NNLO phase space master integrals for two-to-one inclusive cross sections in dimensional regularization

Abstract

We evaluate all phase space master integrals which are required for the total cross section of generic 2 → 1 processes at NNLO as a series expansion in the dimensional regulator ǫ. Away from the limit of threshold production, our expansion includes one order higher than what has been available in the literature. At threshold, we provide expressions which are valid to all orders in terms of Γ functions and hypergeometric functions. These results are a necessary ingredient for the renormalization and mass factorization of singularities in 2 → 1 inclusive cross sections at N 3 LO in QCD.

MT: A Mathematica package to compute convolutions

“…The NNLO master integrals are taken from Ref. [10] (see also [30]) which guarantees that the final result is available including O(ǫ) terms.…”

Towards Higgs production at N3LO

“…These contributions, together with the knowledge of the three-loop Wilson coefficient [2], beta function [17] and splitting functions [18] (as well as the lower order cross sections to higher order in the dimensional regulator ε [19]), are sufficient to obtain the full result for the gluon-fusion cross section at N 3 LO in the soft-virtual approximation. Adding all the contributions together, all the poles in dimensional regularisation cancel.…”

Scale dependence and collinear subtraction terms for Higgs production in gluon fusion at N3LO

“…The double-virtual master integrals can be found in work on the two-loop gluon form factor [48][49][50]. The real-virtual and double-real master integrals were computed by two groups independently during the last year [39,40]. The expression for the bare NNLO cross section in terms of master integrals was kindly provided to us by an author of [11].…”

“…In [39,40], the real-virtual and double-real master integrals of the NNLO cross section have been calculated to higher orders in ǫ. In [41], the convolutions of collinear splitting kernels with lower-order partonic cross sections have been computed, which is also an ingredient for our result and has been re-derived in this work.…”