Journal of High Energy Physics

, 2019:61 | Cite as

A Monte-Carlo simulation of double parton scattering

  • Baptiste CabouatEmail author
  • Jonathan R. Gaunt
  • Kiran Ostrolenk
Open Access
Regular Article - Theoretical Physics


In this work, a new Monte-Carlo simulation of double parton scattering (DPS) at parton level is presented. The simulation is based on the QCD framework developed recently by M. Diehl, J. R. Gaunt and K. Schönwald. With this framework, the dynamics of the 1 2 perturbative splittings is consistently included inside the simulation, with the impact-parameter dependence taken into account. The simulation evolves simultaneously two hard systems from a common hard scale down to the hadronic scale. The evolution is performed using an angular-ordered parton shower which is combined with a set of double parton distributions that depend explicitly on the inter-parton distance. An illustrative study is performed in the context of same-sign WW production at the LHC, with the quark content of the proton being limited to three flavours. In several distributions we see differences compared to DPS models in Herwig, Pythia, and the DPS “pocket formula”.


Phenomenological Models QCD Phenomenology 


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


  1. [1]
    Particle Data Group collaboration, Review of particle physics, Chin. Phys.C 40 (2016) 100001 [INSPIRE].
  2. [2]
    A. Buckley et al., General-purpose event generators for LHC physics, Phys. Rept.504 (2011) 145 [arXiv:1101.2599] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M. Bahr et al., HERWIG++ physics and manual, Eur. Phys. J.C 58 (2008) 639 [arXiv:0803.0883] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    J. Bellm et al., HERWIG 7.0/HERWIG++ 3.0 release note, Eur. Phys. J.C 76 (2016) 196 [arXiv:1512.01178] [INSPIRE].
  5. [5]
    J. Bellm et al., HERWIG 7.1 release note, arXiv:1705.06919 [INSPIRE].
  6. [6]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 physics and manual, JHEP05 (2006) 026 [hep-ph/0603175] [INSPIRE].
  7. [7]
    T. Sjöstrandn et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun.191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
  8. [8]
    S. Schumann and F. Krauss, A Parton shower algorithm based on Catani-Seymour dipole factorisation, JHEP03 (2008) 038 [arXiv:0709.1027] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP02 (2009) 007 [arXiv:0811.4622] [INSPIRE].
  10. [10]
    E. Bothmann et al., Event generation with SHERPA 2.2, SciPost Phys.7 (2019) 034 [arXiv:1905.09127] [INSPIRE].
  11. [11]
    S. Höche and S. Prestel, Triple collinear emissions in parton showers, Phys. Rev.D 96 (2017) 074017 [arXiv:1705.00742] [INSPIRE].
  12. [12]
    S. H¨oche, F. Krauss and S. Prestel, Implementing NLO DGLAP evolution in parton showers, JHEP10 (2017) 093 [arXiv:1705.00982] [INSPIRE].
  13. [13]
    S. Höche, D. Reichelt and F. Siegert, Momentum conservation and unitarity in parton showers and NLL resummation, JHEP01 (2018) 118 [arXiv:1711.03497] [INSPIRE].
  14. [14]
    M. Bury et al., Calculations with off-shell matrix elements, TMD parton densities and TMD parton showers, Eur. Phys. J.C 78 (2018) 137 [arXiv:1712.05932] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    B. Cabouat and T. Sjöstrand, Some dipole shower studies, Eur. Phys. J.C 78 (2018) 226 [arXiv:1710.00391] [INSPIRE].
  16. [16]
    R. Ángeles Martínez et al., Soft gluon evolution and non-global logarithms, JHEP05 (2018) 044 [arXiv:1802.08531] [INSPIRE].
  17. [17]
    M. Dasgupta et al., Logarithmic accuracy of parton showers: a fixed-order study, JHEP09 (2018) 033 [arXiv:1805.09327] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    P. Richardson and S. Webster, Spin correlations in parton shower simulations, arXiv:1807.01955 [INSPIRE].
  19. [19]
    A.H. Hoang, S. Plätzer and D. Samitz, On the cutoff dependence of the quark mass parameter in angular ordered parton showers, JHEP10 (2018) 200 [arXiv:1807.06617] [INSPIRE].
  20. [20]
    S. Plzätzer, M. Sjodahl and J. Thoŕen, Color matrix element corrections for parton showers, JHEP11 (2018) 009 [arXiv:1808.00332] [INSPIRE].
  21. [21]
    K. Cormier et al., Parton shower and matching uncertainties in top quark pair production with HERWIG 7, arXiv:1810.06493 [INSPIRE].
  22. [22]
    Z. Nagy and D.E. Soper, Parton showers with more exact color evolution, Phys. Rev.D 99 (2019) 054009 [arXiv:1902.02105] [INSPIRE].
  23. [23]
    G. Bewick, S. Ferrario Ravasio, P. Richardson and M.H. Seymour, Logarithmic accuracy of angular-ordered parton showers, arXiv:1904.11866 [INSPIRE].
  24. [24]
    J.R. Forshaw, J. Holguin and S. Plätzer, Parton branching at amplitude level, arXiv:1905.08686 [INSPIRE].
  25. [25]
    J.R. Gaunt, Double parton scattering in proton-proton collisions, Ph.D. thesis, Trinity College, University of Cambridge, Cambridge U.K. (2012).Google Scholar
  26. [26]
    M. Diehl and J.R. Gaunt, Double parton scattering theory overview, Adv. Ser. Direct. High Energy Phys.29 (2018) 7 [arXiv:1710.04408] [INSPIRE].CrossRefGoogle Scholar
  27. [27]
    M. Diehl, D. Ostermeier and A. Schafer, Elements of a theory for multiparton interactions in QCD, JHEP03 (2012) 089 [Erratum ibid.03 (2016) 001] [arXiv:1111.0910] [INSPIRE].
  28. [28]
    J.R. Gaunt and W.J. Stirling, Double parton distributions incorporating perturbative QCD evolution and momentum and quark number sum rules, JHEP03 (2010) 005 [arXiv:0910.4347] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  29. [29]
    G.S. Bali et al., Two-current correlations in the pion on the lattice, JHEP12 (2018) 061 [arXiv:1807.03073] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    B. Blok, Yu. Dokshitzer, L. Frankfurt and M. Strikman, The four jet production at LHC and Tevatron in QCD, Phys. Rev.D 83 (2011) 071501 [arXiv:1009.2714] [INSPIRE].
  31. [31]
    H.-M. Chang, A.V. Manohar and W.J. Waalewijn, Double parton correlations in the bag model, Phys. Rev.D 87 (2013) 034009 [arXiv:1211.3132] [INSPIRE].
  32. [32]
    M. Rinaldi, S. Scopetta, M. Traini and V. Vento, Double parton distributions in light-front constituent quark models, Few Body Syst.56 (2015) 515 [arXiv:1411.7566] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    W. Broniowski, E. Ruiz Arriola and K. Golec-Biernat, Generalized valon model for double parton distributions, Few Body Syst.57 (2016) 405 [arXiv:1602.00254] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    M. Bahr, S. Gieseke and M.H. Seymour, Simulation of multiple partonic interactions in HERWIG++, JHEP07 (2008) 076 [arXiv:0803.3633] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    M. Bähr, Underlying event simulation in the Herwig++ event generator, Ph.D. thesis, Karlsruhe University, Karlsruhe, Germany (2008).Google Scholar
  36. [36]
    R. Corke and T. Sjöstrand, Multiparton interactions with an x-dependent proton size, JHEP05 (2011) 009 [arXiv:1101.5953] [INSPIRE].
  37. [37]
    T. Sjöstrand and P.Z. Skands, Multiple interactions and the structure of beam remnants, JHEP03 (2004) 053 [hep-ph/0402078] [INSPIRE].
  38. [38]
    T. Sjöstrand, The development of MPI modeling in PYTHIA, Adv. Ser. Direct. High Energy Phys.29 (2018) 191 [arXiv:1706.02166] [INSPIRE].
  39. [39]
    V.L. Korotkikh and A.M. Snigirev, Double parton correlations versus factorized distributions, Phys. Lett.B 594 (2004) 171 [hep-ph/0404155] [INSPIRE].
  40. [40]
    J.R. Gaunt, Single perturbative splitting diagrams in double parton scattering, JHEP01 (2013) 042 [arXiv:1207.0480] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    A.V. Manohar and W.J. Waalewijn, A QCD analysis of double parton scattering: color correlations, interference effects and evolution, Phys. Rev.D 85 (2012) 114009 [arXiv:1202.3794] [INSPIRE].ADSGoogle Scholar
  42. [42]
    M. Diehl, T. Kasemets and S. Keane, Correlations in double parton distributions: effects of evolution, JHEP05 (2014) 118 [arXiv:1401.1233] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    R. Kirschner, Generalized Lipatov-Altarelli-Parisi equations and jet calculus rules, Phys. Lett.84B (1979) 266 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    V. Shelest, A. Snigirev and G. Zinovjev, Gazing into the multiparton distribution equations in qcd, Phys. Lett.B 113 (1982) 325.ADSCrossRefGoogle Scholar
  45. [45]
    A.M. Snigirev, Double parton distributions in the leading logarithm approximation of perturbative QCD, Phys. Rev.D 68 (2003) 114012 [hep-ph/0304172] [INSPIRE].
  46. [46]
    M.G. Ryskin and A.M. Snigirev, A fresh look at double parton scattering, Phys. Rev.D 83 (2011) 114047 [arXiv:1103.3495] [INSPIRE].ADSGoogle Scholar
  47. [47]
    B. Blok, Yu. Dokshitser, L. Frankfurt and M. Strikman, pQCD physics of multiparton interactions, Eur. Phys. J.C 72 (2012) 1963 [arXiv:1106.5533] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    J.R. Gaunt and W.J. Stirling, Double parton scattering singularity in one-loop integrals, JHEP06 (2011) 048 [arXiv:1103.1888] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  49. [49]
    M.G. Ryskin and A.M. Snigirev, Double parton scattering in double logarithm approximation of perturbative QCD, Phys. Rev.D 86 (2012) 014018 [arXiv:1203.2330] [INSPIRE].
  50. [50]
    A.V. Manohar and W.J. Waalewijn, What is double parton scattering?, Phys. Lett.B 713 (2012) 196 [arXiv:1202.5034] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    B. Blok, Yu. Dokshitzer, L. Frankfurt and M. Strikman, Perturbative QCD correlations in multi-parton collisions, Eur. Phys. J.C 74 (2014) 2926 [arXiv:1306.3763] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    M. Diehl et al., Cancellation of Glauber gluon exchange in the double Drell-Yan process, JHEP01 (2016) 076 [arXiv:1510.08696] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    M.G.A. Buffing, M. Diehl and T. Kasemets, Transverse momentum in double parton scattering: factorisation, evolution and matching, JHEP01 (2018) 044 [arXiv:1708.03528] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  54. [54]
    M. Diehl, J.R. Gaunt and K. Schönwald, Double hard scattering without double counting, JHEP06 (2017) 083 [arXiv:1702.06486] [INSPIRE].
  55. [55]
    M. Diehl, P. Plößl and A. Schäfer, Proof of sum rules for double parton distributions in QCD, Eur. Phys. J.C 79 (2019) 253 [arXiv:1811.00289] [INSPIRE].
  56. [56]
    J.R. Gaunt and T. Kasemets, Transverse momentum dependence in double parton scattering, Adv. High Energy Phys.2019 (2019) 3797394 [arXiv:1812.09099] [INSPIRE].CrossRefGoogle Scholar
  57. [57]
    M. Diehl, J.R. Gaunt, P. Plößl and A. Schäfer, Two-loop splitting in double parton distributions, SciPost Phys.7 (2019) 017 [arXiv:1902.08019] [INSPIRE].
  58. [58]
    A. Kulesza and W.J. Stirling, Like sign W boson production at the LHC as a probe of double parton scattering, Phys. Lett.B 475 (2000) 168 [hep-ph/9912232] [INSPIRE].
  59. [59]
    E. Cattaruzza, A. Del Fabbro and D. Treleani, Fractional momentum correlations in multiple production of W bosons and of b \( \overline{b} \)pairs in high energy pp collisions, Phys. Rev.D 72 (2005) 034022 [hep-ph/0507052] [INSPIRE].
  60. [60]
    E. Maina, Multiple parton interactions in Z + 4j, W ±W ± + 0/2j and W +W + 2j production at the LHC, JHEP09 (2009) 081 [arXiv:0909.1586] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    D. d’Enterria and A.M. Snigirev, Same-sign WW production in proton-nucleus collisions at the LHC as a signal for double parton scattering, Phys. Lett.B 718 (2013) 1395 [arXiv:1211.0197] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    J.R. Gaunt, C.-H. Kom, A. Kulesza and W.J. Stirling, Same-sign W pair production as a probe of double parton scattering at the LHC, Eur. Phys. J.C 69 (2010) 53 [arXiv:1003.3953] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    F.A. Ceccopieri, M. Rinaldi and S. Scopetta, Parton correlations in same-sign W pair production via double parton scattering at the LHC, Phys. Rev.D 95 (2017) 114030 [arXiv:1702.05363] [INSPIRE].ADSGoogle Scholar
  64. [64]
    Q.-H. Cao, Y. Liu, K.-P. Xie and B. Yan, Double parton scattering of weak gauge boson productions at the 13 TeV and 100 TeV proton-proton colliders, Phys. Rev.D 97 (2018) 035013 [arXiv:1710.06315] [INSPIRE].
  65. [65]
    S. Cotogno, T. Kasemets and M. Myska, Spin on same-sign W -boson pair production, Phys. Rev.D 100 (2019) 011503 [arXiv:1809.09024] [INSPIRE].
  66. [66]
    CMS collaboration, Evidence for WW production from double-parton interactions in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, CMS-PAS-SMP-18-015 (2018).Google Scholar
  67. [67]
    B. Blok and P. Gunnellini, Dynamical approach to MPI four-jet production in PYTHIA, Eur. Phys. J.C 75 (2015) 282 [arXiv:1503.08246] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    B. Blok and P. Gunnellini, Dynamical approach to MPI in W+dijet and Z+dijet production within the PYTHIA event generator, Eur. Phys. J.C 76 (2016) 202 [arXiv:1510.07436] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    J.C. Collins, D.E. Soper and G.F. Sterman, Factorization of hard processes in QCD, Adv. Ser. Direct. High Energy Phys.5 (1989) 1 [hep-ph/0409313] [INSPIRE].
  70. [70]
    T. Sjöstrand, Monte Carlo Tools, in the proceedings of the 65thScottish Universities Summer School in Physics: LHC Physics (SUSSP65), August 16–19, St. Andrews, U.K. (2009), arXiv:0911.5286 [INSPIRE].
  71. [71]
    T. Sjöstrand, A model for initial state parton showers, Phys. Lett.157B (1985) 321 [INSPIRE].
  72. [72]
    M. Bengtsson, T. Sjöstrand and M. van Zijl, Initial state radiation effects on W and jet production, Z. Phys.C 32 (1986) 67 [INSPIRE].
  73. [73]
    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].
  74. [74]
    S. Höche and S. Prestel, The midpoint between dipole and parton showers, Eur. Phys. J.C 75 (2015) 461 [arXiv:1506.05057] [INSPIRE].
  75. [75]
    N. Fischer, S. Prestel, M. Ritzmann and P. Skands, Vincia for hadron colliders, Eur. Phys. J.C 76 (2016) 589 [arXiv:1605.06142] [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    L. Lönnblad, ARIADNE version 4: a program for simulation of QCD cascades implementing the color dipole model, Comput. Phys. Commun.71 (1992) 15 [INSPIRE].
  77. [77]
    S. Gieseke, P. Stephens and B. Webber, New formalism for QCD parton showers, JHEP12 (2003) 045 [hep-ph/0310083] [INSPIRE].
  78. [78]
    B.R. Webber, Monte Carlo Simulation of hard hadronic processes, Ann. Rev. Nucl. Part. Sci.36 (1986) 253.ADSCrossRefGoogle Scholar
  79. [79]
    D. Amati et al., A treatment of hard processes sensitive to the infrared structure of QCD, Nucl. Phys.B 173 (1980) 429 [INSPIRE].ADSCrossRefGoogle Scholar
  80. [80]
    M. Ciafaloni and G. Curci, Exponentiation of large N singularities in QCD, Phys. Lett.B 102 (1981) 352.ADSCrossRefGoogle Scholar
  81. [81]
    S. Catani and L. Trentadue, Resummation of the QCD perturbative series for hard processes, Nucl. Phys.B 327 (1989) 323 [INSPIRE].ADSCrossRefGoogle Scholar
  82. [82]
    S. Catani, B.R. Webber and G. Marchesini, QCD coherent branching and semiinclusive processes at large x, Nucl. Phys.B 349 (1991) 635 [INSPIRE].ADSCrossRefGoogle Scholar
  83. [83]
    L. Durand and P. Hong, QCD and rising total cross-sections, Phys. Rev. Lett.58 (1987) 303 [INSPIRE].ADSCrossRefGoogle Scholar
  84. [84]
    R. Corke and T. Sjöstrand, Interleaved parton showers and tuning prospects, JHEP03 (2011) 032 [arXiv:1011.1759] [INSPIRE].
  85. [85]
    F.A. Ceccopieri, A second update on double parton distributions, Phys. Lett.B 734 (2014) 79 [arXiv:1403.2167] [INSPIRE].ADSCrossRefGoogle Scholar
  86. [86]
    O. Fedkevych, Four-jet and three-jet plus gamma DPS production in pp and pA collisions at the LHC, talk given at the 10thWorkshop MPI@LHC, December 10–14, Perugia, Italy (2018).Google Scholar
  87. [87]
    A. Vladimirov, Structure of rapidity divergences in multi-parton scattering soft factors, JHEP04 (2018) 045 [arXiv:1707.07606] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  88. [88]
    M. Diehl and R. Nagar, Factorisation of soft gluons in multiparton scattering, JHEP04 (2019) 124 [arXiv:1812.09509] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  89. [89]
    D. Treleani, Double parton scattering, diffraction and effective cross section, Phys. Rev.D 76 (2007) 076006 [arXiv:0708.2603] [INSPIRE].
  90. [90]
    M. Bahr, M. Myska, M.H. Seymour and A. Siodmok, Extracting σ effectivefrom the CDF γ+3jets measurement, JHEP03 (2013) 129 [arXiv:1302.4325] [INSPIRE].CrossRefADSGoogle Scholar
  91. [91]
    D0 collaboration, Double parton interactions in γ+3 jet events in pp bar collisions \( \sqrt{s} \) = 1.96 TeV., Phys. Rev.D 81 (2010) 052012 [arXiv:0912.5104] [INSPIRE].
  92. [92]
    CDF collaboration, Double parton scattering in \( \overline{p} \)p collisions at \( \sqrt{s} \) = 1.8 TeV, Phys. Rev.D 56 (1997) 3811 [INSPIRE].
  93. [93]
    CDF collaboration, Measurement of double parton scattering in \( \overline{p} \)p collisions at \( \sqrt{s} \) = 1.8 TeV, Phys. Rev. Lett.79 (1997) 584 [INSPIRE].
  94. [94]
    LHCb collaboration, Observation of double charm production involving open charm in pp collisions at s = 7 TeV, JHEP06 (2012) 141 [arXiv:1205.0975] [INSPIRE].
  95. [95]
    ATLAS collaboration, Measurement of hard double-parton interactions in W (→ lν) + 2 jet events at \( \sqrt{s} \) = 7 TeV with the ATLAS detector, New J. Phys.15 (2013) 033038 [arXiv:1301.6872] [INSPIRE].
  96. [96]
    CMS collaboration, Study of double parton scattering using W + 2-jet events in proton-proton collisions at \( \sqrt{s} \) = 7 TeV, JHEP03 (2014) 032 [arXiv:1312.5729] [INSPIRE].
  97. [97]
    LHCb collaboration, Production of associated Y and open charm hadrons in pp collisions at \( \sqrt{s} \) = 7 and 8 TeV via double parton scattering, JHEP07 (2016) 052 [arXiv:1510.05949] [INSPIRE].
  98. [98]
    LHCb collaboration, Measurement of the J/𝜓 pair production cross-section in pp collisions at \( \sqrt{s} \) = 13 TeV, JHEP06 (2017) 047 [Erratum ibid.10 (2017) 068] [arXiv:1612.07451] [INSPIRE].
  99. [99]
    ATLAS collaboration, Measurement of the prompt J/ 𝜓 pair production cross-section in pp collisions at \( \sqrt{s} \) = 8 TeV with the ATLAS detector, Eur. Phys. J.C 77 (2017) 76 [arXiv:1612.02950] [INSPIRE].
  100. [100]
    ATLAS collaboration, Study of hard double-parton scattering in four-jet events in pp collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS experiment, JHEP11 (2016) 110 [arXiv:1608.01857] [INSPIRE].
  101. [101]
    CMS collaboration, Constraints on the double-parton scattering cross section from same-sign W boson pair production in proton-proton collisions at \( \sqrt{s} \) = 8 TeV, JHEP02 (2018) 032 [arXiv:1712.02280] [INSPIRE].
  102. [102]
    M. Diehl, T. Feldmann, R. Jakob and P. Kroll, Generalized parton distributions from nucleon form-factor data, Eur. Phys. J.C 39 (2005) 1 [hep-ph/0408173] [INSPIRE].
  103. [103]
    M. Diehl and W. Kugler, Some numerical studies of the evolution of generalized parton distributions, Phys. Lett.B 660 (2008) 202 [arXiv:0711.2184] [INSPIRE].ADSCrossRefGoogle Scholar
  104. [104]
    H1 collaboration, Elastic J/𝜓 production at HERA, Eur. Phys. J.C 46 (2006) 585 [hep-ex/0510016] [INSPIRE].
  105. [105]
    R. Kleiss and R. Verheyen, Competing Sudakov veto algorithms, Eur. Phys. J.C 76 (2016) 359 [arXiv:1605.09246] [INSPIRE].ADSCrossRefGoogle Scholar
  106. [106]
    G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys.B 72 (1974) 461 [INSPIRE].
  107. [107]
    F.A. Ceccopieri, An update on the evolution of double parton distributions, Phys. Lett.B 697 (2011) 482 [arXiv:1011.6586] [INSPIRE].ADSCrossRefGoogle Scholar
  108. [108]
    M. Diehl and T. Kasemets, Positivity bounds on double parton distributions, JHEP05 (2013) 150 [arXiv:1303.0842] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  109. [109]
    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].ADSzbMATHCrossRefGoogle Scholar
  110. [110]
    A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Heavy-quark mass dependence in global PDF analyses and 3- and 4-flavour parton distributions, Eur. Phys. J.C 70 (2010) 51 [arXiv:1007.2624] [INSPIRE].ADSCrossRefGoogle Scholar
  111. [111]
    A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Uncertainties on α sin global PDF analyses and implications for predicted hadronic cross sections, Eur. Phys. J.C 64 (2009) 653 [arXiv:0905.3531] [INSPIRE].CrossRefADSGoogle Scholar
  112. [112]
    HL-LHC, HE-LHC Working Group collaboration, Standard model physics at the HL-LHC and HE-LHC, arXiv:1902.04070 [INSPIRE].
  113. [113]
    M. Bengtsson and T. Sjöstrand, Coherent parton showers versus matrix elements: implications of PETRA-PEP data, Phys. Lett.B 185 (1987) 435 [INSPIRE].
  114. [114]
    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].
  115. [115]
    M.H. Seymour, Matrix element corrections to parton shower algorithms, Comput. Phys. Commun.90 (1995) 95 [hep-ph/9410414] [INSPIRE].
  116. [116]
    G. Miu and T. Sjöstrand, W production in an improved parton shower approach, Phys. Lett.B 449 (1999) 313 [hep-ph/9812455] [INSPIRE].
  117. [117]
    L. Lönnblad, Small x effects in W + jets production at the Tevatron, Nucl. Phys.B 458 (1996) 215 [hep-ph/9508261] [INSPIRE].
  118. [118]
    S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP06 (2002) 029 [hep-ph/0204244] [INSPIRE].
  119. [119]
    S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with parton shower simulations: the POWHEG method, JHEP11 (2007) 070 [arXiv:0709.2092] [INSPIRE].ADSCrossRefGoogle Scholar
  120. [120]
    P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP11 (2004) 040 [hep-ph/0409146] [INSPIRE].
  121. [121]
    S. Catani, F. Krauss, R. Kuhn and B.R. Webber, QCD matrix elements + parton showers, JHEP11 (2001) 063 [hep-ph/0109231] [INSPIRE].
  122. [122]
    L. Lönnblad, Correcting the color dipole cascade model with fixed order matrix elements, JHEP05 (2002) 046 [hep-ph/0112284] [INSPIRE].
  123. [123]
    S. Mrenna and P. Richardson, Matching matrix elements and parton showers with HERWIG and PYTHIA, JHEP05 (2004) 040 [hep-ph/0312274] [INSPIRE].
  124. [124]
    A. Buckley et al., Rivet user manual, Comput. Phys. Commun.184 (2013) 2803 [arXiv:1003.0694] [INSPIRE].ADSCrossRefGoogle Scholar
  125. [125]
    J.C. Collins and J.A.M. Vermaseren, Axodraw version 2, arXiv:1606.01177 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Baptiste Cabouat
    • 1
    Email author
  • Jonathan R. Gaunt
    • 2
  • Kiran Ostrolenk
    • 1
  1. 1.School of Physics and AstronomyUniversity of ManchesterManchesterU.K.
  2. 2.CERN Theory DivisionGeneva 23Switzerland

Personalised recommendations