Higgs-boson production at small transverse momentum

  • Thomas BecherEmail author
  • Matthias Neubert
  • Daniel Wilhelm


Using methods from effective field theory, we have recently developed a novel, systematic framework for the calculation of the cross sections for electroweak gauge-boson production at small and very small transverse momentum q T , in which large logarithms of the scale ratio m V /q T are resummed to all orders. This formalism is applied to the production of Higgs bosons in gluon fusion at the LHC. The production cross section receives logarithmically enhanced corrections from two sources: the running of the hard matching coefficient and the collinear factorization anomaly. The anomaly leads to the dynamical generation of a non-perturbative scale \( {q_{*}}\tilde{\mkern6mu} {m_H}{e^{{{{{-\mathrm{const}}} \left/ {{{\alpha_s}\left( {{m_H}} \right)}} \right.}}}}\approx 8 \) GeV, which protects the process from receiving large long-distance hadronic contributions. We present numerical predictions for the transverse-momentum spectrum of Higgs bosons produced at the LHC, finding that it is quite insensitive to hadronic effects.


Higgs Physics Resummation Renormalization Group QCD 


  1. [1]
    J.C. Collins, D.E. Soper and G.F. Sterman, Transverse momentum distribution in Drell-Yan pair and W and Z boson production, Nucl. Phys. B 250 (1985) 199 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    G. Ladinsky and C. Yuan, The nonperturbative regime in QCD resummation for gauge boson production at hadron colliders, Phys. Rev. D 50 (1994) 4239 [hep-ph/9311341] [INSPIRE].ADSGoogle Scholar
  3. [3]
    Q.-H. Cao, C.-R. Chen, C. Schmidt and C.-P. Yuan, Improved predictions for Higgs Q T at the Tevatron and the LHC, arXiv:0909.2305 [INSPIRE].
  4. [4]
    D. de Florian, G. Ferrera, M. Grazzini and D. Tommasini, Transverse-momentum resummation: Higgs boson production at the Tevatron and the LHC, JHEP 11 (2011) 064 [arXiv:1109.2109] [INSPIRE].CrossRefGoogle Scholar
  5. [5]
    G. Bozzi, S. Catani, G. Ferrera, D. de Florian and M. Grazzini, Production of Drell-Yan lepton pairs in hadron collisions: transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy, Phys. Lett. B 696 (2011) 207 [arXiv:1007.2351] [INSPIRE].ADSGoogle Scholar
  6. [6]
    J. Wang, C.S. Li, Z. Li, C. Yuan and H.T. Li, Improved resummation prediction on Higgs production at hadron colliders, Phys. Rev. D 86 (2012) 094026 [arXiv:1205.4311] [INSPIRE].ADSGoogle Scholar
  7. [7]
    S. Catani and M. Grazzini, Higgs boson production at hadron colliders: hard-collinear coefficients at the NNLO, Eur. Phys. J. C 72 (2012) 2013 [Erratum ibid. C 72 (2012) 2132] [arXiv:1106.4652] [INSPIRE].
  8. [8]
    C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].ADSGoogle Scholar
  9. [9]
    C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [INSPIRE].ADSGoogle Scholar
  10. [10]
    M. Beneke, A. Chapovsky, M. Diehl and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power, Nucl. Phys. B 643 (2002) 431 [hep-ph/0206152] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    T. Becher and M. Neubert, Drell-Yan production at small q T , transverse parton distributions and the collinear anomaly, Eur. Phys. J. C 71 (2011) 1665 [arXiv:1007.4005] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    J.-Y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, A formalism for the systematic treatment of rapidity logarithms in quantum field theory, JHEP 05 (2012) 084 [arXiv:1202.0814] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    M.G. Echevarria, A. Idilbi and I. Scimemi, Factorization theorem for Drell-Yan at low q T and transverse momentum distributions on-the-light-cone, JHEP 07 (2012) 002 [arXiv:1111.4996] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    Y. Gao, C.S. Li and J.J. Liu, Transverse momentum resummation for Higgs production in soft-collinear effective theory, Phys. Rev. D 72 (2005) 114020 [hep-ph/0501229] [INSPIRE].ADSGoogle Scholar
  15. [15]
    A. Idilbi, X.-d. Ji and F. Yuan, Transverse momentum distribution through soft-gluon resummation in effective field theory, Phys. Lett. B 625 (2005) 253 [hep-ph/0507196] [INSPIRE].ADSGoogle Scholar
  16. [16]
    S. Mantry and F. Petriello, Factorization and resummation of Higgs boson differential distributions in soft-collinear effective theory, Phys. Rev. D 81 (2010) 093007 [arXiv:0911.4135] [INSPIRE].ADSGoogle Scholar
  17. [17]
    T. Becher, M. Neubert and D. Wilhelm, Electroweak gauge-boson production at small q T : infrared safety from the collinear anomaly, JHEP 02 (2012) 124 [arXiv:1109.6027] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    G. Parisi and R. Petronzio, Small transverse momentum distributions in hard processes, Nucl. Phys. B 154 (1979) 427 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    A. Banfi, G.P. Salam and G. Zanderighi, NLL+NNLO predictions for jet-veto efficiencies in Higgs-boson and Drell-Yan production, JHEP 06 (2012) 159 [arXiv:1203.5773] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    T. Becher and M. Neubert, Factorization and NNLL resummation for Higgs production with a jet veto, JHEP 07 (2012) 108 [arXiv:1205.3806] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    F.J. Tackmann, J.R. Walsh and S. Zuberi, Resummation properties of jet vetoes at the LHC, Phys. Rev. D 86 (2012) 053011 [arXiv:1206.4312] [INSPIRE].ADSGoogle Scholar
  22. [22]
    A. Banfi, P.F. Monni, G.P. Salam and G. Zanderighi, Higgs and Z-boson production with a jet veto, Phys. Rev. Lett. 109 (2012) 202001 [arXiv:1206.4998] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    X. Liu and F. Petriello, Resummation of jet-veto logarithms in hadronic processes containing jets, Phys. Rev. D 87 (2013) 014018 [arXiv:1210.1906] [INSPIRE].ADSGoogle Scholar
  24. [24]
    S. Catani and M. Grazzini, QCD transverse-momentum resummation in gluon fusion processes, Nucl. Phys. B 845 (2011) 297 [arXiv:1011.3918] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    T. Becher, M. Neubert and D. Wilhelm, CuTe webpageresummed transverse momentum distributions for Drell-Yan, W, Z and Higgs production,
  26. [26]
    J.C. Collins and D.E. Soper, Parton distribution and decay functions, Nucl. Phys. B 194 (1982) 445 [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Factorization at the LHC: from PDFs to initial state jets, Phys. Rev. D 81 (2010) 094035 [arXiv:0910.0467] [INSPIRE].ADSGoogle Scholar
  28. [28]
    I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, The quark beam function at NNLL, JHEP 09 (2010) 005 [arXiv:1002.2213] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    A. Jain, M. Procura and W.J. Waalewijn, Fully-unintegrated parton distribution and fragmentation functions at perturbative k T, JHEP 04 (2012) 132 [arXiv:1110.0839] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    T. Becher and G. Bell, Analytic regularization in soft-collinear effective theory, Phys. Lett. B 713 (2012) 41 [arXiv:1112.3907] [INSPIRE].ADSGoogle Scholar
  31. [31]
    J.-y. Chiu, F. Golf, R. Kelley and A.V. Manohar, Electroweak corrections in high energy processes using effective field theory, Phys. Rev. D 77 (2008) 053004 [arXiv:0712.0396] [INSPIRE].ADSGoogle Scholar
  32. [32]
    T. Becher and M. Neubert, On the structure of infrared singularities of gauge-theory amplitudes, JHEP 06 (2009) 081 [arXiv:0903.1126] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett. 102 (2009) 162001 [arXiv:0901.0722] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    S. Frixione, P. Nason and G. Ridolfi, Problems in the resummation of soft gluon effects in the transverse momentum distributions of massive vector bosons in hadronic collisions, Nucl. Phys. B 542 (1999) 311 [hep-ph/9809367] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    J.-Y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, private communication.Google Scholar
  36. [36]
    A. Martin, W. Stirling, R. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) 189 [arXiv:0901.0002] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    V. Ahrens, T. Becher, M. Neubert and L.L. Yang, Renormalization-group improved prediction for Higgs production at hadron colliders, Eur. Phys. J. C 62 (2009) 333 [arXiv:0809.4283] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    V. Ahrens, T. Becher, M. Neubert and L.L. Yang, Origin of the large perturbative corrections to Higgs production at hadron colliders, Phys. Rev. D 79 (2009) 033013 [arXiv:0808.3008] [INSPIRE].ADSGoogle Scholar
  39. [39]
    A.V. Konychev and P.M. Nadolsky, Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production, Phys. Lett. B 633 (2006) 710 [hep-ph/0506225] [INSPIRE].ADSGoogle Scholar
  40. [40]
    D. de Florian, M. Grazzini and Z. Kunszt, Higgs production with large transverse momentum in hadronic collisions at next-to-leading order, Phys. Rev. Lett. 82 (1999) 5209 [hep-ph/9902483] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    V. Ravindran, J. Smith and W. Van Neerven, Next-to-leading order QCD corrections to differential distributions of Higgs boson production in hadron hadron collisions, Nucl. Phys. B 634 (2002) 247 [hep-ph/0201114] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    C.J. Glosser and C.R. Schmidt, Next-to-leading corrections to the Higgs boson transverse momentum spectrum in gluon fusion, JHEP 12 (2002) 016 [hep-ph/0209248] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    J. Campbell, K. Ellis and C. Williams, MCFM webpageMonte Carlo for FeMtobarn processes,
  44. [44]
    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
  45. [45]
    T. Gehrmann, T. Lübbert and L.L. Yang, Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case, Phys. Rev. Lett. 109 (2012) 242003 [arXiv:1209.0682] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    R.D. Ball et al., Parton distributions with LHC data, Nucl. Phys. B 867 (2013) 244 [arXiv:1207.1303] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Thomas Becher
    • 1
    Email author
  • Matthias Neubert
    • 2
  • Daniel Wilhelm
    • 2
  1. 1.Albert Einstein Center for Fundamental Physics, Institut für Theoretische PhysikUniversität BernBernSwitzerland
  2. 2.PRISMA Cluster of Excellence & Mainz Institute for Theoretical PhysicsJohannes Gutenberg UniversityMainzGermany

Personalised recommendations