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Journal of High Energy Physics

, 2018:38 | Cite as

Independently parameterised momenta variables and Monte Carlo IR subtraction

  • Peter Cox
  • Tom MeliaEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We introduce a system of parameters for the Monte Carlo generation of Lorentz invariant phase space that is particularly well-suited to the treatment of the infrared divergences that occur in the most singular, Born-like configurations of 1 → n QCD processes. A key feature is that particle momenta are generated independently of one another, leading to a simple parameterisation of all such IR limits. We exemplify the use of these variables in conjunction with the projection to Born subtraction technique at next-to-next-to-leading order. The geometric origins of this parameterisation lie in a coordinate chart on a Grassmannian manifold.

Keywords

NLO Computations QCD Phenomenology 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [INSPIRE].
  2. [2]
    A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Gluon-gluon antenna functions from Higgs boson decay, Phys. Lett. B 612 (2005) 49 [hep-ph/0502110] [INSPIRE].
  3. [3]
    A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Quark-gluon antenna functions from neutralino decay, Phys. Lett. B 612 (2005) 36 [hep-ph/0501291] [INSPIRE].
  4. [4]
    A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP 04 (2007) 016 [hep-ph/0612257] [INSPIRE].
  5. [5]
    A. Daleo, A. Gehrmann-De Ridder, T. Gehrmann and G. Luisoni, Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, JHEP 01 (2010) 118 [arXiv:0912.0374] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  6. [6]
    T. Gehrmann and P.F. Monni, Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, JHEP 12 (2011) 049 [arXiv:1107.4037] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  7. [7]
    R. Boughezal, A. Gehrmann-De Ridder and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours, JHEP 02 (2011) 098 [arXiv:1011.6631] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  8. [8]
    A. Gehrmann-De Ridder, T. Gehrmann and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations, JHEP 10 (2012) 047 [arXiv:1207.5779] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  9. [9]
    J. Currie, E.W.N. Glover and S. Wells, Infrared structure at NNLO using antenna subtraction, JHEP 04 (2013) 066 [arXiv:1301.4693] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B 693 (2010) 259 [arXiv:1005.0274] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M. Czakon, Double-real radiation in hadronic top quark pair production as a proof of a certain concept, Nucl. Phys. B 849 (2011) 250 [arXiv:1101.0642] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  12. [12]
    M. Czakon and D. Heymes, Four-dimensional formulation of the sector-improved residue subtraction scheme, Nucl. Phys. B 890 (2014) 152 [arXiv:1408.2500] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  13. [13]
    R. Boughezal, K. Melnikov and F. Petriello, A subtraction scheme for NNLO computations, Phys. Rev. D 85 (2012) 034025 [arXiv:1111.7041] [INSPIRE].ADSGoogle Scholar
  14. [14]
    M. Cacciari, F.A. Dreyer, A. Karlberg, G.P. Salam and G. Zanderighi, Fully differential vector-boson-fusion Higgs production at next-to-next-to-leading order, Phys. Rev. Lett. 115 (2015) 082002 [Erratum ibid. 120 (2018) 139901] [arXiv:1506.02660] [INSPIRE].
  15. [15]
    S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett. 98 (2007) 222002 [hep-ph/0703012] [INSPIRE].
  16. [16]
    M. Grazzini, NNLO predictions for the Higgs boson signal in the HWWℓνℓν and HZZ → 4ℓ decay channels, JHEP 02 (2008) 043 [arXiv:0801.3232] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    R. Boughezal, C. Focke, X. Liu and F. Petriello, W-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, Phys. Rev. Lett. 115 (2015) 062002 [arXiv:1504.02131] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    J. Gaunt, M. Stahlhofen, F.J. Tackmann and J.R. Walsh, N-jettiness subtractions for NNLO QCD calculations, JHEP 09 (2015) 058 [arXiv:1505.04794] [INSPIRE].CrossRefGoogle Scholar
  19. [19]
    V. Del Duca, C. Duhr, A. Kardos, G. Somogyi and Z. Trócsányi, Three-jet production in electron-positron collisions at next-to-next-to-leading order accuracy, Phys. Rev. Lett. 117 (2016) 152004 [arXiv:1603.08927] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    V. Del Duca et al., Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions, Phys. Rev. D 94 (2016) 074019 [arXiv:1606.03453] [INSPIRE].ADSGoogle Scholar
  21. [21]
    M. Grazzini, S. Kallweit, S. Pozzorini, D. Rathlev and M. Wiesemann, W + W production at the LHC: fiducial cross sections and distributions in NNLO QCD, JHEP 08 (2016) 140 [arXiv:1605.02716] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    S. Dawson, P. Jaiswal, Y. Li, H. Ramani and M. Zeng, Resummation of jet veto logarithms at N 3 LL a + NNLO for W + W production at the LHC, Phys. Rev. D 94 (2016) 114014 [arXiv:1606.01034] [INSPIRE].ADSGoogle Scholar
  23. [23]
    F. Caola, K. Melnikov and R. Röntsch, Nested soft-collinear subtractions in NNLO QCD computations, Eur. Phys. J. C 77 (2017) 248 [arXiv:1702.01352] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    F. Caola, M. Delto, H. Frellesvig and K. Melnikov, The double-soft integral for an arbitrary angle between hard radiators, Eur. Phys. J. C 78 (2018) 687 [arXiv:1807.05835] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    J.M. Campbell, R.K. Ellis, R. Mondini and C. Williams, The NNLO QCD soft function for 1-jettiness, Eur. Phys. J. C 78 (2018) 234 [arXiv:1711.09984] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    I. Moult, L. Rothen, I.W. Stewart, F.J. Tackmann and H.X. Zhu, N-jettiness subtractions for ggH at subleading power, Phys. Rev. D 97 (2018) 014013 [arXiv:1710.03227] [INSPIRE].ADSGoogle Scholar
  27. [27]
    M.A. Ebert, I. Moult, I.W. Stewart, F.J. Tackmann, G. Vita and H.X. Zhu, Power corrections for N-jettiness subtractions at \( \mathcal{O} \)(α s), arXiv:1807.10764 [INSPIRE].
  28. [28]
    F. Herzog, Geometric IR subtraction for final state real radiation, JHEP 08 (2018) 006 [arXiv:1804.07949] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    L. Magnea, E. Maina, G. Pelliccioli, C. Signorile-Signorile, P. Torrielli and S. Uccirati, Local analytic sector subtraction at NNLO, arXiv:1806.09570 [INSPIRE].
  30. [30]
    F. Dulat, B. Mistlberger and A. Pelloni, Differential Higgs production at N 3 LO beyond threshold, JHEP 01 (2018) 145 [arXiv:1710.03016] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    J. Currie, T. Gehrmann, E.W.N. Glover, A. Huss, J. Niehues and A. Vogt, N 3 LO corrections to jet production in deep inelastic scattering using the Projection-to-Born method, JHEP 05 (2018) 209 [arXiv:1803.09973] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    L. Cieri, X. Chen, T. Gehrmann, E.W.N. Glover and A. Huss, Higgs boson production at the LHC using the q T subtraction formalism at N 3 LO QCD, arXiv:1807.11501 [INSPIRE].
  33. [33]
    E.L. Berger, J. Gao, C.P. Yuan and H.X. Zhu, NNLO QCD corrections to t-channel single top-quark production and decay, Phys. Rev. D 94 (2016) 071501 [arXiv:1606.08463] [INSPIRE].ADSGoogle Scholar
  34. [34]
    R. Kleiss, W.J. Stirling and S.D. Ellis, A new Monte Carlo treatment of multiparticle phase space at high-energies, Comput. Phys. Commun. 40 (1986) 359 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    B. Henning and T. Melia, in preparation, (2018).Google Scholar
  36. [36]
    N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A duality for the S matrix, JHEP 03 (2010) 020 [arXiv:0907.5418] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    S. Badger, C. Brønnum-Hansen, H.B. Hartanto and T. Peraro, First look at two-loop five-gluon scattering in QCD, Phys. Rev. Lett. 120 (2018) 092001 [arXiv:1712.02229] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  38. [38]
    S. Badger et al., Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD, PoS(LL2018)006 (2018) [arXiv:1807.09709] [INSPIRE].
  39. [39]
    H. Murayama, Notes on Faddeev-Popov ghosts, (2007).Google Scholar
  40. [40]
    S. Catani and M.H. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [Erratum ibid. B 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
  41. [41]
    A. Gehrmann-De Ridder, T. Gehrmann and G. Heinrich, Four particle phase space integrals in massless QCD, Nucl. Phys. B 682 (2004) 265 [hep-ph/0311276] [INSPIRE].
  42. [42]
    C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD, Nucl. Phys. B 646 (2002) 220 [hep-ph/0207004] [INSPIRE].
  43. [43]
    A.V. Smirnov, Algorithm FIREFeynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  44. [44]
    A.V. Smirnov and V.A. Smirnov, FIRE4, LiteRed and accompanying tools to solve integration by parts relations, Comput. Phys. Commun. 184 (2013) 2820 [arXiv:1302.5885] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced StudyUniversity of TokyoKashiwaJapan

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