Double-Higgs boson production in the high-energy limit: planar master integrals

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 -

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

“…The use of differential equations solves this issue [29,31,32,34]. We use the differential equation with respect to m 2 t to obtain higher order corrections in m 2 t .…”

Section: Higher Order Terms In M Tmentioning

confidence: 99%

“…Concerning the Higgs+jet production cross section, the expansion in the small bottom quark mass m b m H [29,30] and in the small top quark and Higgs masses m t > m H [31] are performed. For the Higgs pair production cross section, the expansion in small m t for the planar master integrals [32] and in small Higgs transverse momentum [33] are performed. The rest of the master integrals of Higgs pair production in the small-m t expansion are obtained in Ref.…”

Section: Introductionmentioning

confidence: 99%

High-energy expansion of two-loop massive four-point diagrams

Mishima

2019

Self Cite

We apply the method of regions to the massive two-loop integrals appearing in the Higgs pair production cross section at the next-to-leading order, in the high energy limit. For the non-planar integrals, a subtle problem arises because of the indefinite sign of the second Symanzik polynomial. We solve this problem by performing an analytic continuation of the Mandelstam variables such that the second Symanzik polynomial has a definite sign. Furthermore, we formulate the procedure of applying the method of regions systematically. As a by-product of the analytic continuation of the Mandelstam variables, we obtain crossing relations between integrals in a simple and systematic way. In our formulation, a concept of "template integral" is introduced, which represents and controls the contribution of each region. All of the template integrals needed in the computation of the Higgs pair production at the next-to-leading order are given explicitly. We also develop techniques to solve Mellin-Barnes integrals, and show them in detail. Although most of the calculation is shown for the concrete example of the Higgs pair production process, the application to other similar processes is straightforward, and we anticipate that our method can be useful also for other cases.

“…On the other hand, 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. [60][61][62][63][64][65]). Therefore, in the multivariate case, it is desirable to study a systematic approach to obtain results in all points of the kinematic regions.…”

Section: Introductionmentioning

confidence: 99%

Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops

Moriello

2020

128

133

We obtain generalised power series expansions for a family of planar twoloop master integrals relevant for the QCD corrections to Higgs + jet production, with physical heavy-quark mass dependence. This is achieved by defining differential equations along contours connecting two fixed points, and by solving them in terms of one-dimensional generalised power series. The procedure is efficient and can be repeated in order to reach any