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

By R. Bonciani, V. Duca, Hjalte Frellesvig, J. Henn, F. Moriello, Vladimir A. Smirnov. 2016

145 citations recorded by the source corpus.

A bstractWe 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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e6ead90afc2e2c58149d8e2cc211960371bbd146

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In Nuclear and High Energy Physics

Citations in the corpus

Collider physics at the precision frontier (2020, background): “henomenological applications of elliptic integrals are the analytic results for the complete set of 2-loop master integrals entering Higgs+jet 50 production at NLO with full top quark mass dependence [631, 161, 632, 94], the three-loop corrections to the ˆparameter with non-vanishing b-quark mass [6”
On the maximal cut of Feynman integrals and the solution of their differential equations (2016, background): “mogeneous equation for = 0 can be rather simply obtained from the maximal cut of the integral evaluated in d= 4. We will work out explicitly dierent examples, including the double box considered in [18]. While this will allow us to produce equivalent results, we believe that our approach has an inte”
Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, background): “This continues the study from Les Houches 2015, where good agreement was shown between fixed order and parton shower Monte Carlo predictions (for non-Sudakov observables) for Higgs+jets production with one value of R (0.4).”
Decomposition of Feynman integrals on the maximal cut by intersection numbers (2019, background): “In this section we discuss planar seven-propagator integrals contributing to Higgs+jet (H+j) production [47, 111, 112] and double Higgs (HH) production [44, 45], portrayed in Fig.”
Cuts of Feynman Integrals in Baikov representation (2017, background): “when for instance enough internal masses are introduced, MI are not anymore expressible in terms of GPs, and in fact a new class of functions involving elliptic integrals is needed [60, 61, 62, 63, 64].”
Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism (2017, background): “Our paper is not the first to consider elliptic generalisations of MPLs [12, 15, 17, 18, 22, 29, 39, 42, 43] or iterated integrals over integration kernels that involve square roots of polynomials of degree greater than two [44] have been considered.”
Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series (2018, unknown): “[40, 57], and the latter satisfy a set of coupled homogeneous first order differential equations, ∂λK(λ) = − 1 2λ K(λ) + 1 2λ(1 − λ) E(λ) , ∂λE(λ) = − 1 2λ K(λ) + 1 2λ E(λ) , (4.”