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Universality of next-to-leading power threshold effects for colourless final states in hadronic collisions

A preprint version of the article is available at arXiv.

Abstract

We consider the production of an arbitrary number of colour-singlet particles near partonic threshold, and show that next-to-leading order cross sections for this class of processes have a simple universal form at next-to-leading power (NLP) in the energy of the emitted gluon radiation. Our analysis relies on a recently derived factorisation formula for NLP threshold effects at amplitude level, and therefore applies both if the leading-order process is tree-level and if it is loop-induced. It holds for differential distributions as well. The results can furthermore be seen as applications of recently derived next-to-soft theorems for gauge theory amplitudes. We use our universal expression to re-derive known results for the production of up to three Higgs bosons at NLO in the large top mass limit, and for the hadro-production of a pair of electroweak gauge bosons. Finally, we present new analytic results for Higgs boson pair production at NLO and NLP, with exact top-mass dependence.

References

  1. J.R. Andersen et al., Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report, in 9th Les Houches Workshop on Physics at TeV Colliders (PhysTeV 2015) Les Houches, France, June 1-19, 2015, arXiv:1605.04692 [INSPIRE].

  2. G.F. Sterman, Summation of Large Corrections to Short Distance Hadronic Cross-Sections, Nucl. Phys. B 281 (1987) 310 [INSPIRE].

    ADS  Article  Google Scholar 

  3. S. Catani and L. Trentadue, Resummation of the QCD Perturbative Series for Hard Processes, Nucl. Phys. B 327 (1989) 323 [INSPIRE].

    ADS  Article  Google Scholar 

  4. G.P. Korchemsky and G. Marchesini, Resummation of large infrared corrections using Wilson loops, Phys. Lett. B 313 (1993) 433 [INSPIRE].

    ADS  Article  Google Scholar 

  5. G.P. Korchemsky and G. Marchesini, Structure function for large x and renormalization of Wilson loop, Nucl. Phys. B 406 (1993) 225 [hep-ph/9210281] [INSPIRE].

  6. H. Contopanagos, E. Laenen and G.F. Sterman, Sudakov factorization and resummation, Nucl. Phys. B 484 (1997) 303 [hep-ph/9604313] [INSPIRE].

  7. S. Forte and G. Ridolfi, Renormalization group approach to soft gluon resummation, Nucl. Phys. B 650 (2003) 229 [hep-ph/0209154] [INSPIRE].

  8. T.O. Eynck, E. Laenen and L. Magnea, Exponentiation of the Drell-Yan cross-section near partonic threshold in the DIS and MS-bar schemes, JHEP 06 (2003) 057 [hep-ph/0305179] [INSPIRE].

  9. A. Banfi, G.P. Salam and G. Zanderighi, Principles of general final-state resummation and automated implementation, JHEP 03 (2005) 073 [hep-ph/0407286] [INSPIRE].

  10. T. Becher and M. Neubert, Threshold resummation in momentum space from effective field theory, Phys. Rev. Lett. 97 (2006) 082001 [hep-ph/0605050] [INSPIRE].

  11. G. Luisoni and S. Marzani, QCD resummation for hadronic final states, J. Phys. G 42 (2015) 103101 [arXiv:1505.04084] [INSPIRE].

  12. N. Kidonakis, Soft-gluon resummations and NNNLO expansions, PoS(EPS-HEP 2013)432 [arXiv:1309.1442] [INSPIRE].

  13. M. Krämer, E. Laenen and M. Spira, Soft gluon radiation in Higgs boson production at the LHC, Nucl. Phys. B 511 (1998) 523 [hep-ph/9611272] [INSPIRE].

  14. 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].

    ADS  Article  Google Scholar 

  15. 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].

    ADS  Article  Google Scholar 

  16. C. Anastasiou et al., Higgs boson gluon-fusion production at threshold in N 3 LO QCD, Phys. Lett. B 737 (2014) 325 [arXiv:1403.4616] [INSPIRE].

    ADS  Article  Google Scholar 

  17. C. Anastasiou et al., Higgs Boson GluonFfusion Production Beyond Threshold in N 3 LO QCD, JHEP 03 (2015) 091 [arXiv:1411.3584] [INSPIRE].

    Article  Google Scholar 

  18. 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].

    ADS  Article  Google Scholar 

  19. E. Laenen, L. Magnea and G. Stavenga, On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections, Phys. Lett. B 669 (2008) 173 [arXiv:0807.4412] [INSPIRE].

    ADS  Article  Google Scholar 

  20. E. Laenen, G. Stavenga and C.D. White, Path integral approach to eikonal and next-to-eikonal exponentiation, JHEP 03 (2009) 054 [arXiv:0811.2067] [INSPIRE].

    ADS  Article  Google Scholar 

  21. E. Laenen, L. Magnea, G. Stavenga and C.D. White, Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach, JHEP 01 (2011) 141 [arXiv:1010.1860] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  22. D. Bonocore, E. Laenen, L. Magnea, L. Vernazza and C.D. White, The method of regions and next-to-soft corrections in Drell-Yan production, Phys. Lett. B 742 (2015) 375 [arXiv:1410.6406] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  23. D. Bonocore, E. Laenen, L. Magnea, S. Melville, L. Vernazza and C.D. White, A factorization approach to next-to-leading-power threshold logarithms, JHEP 06 (2015) 008 [arXiv:1503.05156] [INSPIRE].

    ADS  Article  Google Scholar 

  24. D. Bonocore, E. Laenen, L. Magnea, L. Vernazza and C.D. White, Non-abelian factorisation for next-to-leading-power threshold logarithms, JHEP 12 (2016) 121 [arXiv:1610.06842] [INSPIRE].

    ADS  Article  Google Scholar 

  25. S. Moch and A. Vogt, Threshold Resummation of the Structure Function F(L), JHEP 04 (2009) 081 [arXiv:0902.2342] [INSPIRE].

    ADS  Article  Google Scholar 

  26. S. Moch and A. Vogt, On non-singlet physical evolution kernels and large-x coefficient functions in perturbative QCD, JHEP 11 (2009) 099 [arXiv:0909.2124] [INSPIRE].

    ADS  Article  Google Scholar 

  27. G. Soar, S. Moch, J.A.M. Vermaseren and A. Vogt, On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x, Nucl. Phys. B 832 (2010) 152 [arXiv:0912.0369] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  28. A.A. Almasy, G. Soar and A. Vogt, Generalized double-logarithmic large-x resummation in inclusive deep-inelastic scattering, JHEP 03 (2011) 030 [arXiv:1012.3352] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  29. N.A. Lo Presti, A.A. Almasy and A. Vogt, Leading large-x logarithms of the quark-gluon contributions to inclusive Higgs-boson and lepton-pair production, Phys. Lett. B 737 (2014) 120 [arXiv:1407.1553] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  30. D. de Florian, J. Mazzitelli, S. Moch and A. Vogt, Approximate N 3 LO Higgs-boson production cross section using physical-kernel constraints, JHEP 10 (2014) 176 [arXiv:1408.6277] [INSPIRE].

    ADS  Article  Google Scholar 

  31. G. Grunberg and V. Ravindran, On threshold resummation beyond leading 1-x order, JHEP 10 (2009) 055 [arXiv:0902.2702] [INSPIRE].

    ADS  Article  Google Scholar 

  32. G. Grunberg, Large-x structure of physical evolution kernels in Deep Inelastic Scattering, Phys. Lett. B 687 (2010) 405 [arXiv:0911.4471] [INSPIRE].

    ADS  Article  Google Scholar 

  33. A.J. Larkoski, D. Neill and I.W. Stewart, Soft Theorems from Effective Field Theory, JHEP 06 (2015) 077 [arXiv:1412.3108] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  34. D.W. Kolodrubetz, I. Moult and I.W. Stewart, Building Blocks for Subleading Helicity Operators, JHEP 05 (2016) 139 [arXiv:1601.02607] [INSPIRE].

    ADS  Article  Google Scholar 

  35. I. Moult, L. Rothen, I.W. Stewart, F.J. Tackmann and H.X. Zhu, Subleading Power Corrections for N-Jettiness Subtractions, Phys. Rev. D 95 (2017) 074023 [arXiv:1612.00450] [INSPIRE].

    ADS  Google Scholar 

  36. R. Boughezal, X. Liu and F. Petriello, Power Corrections in the N-jettiness Subtraction Scheme, JHEP 03 (2017) 160 [arXiv:1612.02911] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  37. I. Moult, I.W. Stewart and G. Vita, A subleading operator basis and matching for ggH, JHEP 07 (2017) 067 [arXiv:1703.03408] [INSPIRE].

    ADS  Article  Google Scholar 

  38. I. Feige, D.W. Kolodrubetz, I. Moult and I.W. Stewart, A Complete Basis of Helicity Operators for Subleading Factorization, arXiv:1703.03411 [INSPIRE].

  39. H. Gervais, Soft Photon Theorem for High Energy Amplitudes in Yukawa and Scalar Theories, Phys. Rev. D 95 (2017) 125009 [arXiv:1704.00806] [INSPIRE].

    ADS  Google Scholar 

  40. H. Gervais, Soft Graviton Emission at High and Low Energies in Yukawa and Scalar Theories, Phys. Rev. D 96 (2017) 065007 [arXiv:1706.03453] [INSPIRE].

  41. F.E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions, Phys. Rev. 110 (1958) 974 [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  42. T.H. Burnett and N.M. Kroll, Extension of the low soft photon theorem, Phys. Rev. Lett. 20 (1968) 86 [INSPIRE].

    ADS  Article  Google Scholar 

  43. V. Del Duca, High-energy Bremsstrahlung Theorems for Soft Photons, Nucl. Phys. B 345 (1990) 369 [INSPIRE].

  44. E. Casali, Soft sub-leading divergences in Yang-Mills amplitudes, JHEP 08 (2014) 077 [arXiv:1404.5551] [INSPIRE].

    ADS  Article  Google Scholar 

  45. C.D. White, Factorization Properties of Soft Graviton Amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  46. F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].

  47. S. Dawson, S. Dittmaier and M. Spira, Neutral Higgs boson pair production at hadron colliders: QCD corrections, Phys. Rev. D 58 (1998) 115012 [hep-ph/9805244] [INSPIRE].

  48. D. de Florian and J. Mazzitelli, Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD, Phys. Rev. Lett. 111 (2013) 201801 [arXiv:1309.6594] [INSPIRE].

    ADS  Article  Google Scholar 

  49. D. de Florian et al., Differential Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD, JHEP 09 (2016) 151 [arXiv:1606.09519] [INSPIRE].

    ADS  Article  Google Scholar 

  50. D. de Florian and J. Mazzitelli, Two-loop corrections to the triple Higgs boson production cross section, JHEP 02 (2017) 107 [arXiv:1610.05012] [INSPIRE].

    ADS  Article  Google Scholar 

  51. E.W.N. Glover and J.J. van der Bij, Higgs boson pair production via gluon fusion, Nucl. Phys. B 309 (1988) 282 [INSPIRE].

    ADS  Article  Google Scholar 

  52. T. Plehn, M. Spira and P.M. Zerwas, Pair production of neutral Higgs particles in gluon-gluon collisions, Nucl. Phys. B 479 (1996) 46 [Erratum ibid. B 531 (1998) 655] [hep-ph/9603205] [INSPIRE].

  53. S. Borowka et al., Full top quark mass dependence in Higgs boson pair production at NLO, JHEP 10 (2016) 107 [arXiv:1608.04798] [INSPIRE].

    ADS  Article  Google Scholar 

  54. R. Frederix et al., Higgs pair production at the LHC with NLO and parton-shower effects, Phys. Lett. B 732 (2014) 142 [arXiv:1401.7340] [INSPIRE].

    ADS  Article  Google Scholar 

  55. D.Y. Shao, C.S. Li, H.T. Li and J. Wang, Threshold resummation effects in Higgs boson pair production at the LHC, JHEP 07 (2013) 169 [arXiv:1301.1245] [INSPIRE].

    ADS  Article  Google Scholar 

  56. J. Grigo, J. Hoff, K. Melnikov and M. Steinhauser, On the Higgs boson pair production at the LHC, Nucl. Phys. B 875 (2013) 1 [arXiv:1305.7340] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  57. T. Plehn and M. Rauch, The quartic Higgs coupling at hadron colliders, Phys. Rev. D 72 (2005) 053008 [hep-ph/0507321] [INSPIRE].

  58. F. Maltoni, E. Vryonidou and M. Zaro, Top-quark mass effects in double and triple Higgs production in gluon-gluon fusion at NLO, JHEP 11 (2014) 079 [arXiv:1408.6542] [INSPIRE].

    ADS  Article  Google Scholar 

  59. B. Hespel, F. Maltoni and E. Vryonidou, Higgs and Z boson associated production via gluon fusion in the SM and the 2HDM, JHEP 06 (2015) 065 [arXiv:1503.01656] [INSPIRE].

    ADS  Article  Google Scholar 

  60. R. Gastmans and T.T. Wu, The ubiquitous photon: Helicity method for QED and QCD, International series of monographs on physics, 80, Clarendon, Oxford, U.K. (1990).

  61. S. Frixione, A next-to-leading order calculation of the cross-section for the production of W + W pairs in hadronic collisions, Nucl. Phys. B 410 (1993) 280 [INSPIRE].

    ADS  Article  Google Scholar 

  62. L.J. Dixon, L. Magnea and G.F. Sterman, Universal structure of subleading infrared poles in gauge theory amplitudes, JHEP 08 (2008) 022 [arXiv:0805.3515] [INSPIRE].

    ADS  Article  Google Scholar 

  63. G. Grammer Jr. and D.R. Yennie, Improved treatment for the infrared divergence problem in quantum electrodynamics, Phys. Rev. D 8 (1973) 4332 [INSPIRE].

    ADS  Google Scholar 

  64. C.D. White, Diagrammatic insights into next-to-soft corrections, Phys. Lett. B 737 (2014) 216 [arXiv:1406.7184] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  65. R. Hamberg, W.L. van Neerven and T. Matsuura, A complete calculation of the order α 2 s correction to the Drell-Yan K factor, Nucl. Phys. B 359 (1991) 343 [Erratum ibid. B 644 (2002) 403] [INSPIRE].

  66. S. Dawson, Radiative corrections to Higgs boson production, Nucl. Phys. B 359 (1991) 283 [INSPIRE].

    ADS  Article  Google Scholar 

  67. C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD, Nucl. Phys. B 646 (2002) 220 [hep-ph/0207004] [INSPIRE].

  68. R.V. Harlander and W.B. Kilgore, Next-to-next-to-leading order Higgs production at hadron colliders, Phys. Rev. Lett. 88 (2002) 201801 [hep-ph/0201206] [INSPIRE].

  69. V. Ravindran, J. Smith and W.L. van Neerven, NNLO corrections to the total cross-section for Higgs boson production in hadron hadron collisions, Nucl. Phys. B 665 (2003) 325 [hep-ph/0302135] [INSPIRE].

  70. 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].

  71. R.V. Harlander and K.J. Ozeren, Finite top mass effects for hadronic Higgs production at next-to-next-to-leading order, JHEP 11 (2009) 088 [arXiv:0909.3420] [INSPIRE].

    ADS  Article  Google Scholar 

  72. A. Pak, M. Rogal and M. Steinhauser, Finite top quark mass effects in NNLO Higgs boson production at LHC, JHEP 02 (2010) 025 [arXiv:0911.4662] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  73. B. Mele, P. Nason and G. Ridolfi, QCD radiative corrections to Z boson pair production in hadronic collisions, Nucl. Phys. B 357 (1991) 409 [INSPIRE].

    ADS  Article  Google Scholar 

  74. A. Lazopoulos, K. Melnikov and F. Petriello, QCD corrections to tri-boson production, Phys. Rev. D 76 (2007) 014001 [hep-ph/0703273] [INSPIRE].

  75. F. Campanario, V. Hankele, C. Oleari, S. Prestel and D. Zeppenfeld, QCD corrections to charged triple vector boson production with leptonic decay, Phys. Rev. D 78 (2008) 094012 [arXiv:0809.0790] [INSPIRE].

    ADS  Google Scholar 

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Del Duca, V., Laenen, E., Magnea, L. et al. Universality of next-to-leading power threshold effects for colourless final states in hadronic collisions. J. High Energ. Phys. 2017, 57 (2017). https://doi.org/10.1007/JHEP11(2017)057

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Keywords

  • NLO Computations
  • QCD Phenomenology