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.
Highlights
We provide a choice of basis for the polylogarithmic sectors, that puts the system of differential equations in canonical form
Leading-order production requires the evaluation of one-loop amplitudes, the next-to-leading order (NLO) QCD corrections involve the evaluation of two-loop amplitudes, and so on
For Higgs production in association with one jet or for the Higgs pT distribution one can show that the Higgs Effective Field Theory (HEFT) can be applied when the Higgs mass is smaller than the heavy-quark mass, mH mQ, and when the jet or Higgs transverse momenta are smaller than the heavy-quark mass, pT mQ [24, 25], by using the leading-order results [18, 19] as a benchmark
Summary
P1-P7 are propagators while P8 and P9 are numerator factors, so a8 and a9 are restricted to non-positive integers. The kinematics is such that p21 = p22 = p23 = 0, and s = (p1+p2), t = (p1+p3), u = (p2+p3), p24 = (p1+p2+p3)2 = s+t+u. It is shown in appendix C that the maximal cuts associated to integral sectors 126 and 127 are elliptic integrals. We refer to these sectors as the elliptic sectors, while the remaining sectors will be referred to as the polylogarithmic sectors. To obtain closed form systems of differential equations for the master integrals, we have to perform IBP-reductions, for which we used the programs FIRE [32,33,34,35] and Kira [36, 37]
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