Double-real contribution to the quark beam function at N3LO QCD

Abstract

We compute the master integrals required for the calculation of the doublereal emission contributions to the matching coefficients of 0-jettiness beam functions at next-to-next-to-next-to-leading order in perturbative QCD. As an application, we combine these integrals and derive the double-real gluon emission contribution to the matching coefficient I qq (t, z) of the quark beam function.

Triple-real contribution to the quark beam function in QCD at next-to-next-to-next-to-leading order

“…We studied the double-real single-virtual contribution in Ref. [42] and the triple-real contribution in this paper. The so far unattended contribution is the singlereal double-virtual one; its computation will require us to understand how to compute a massless two-loop three-point function in an axial gauge.…”

“…Although such a computation appears to be quite challenging, we believe that it can be dealt with using calculational methods developed both in this paper and in Ref. [42].…”

“…We follow the discussion in Ref. [42], where the master integrals for the double-real single-virtual contribution to I qq were computed. We consider a massless quark with momentum p which emits three collinear gluons with momenta k i , i = 1, 2, 3, and enters the hard process with momentum p * q(p) → q * (p * ) + g(k 1 ) + g(k 2 ) + g(k 3 ) ,…”

“…In Ref. [42] we have considered similar phase-space integrals, albeit in a situation where one of the gluons was virtual and two were real. The double-virtual single-real master integrals in that paper were checked numerically using the Mellin-Barnes (MB) integration, following the discussion in Ref.…”

Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-Ncapproximation

“…In principle, the required computations are similar to what has already been done in Refs. [28,29] but, due to proliferation of integrals required for multi-quark final states, the calculations have not been finalized.…”