Evaluating a family of two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence

Abstract

We present the analytic computation of a family of non-planar master integrals which contribute to the two-loop scattering amplitudes for Higgs plus one jet production, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to inclusive Higgs production and for the NLO corrections to Higgs production in association with a jet, in QCD. The computation of the integrals is performed with the method of differential equations. We provide a choice of basis for the polylogarithmic sectors, that puts the system of differential equations in canonical form. Solutions up to weight 2 are provided in terms of logarithms and dilogarithms, and 1-fold integral solutions are provided at weight 3 and 4. There are two elliptic sectors in the family, which are computed by solving their associated set of differential equations in terms of generalized power series. The resulting series may be truncated to obtain numerical results with high precision. The series solution renders the analytic continuation to the physical region straightforward. Moreover, we show how the series expansion method can be used to obtain accurate numerical results for all the master integrals of the family in all kinematic regions. arXiv:1907.13156v2 [hep-ph] 1 Aug 2019Contents P 3 = m 2 − (k 2 +p 1 +p 2 ) 2 , P 6 = m 2 − (k 1 −k 2 ) 2 , P 9 = m 2 − (k 1 −k 2 −p 1 −p 2 ) 2 .-3 -

Two-Loop QCD Corrections to the Higgs Plus Three-parton Amplitudes with Top Mass Correction

“…The cancellation of these unphyical poles links terms with different transcendetal degrees, and may be used to constrain the lower transcendentality parts of the amplitude from the higher transcendentality pieces. The analytical expressions of a subset of two-loop non-planar master integrals form Higgs to 3 parton amplitude with finite top quark was obtained recently [93] (which corresponding NLO order in the Higgs EFT expansion). These integrals contains elliptical sectors.…”

Rooting out letters: octagonal symbol alphabets and algebraic number theory

“…While previous forays have involved heuristic or numerical elements (e.g. [72,73]), our use of factorization in prime ideals should yield a more canonical and complete analysis of the relations between algebraic letters, and we believe similar methods should be applicable elsewhere.…”

The l-loop banana amplitude from GKZ systems and relative Calabi-Yau periods

“…Different proper selections of l-vectors should at the end yield the same results for the Feynman graph. 19 For l = 3 one can easily get all 2 6 star triangulations but for l = 4 there is an extremely large number of different star triangulations, which we have estimated to be 6 20 . Listing all of them cannot be done by a desktop computer.…”

“…Only for the two-loop amplitude the dependence on all three parameters has been calculated so far 8 in [18]. The knowledge of the general mass dependence is not only important from a conceptual point but it is also required in the computation of higher loop corrections to certain processes studied at the Large Hadron Collider, as for example in Higgs production processes [19]. It turned out that the integral is closely related to the period integral of the local mirror M of the non-compact Calabi-Yau three-fold W defined as total space of the anti-canonical line bundle over the degree three del Pezzo surface S, which is P 2 blown up in three generic points.…”