Advertisement

Journal of High Energy Physics

, 2018:19 | Cite as

Planar master integrals for the two-loop light-fermion electroweak corrections to Higgs plus jet production

  • Matteo BecchettiEmail author
  • Roberto Bonciani
  • Valerio Casconi
  • Vittorio Del Duca
  • Francesco Moriello
Open Access
Regular Article - Theoretical Physics

Abstract

We present the analytic calculation of the planar master integrals which contribute to compute the two-loop light-fermion electroweak corrections to the production of a Higgs boson in association with a jet in gluon-gluon fusion. The complete dependence on the electroweak-boson mass is retained. The master integrals are evaluated by means of the differential equations method and the analytic results are expressed in terms of multiple polylogarithms up to weight four.

Keywords

NLO Computations 

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]
    ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
  2. [2]
    CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
  3. [3]
    LHC Higgs Cross Section Working Group collaboration, S. Dittmaier et al., Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables, arXiv:1101.0593 [INSPIRE].
  4. [4]
    S. Dittmaier et al., Handbook of LHC Higgs Cross Sections: 2. Differential Distributions, arXiv:1201.3084 [INSPIRE].
  5. [5]
    LHC Higgs Cross Section Working Group collaboration, J.R. Andersen et al., Handbook of LHC Higgs Cross Sections: 3. Higgs Properties, arXiv:1307.1347 [INSPIRE].
  6. [6]
    LHC Higgs Cross Section Working Group collaboration, D. de Florian et al., Handbook of LHC Higgs Cross Sections: 4. Deciphering the Nature of the Higgs Sector, arXiv:1610.07922 [INSPIRE].
  7. [7]
    D. Graudenz, M. Spira and P.M. Zerwas, QCD corrections to Higgs boson production at proton proton colliders, Phys. Rev. Lett. 70 (1993) 1372 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    M. Spira, A. Djouadi, D. Graudenz and P.M. Zerwas, Higgs boson production at the LHC, Nucl. Phys. B 453 (1995) 17 [hep-ph/9504378] [INSPIRE].
  9. [9]
    R. Harlander and P. Kant, Higgs production and decay: Analytic results at next-to-leading order QCD, JHEP 12 (2005) 015 [hep-ph/0509189] [INSPIRE].
  10. [10]
    C. Anastasiou, S. Beerli, S. Bucherer, A. Daleo and Z. Kunszt, Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop, JHEP 01 (2007) 082 [hep-ph/0611236] [INSPIRE].
  11. [11]
    U. Aglietti, R. Bonciani, G. Degrassi and A. Vicini, Analytic Results for Virtual QCD Corrections to Higgs Production and Decay, JHEP 01 (2007) 021 [hep-ph/0611266] [INSPIRE].
  12. [12]
    R. Bonciani, G. Degrassi and A. Vicini, Scalar particle contribution to Higgs production via gluon fusion at NLO, JHEP 11 (2007) 095 [arXiv:0709.4227] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    C. Anastasiou, C. Duhr, F. Dulat and B. Mistlberger, Soft triple-real radiation for Higgs production at N3LO, JHEP 07 (2013) 003 [arXiv:1302.4379] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    C. Anastasiou, C. Duhr, F. Dulat, F. Herzog and B. Mistlberger, Real-virtual contributions to the inclusive Higgs cross-section at N 3 LO, JHEP 12 (2013) 088 [arXiv:1311.1425] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    C. Anastasiou, C. Duhr, F. Dulat, E. Furlan, T. Gehrmann, F. Herzog et al., Higgs Boson GluonFfusion Production Beyond Threshold in N 3 LO QCD, JHEP 03 (2015) 091 [arXiv:1411.3584] [INSPIRE].CrossRefGoogle Scholar
  16. [16]
    Y. Li, A. von Manteuffel, R.M. Schabinger and H.X. Zhu, Soft-virtual corrections to Higgs production at N 3 LO, Phys. Rev. D 91 (2015) 036008 [arXiv:1412.2771] [INSPIRE].ADSGoogle Scholar
  17. [17]
    C. Anastasiou, C. Duhr, F. Dulat, F. Herzog and B. Mistlberger, Higgs Boson Gluon-Fusion Production in QCD at Three Loops, Phys. Rev. Lett. 114 (2015) 212001 [arXiv:1503.06056] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    C. Anastasiou, C. Duhr, F. Dulat, E. Furlan, T. Gehrmann, F. Herzog et al., High precision determination of the gluon fusion Higgs boson cross-section at the LHC, JHEP 05 (2016) 058 [arXiv:1602.00695] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    R.V. Harlander and T. Neumann, Probing the nature of the Higgs-gluon coupling, Phys. Rev. D 88 (2013) 074015 [arXiv:1308.2225] [INSPIRE].ADSGoogle Scholar
  20. [20]
    A. Banfi, A. Martin and V. Sanz, Probing top-partners in Higgs+jets, JHEP 08 (2014) 053 [arXiv:1308.4771] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    A. Azatov and A. Paul, Probing Higgs couplings with high p T Higgs production, JHEP 01 (2014) 014 [arXiv:1309.5273] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    C. Grojean, E. Salvioni, M. Schlaffer and A. Weiler, Very boosted Higgs in gluon fusion, JHEP 05 (2014) 022 [arXiv:1312.3317] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    M. Schlaffer, M. Spannowsky, M. Takeuchi, A. Weiler and C. Wymant, Boosted Higgs Shapes, Eur. Phys. J. C 74 (2014) 3120 [arXiv:1405.4295] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    M. Buschmann, C. Englert, D. Goncalves, T. Plehn and M. Spannowsky, Resolving the Higgs-Gluon Coupling with Jets, Phys. Rev. D 90 (2014) 013010 [arXiv:1405.7651] [INSPIRE].ADSGoogle Scholar
  25. [25]
    S. Dawson, I.M. Lewis and M. Zeng, Effective field theory for Higgs boson plus jet production, Phys. Rev. D 90 (2014) 093007 [arXiv:1409.6299] [INSPIRE].ADSGoogle Scholar
  26. [26]
    M. Buschmann, D. Goncalves, S. Kuttimalai, M. Schonherr, F. Krauss and T. Plehn, Mass Effects in the Higgs-Gluon Coupling: Boosted vs Off-Shell Production, JHEP 02 (2015) 038 [arXiv:1410.5806] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    D. Ghosh and M. Wiebusch, Dimension-six triple gluon operator in Higgs+jet observables, Phys. Rev. D 91 (2015) 031701 [arXiv:1411.2029] [INSPIRE].ADSGoogle Scholar
  28. [28]
    S. Dawson, I.M. Lewis and M. Zeng, Usefulness of effective field theory for boosted Higgs production, Phys. Rev. D 91 (2015) 074012 [arXiv:1501.04103] [INSPIRE].ADSGoogle Scholar
  29. [29]
    U. Langenegger, M. Spira and I. Strebel, Testing the Higgs Boson Coupling to Gluons, arXiv:1507.01373 [INSPIRE].
  30. [30]
    A. Azatov, C. Grojean, A. Paul and E. Salvioni, Resolving gluon fusion loops at current and future hadron colliders, JHEP 09 (2016) 123 [arXiv:1608.00977] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    M. Grazzini, A. Ilnicka, M. Spira and M. Wiesemann, Modeling BSM effects on the Higgs transverse-momentum spectrum in an EFT approach, JHEP 03 (2017) 115 [arXiv:1612.00283] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    R. Boughezal, F. Caola, K. Melnikov, F. Petriello and M. Schulze, Higgs boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, JHEP 06 (2013) 072 [arXiv:1302.6216] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    X. Chen, T. Gehrmann, E.W.N. Glover and M. Jaquier, Precise QCD predictions for the production of Higgs + jet final states, Phys. Lett. B 740 (2015) 147 [arXiv:1408.5325] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    R. Boughezal, F. Caola, K. Melnikov, F. Petriello and M. Schulze, Higgs boson production in association with a jet at next-to-next-to-leading order, Phys. Rev. Lett. 115 (2015) 082003 [arXiv:1504.07922] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    R. Boughezal, C. Focke, W. Giele, X. Liu and F. Petriello, Higgs boson production in association with a jet at NNLO using jettiness subtraction, Phys. Lett. B 748 (2015) 5 [arXiv:1505.03893] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    X. Chen, J. Cruz-Martinez, T. Gehrmann, E.W.N. Glover and M. Jaquier, NNLO QCD corrections to Higgs boson production at large transverse momentum, JHEP 10 (2016) 066 [arXiv:1607.08817] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    M. Grazzini and H. Sargsyan, Heavy-quark mass effects in Higgs boson production at the LHC, JHEP 09 (2013) 129 [arXiv:1306.4581] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    R.K. Ellis, I. Hinchliffe, M. Soldate and J.J. van der Bij, Higgs Decay to tau+ tau-: A Possible Signature of Intermediate Mass Higgs Bosons at the SSC, Nucl. Phys. B 297 (1988) 221 [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    R.P. Kauffman, Higgs boson p T in gluon fusion, Phys. Rev. D 44 (1991) 1415 [INSPIRE].ADSGoogle Scholar
  40. [40]
    S.P. Jones, M. Kerner and G. Luisoni, Next-to-Leading-Order QCD Corrections to Higgs Boson Plus Jet Production with Full Top-Quark Mass Dependence, Phys. Rev. Lett. 120 (2018) 162001 [arXiv:1802.00349] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    J.M. Lindert, K. Kudashkin, K. Melnikov and C. Wever, Higgs bosons with large transverse momentum at the LHC, Phys. Lett. B 782 (2018) 210 [arXiv:1801.08226] [INSPIRE].ADSGoogle Scholar
  42. [42]
    T. Neumann, NLO Higgs+jet at Large Transverse Momenta Including Top Quark Mass Effects, J. Phys. Comm. 2 (2018) 095017 [arXiv:1802.02981] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    K. Kudashkin, K. Melnikov and C. Wever, Two-loop amplitudes for processes ggHg,qgHq and \( q\overline{q}\to Hg \) at large Higgs transverse momentum, JHEP 02 (2018) 135 [arXiv:1712.06549] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    J.M. Lindert, K. Melnikov, L. Tancredi and C. Wever, Top-bottom interference effects in Higgs plus jet production at the LHC, Phys. Rev. Lett. 118 (2017) 252002 [arXiv:1703.03886] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    F. Caola, J.M. Lindert, K. Melnikov, P.F. Monni, L. Tancredi and C. Wever, Bottom-quark effects in Higgs production at intermediate transverse momentum, JHEP 09 (2018) 035 [arXiv:1804.07632] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    K. Melnikov, L. Tancredi and C. Wever, Two-loop ggHg amplitude mediated by a nearly massless quark, JHEP 11 (2016) 104 [arXiv:1610.03747] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    K. Melnikov, L. Tancredi and C. Wever, Two-loop amplitudes for qgHq and \( q\overline{q}\to Hg \) mediated by a nearly massless quark, Phys. Rev. D 95 (2017) 054012 [arXiv:1702.00426] [INSPIRE].ADSGoogle Scholar
  48. [48]
    R. Bonciani, V. Del Duca, H. Frellesvig, J.M. Henn, F. Moriello and V.A. Smirnov, Two-loop planar master integrals for Higgs→ 3 partons with full heavy-quark mass dependence, JHEP 12 (2016) 096 [arXiv:1609.06685] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    U. Aglietti, R. Bonciani, G. Degrassi and A. Vicini, Two loop light fermion contribution to Higgs production and decays, Phys. Lett. B 595 (2004) 432 [hep-ph/0404071] [INSPIRE].
  50. [50]
    U. Aglietti, R. Bonciani, G. Degrassi and A. Vicini, Master integrals for the two-loop light fermion contributions to ggH and Hγγ, Phys. Lett. B 600 (2004) 57 [hep-ph/0407162] [INSPIRE].
  51. [51]
    G. Degrassi and F. Maltoni, Two-loop electroweak corrections to Higgs production at hadron colliders, Phys. Lett. B 600 (2004) 255 [hep-ph/0407249] [INSPIRE].
  52. [52]
    G. Degrassi and F. Maltoni, Two-loop electroweak corrections to the Higgs-boson decay Hγγ, Nucl. Phys. B 724 (2005) 183[hep-ph/0504137] [INSPIRE].
  53. [53]
    S. Actis, G. Passarino, C. Sturm and S. Uccirati, NLO Electroweak Corrections to Higgs Boson Production at Hadron Colliders, Phys. Lett. B 670 (2008) 12 [arXiv:0809.1301] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    M. Bonetti, K. Melnikov and L. Tancredi, Two-loop electroweak corrections to Higgs-gluon couplings to higher orders in the dimensional regularization parameter, Nucl. Phys. B 916 (2017) 709 [arXiv:1610.05497] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  55. [55]
    M. Bonetti, K. Melnikov and L. Tancredi, Three-loop mixed QCD-electroweak corrections to Higgs boson gluon fusion, Phys. Rev. D 97 (2018) 034004 [arXiv:1711.11113] [INSPIRE].ADSGoogle Scholar
  56. [56]
    C. Anastasiou, R. Boughezal and F. Petriello, Mixed QCD-electroweak corrections to Higgs boson production in gluon fusion, JHEP 04 (2009) 003 [arXiv:0811.3458] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    M. Bonetti, K. Melnikov and L. Tancredi, Higher order corrections to mixed QCD-EW contributions to Higgs boson production in gluon fusion, Phys. Rev. D 97 (2018) 056017 [Erratum ibid. D 97 (2018) 099906] [arXiv:1801.10403] [INSPIRE].
  58. [58]
    A.V. Smirnov, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun. 189 (2015) 182 [arXiv:1408.2372] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  59. [59]
    R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
  60. [60]
    C. Anastasiou and A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations, JHEP 07 (2004) 046 [hep-ph/0404258] [INSPIRE].
  61. [61]
    A. von Manteuffel and C. Studerus, Reduze 2 - Distributed Feynman Integral Reduction, arXiv:1201.4330 [INSPIRE].
  62. [62]
    P. Maierhöfer, J. Usovitsch and P. Uwer, KiraA Feynman integral reduction program, Comput. Phys. Commun. 230 (2018) 99 [arXiv:1705.05610] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    K.G. Chetyrkin and F.V. Tkachov, Integration by Parts: The Algorithm to Calculate β-functions in 4 Loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    F.V. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions, Phys. Lett. 100B (1981) 65 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  65. [65]
    S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
  66. [66]
    T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [INSPIRE].
  67. [67]
    A.V. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation, Phys. Lett. B 254 (1991) 158 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  68. [68]
    E. Remiddi, Differential equations for Feynman graph amplitudes, Nuovo Cim. A 110 (1997) 1435 [hep-th/9711188] [INSPIRE].ADSGoogle Scholar
  69. [69]
    T. Gehrmann and E. Remiddi, Analytic continuation of massless two loop four point functions, Nucl. Phys. B 640 (2002) 379 [hep-ph/0207020] [INSPIRE].
  70. [70]
    M. Argeri and P. Mastrolia, Feynman Diagrams and Differential Equations, Int. J. Mod. Phys. A 22 (2007) 4375 [arXiv:0707.4037] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  71. [71]
    J.M. Henn, Lectures on differential equations for Feynman integrals, J. Phys. A 48 (2015) 153001 [arXiv:1412.2296] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  72. [72]
    J.M. Henn, Multiloop integrals in dimensional regularization made simple, Phys. Rev. Lett. 110 (2013) 251601 [arXiv:1304.1806] [INSPIRE].ADSCrossRefGoogle Scholar
  73. [73]
    M. Argeri, S. Di Vita, P. Mastrolia, E. Mirabella, J. Schlenk, U. Schubert et al., Magnus and Dyson Series for Master Integrals, JHEP 03 (2014) 082 [arXiv:1401.2979] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  74. [74]
    R.N. Lee, Reducing differential equations for multiloop master integrals, JHEP 04 (2015) 108 [arXiv:1411.0911] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  75. [75]
    A. Georgoudis, K.J. Larsen and Y. Zhang, Azurite: An algebraic geometry based package for finding bases of loop integrals, Comput. Phys. Commun. 221 (2017) 203 [arXiv:1612.04252] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  76. [76]
    T. Gehrmann, A. von Manteuffel, L. Tancredi and E. Weihs, The two-loop master integrals for \( q\overline{q}\to VV \), JHEP 06 (2014) 032 [arXiv:1404.4853] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    M. Becchetti and R. Bonciani, Two-Loop Master Integrals for the Planar QCD Massive Corrections to Di-photon and Di-jet Hadro-production, JHEP 01 (2018) 048 [arXiv:1712.02537] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    K.-T. Chen, Iterated path integrals, Bull. Am. Math. Soc. 83 (1977) 831.MathSciNetCrossRefzbMATHGoogle Scholar
  79. [79]
    A. Goncharov, Polylogarithms in arithmetic and geometry, Proceedings of the International Congress of Mathematicians 1,2 (1995) 374.MathSciNetCrossRefzbMATHGoogle Scholar
  80. [80]
    A.B. Goncharov, Multiple polylogarithms and mixed Tate motives, math/0103059 [INSPIRE].
  81. [81]
    E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
  82. [82]
    C.W. Bauer, A. Frink and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language, J. Symb. Comput. 33 (2000) 1 [cs/0004015].
  83. [83]
    J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms, Comput. Phys. Commun. 167 (2005) 177 [hep-ph/0410259] [INSPIRE].
  84. [84]
    A.V. Smirnov, FIESTA4: Optimized Feynman integral calculations with GPU support, Comput. Phys. Commun. 204 (2016) 189 [arXiv:1511.03614] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  85. [85]
    U. Aglietti and R. Bonciani, Master integrals with one massive propagator for the two loop electroweak form-factor, Nucl. Phys. B 668 (2003) 3 [hep-ph/0304028] [INSPIRE].
  86. [86]
    U. Aglietti and R. Bonciani, Master integrals with 2 and 3 massive propagators for the 2 loop electroweak form-factorplanar case, Nucl. Phys. B 698 (2004) 277 [hep-ph/0401193] [INSPIRE].
  87. [87]
    A.B. Goncharov, Multiple polylogarithms and mixed Tate motives, math/0103059 [INSPIRE].
  88. [88]
    A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical Polylogarithms for Amplitudes and Wilson Loops, Phys. Rev. Lett. 105 (2010) 151605 [arXiv:1006.5703] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  89. [89]
    C. Duhr, H. Gangl and J.R. Rhodes, From polygons and symbols to polylogarithmic functions, JHEP 10 (2012) 075 [arXiv:1110.0458] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Sapienza — Università di Roma, Dipartimento di FisicaRomeItaly
  2. 2.INFN Sezione di RomaRomeItaly
  3. 3.ETH ZürichInstitut für theoretische PhysikZürichSwitzerland

Personalised recommendations