7 TeV with the ATLAS detector, Phys. Rev. D 83 (2011) 112001 [arXiv:1012.0791] [INSPIRE].ADSGoogle Scholar
  53. [53]
    P. Bartalini et al., Multi-Parton Interactions at the LHC, arXiv:1111.0469 [INSPIRE].
  54. [54]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    R. Corke, Multiple Interactions in PYTHIA 8, arXiv:0901.2852 [INSPIRE].
  56. [56]
    R. Corke and T. Sjöstrand, Multiparton Interactions and Rescattering, JHEP 01 (2010) 035 [arXiv:0911.1909] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    R. Corke and T. Sjöstrand, Multiparton Interactions with an x-dependent Proton Size, JHEP 05 (2011) 009 [arXiv:1101.5953] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Dept. of Astronomy and Theoretical PhysicsLund UniversityLundSweden

Personalised recommendations