A numerical routine for the crossed vertex diagram with a massive-particle loop

Self Cite

We compute the next-to-leading virtual QCD corrections to the partonic cross section of the production of a Higgs boson in association with a Z boson in gluon fusion. The calculation is based on the recently introduced method of evaluating the amplitude via an expansion in terms of a small transverse momentum. We generalize the method to the case of different masses in the final state and of a process not symmetric in the forward-backward direction exchange. Our analytic approach gives a very good approximation (better than percent) of the partonic cross section in the center of mass energy region up to ∼ 750 GeV, where at the LHC ∼ 98% of the total hadronic cross section is concentrated.

Section: Outline Of the Nlo Computationsupporting

confidence: 60%

Virtual corrections to gg → ZH via a transverse momentum expansion

Alasfar

Degrassi

Giardino

et al. 2021

Self Cite

“…For an application of series expansion methods to single scale integrals see e.g. [76,[85][86][87][88][89][90]. For integrals depending on several scales, multivariate series expansions have been used for special kinematic configurations (typically small or large energy limits, see e.g.…”

Section: Series Solution Of the Differential Equationsmentioning

confidence: 99%

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

Bonciani

Duca

Frellesvig

et al. 2020

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 -

“…We consider the series expansion strategy outlined in [2,3] (see also [11,[85][86][87][88][89][90] for the application of expansion methods to single scale processes, and [91][92][93][94][95][96] for expansion methods applied to multiscale problems in particular kinematic limits). The strategy relies on parametrizing the integrals along straight line segments, for which we solve the corresponding differential equations in terms of one-dimensional generalized series.…”

Section: Series Expansion Along Contoursmentioning

confidence: 99%

The complete set of two-loop master integrals for Higgs + jet production in QCD

Frellesvig

Hidding

Maestri

et al. 2020

In this paper we complete the computation of the two-loop master integrals relevant for Higgs plus one jet production initiated in [1-3]. Specifically, we compute the remaining family of non-planar master integrals. The computation is performed by defining differential equations along contours in the kinematic space, and by solving them in terms of one-dimensional generalized power series. This method allows for the efficient evaluation of the integrals in all kinematic regions, with high numerical precision. We show the generality of our approach by considering both the top-and the bottom-quark contributions. This work along with [1-3] provides the full set of master integrals relevant for the NLO corrections to Higgs plus one jet production, and for the real-virtual contributions to the NNLO corrections to inclusive Higgs production in QCD in the full theory.