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Journal of High Energy Physics

, 2016:96 | Cite as

Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence

  • Roberto Bonciani
  • Vittorio Del Duca
  • Hjalte Frellesvig
  • Johannes M. Henn
  • Francesco MorielloEmail author
  • Vladimir A. Smirnov
Open Access
Regular Article - Theoretical Physics

Abstract

We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs→ 3 partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to fully inclusive Higgs production and to the NLO corrections to Higgs production in association with a jet, in the full theory. The computation is performed using the differential equations method. Whenever possible, a basis of master integrals that are pure functions of uniform weight is used. The result is expressed in terms of one-fold integrals of polylogarithms and elementary functions up to transcendental weight four. Two integral sectors are expressed in terms of elliptic integrals. We show that by introducing a one-dimensional parametrization of the integrals the relevant second order differential equation can be readily solved, and the solution can be expressed to all orders of the dimensional regularization parameter in terms of iterated integrals over elliptic kernels. We express the result for the elliptic sectors in terms of two and three-fold iterated integrals, which we find suitable for numerical evaluations. This is the first time that four-point multiscale Feynman integrals have been computed in a fully analytic way in terms of elliptic integrals.

Keywords

Perturbative QCD Scattering Amplitudes 

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.

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Roberto Bonciani
    • 1
    • 2
  • Vittorio Del Duca
    • 3
    • 4
  • Hjalte Frellesvig
    • 5
  • Johannes M. Henn
    • 6
  • Francesco Moriello
    • 1
    • 2
    • 3
    Email author
  • Vladimir A. Smirnov
    • 7
  1. 1.Dipartimento di Fisica, Sapienza — Università di RomaRomeItaly
  2. 2.INFN Sezione di RomaRomeItaly
  3. 3.ETH Zurich, Institut fur theoretische PhysikZurichSwitzerland
  4. 4.INFN Laboratori Nazionali di FrascatiFrascati, RomaItaly
  5. 5.Institute of Nuclear and Particle Physics, NCSR DemokritosAgia ParaskeviGreece
  6. 6.PRISMA Cluster of Excellence, Johannes Gutenberg UniversityMainzGermany
  7. 7.Skobeltsyn Inst. of Nuclear Physics of Moscow State UniversityMoscowRussia

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