Abstract
A method for calculating phase-space master integrals for the decay process $1 \to n$ massless partons in QCD using integration-by-parts and differential equations techniques is discussed. The method is based on the appropriate choice of the basis for master integrals which leads to significant simplification of differential equations. We describe an algorithm how to construct the desirable basis, so that the resulting system of differential equations can be recursively solved in terms of (G)HPLs as a series in the dimensional regulator $\epsilon$ to any order. We demonstrate its power by calculating master integrals for the NLO time-like splitting functions and discuss future applications of the proposed method at the NNLO precision.
Highlights
A must-have piece for numerical calculations of N3LO contributions to the three-jet rate from the γ∗ → 6 partons process
The method is based on the appropriate choice of the basis for master integrals which leads to significant simplification of differential equations
In this paper we proposed a method for calculating phase-space integrals for the decay process 1 → n massless partons in QCD using integration-by-parts and differential equations techniques
Summary
Let us briefly review the main facts on splitting functions in the collinear factorization formalism of QCD, mainly for notation consistency. The scale dependence of the fragmentation distributions is controlled by the so-called time-like splitting functions PbTa(x), and is given by d d ln q2. For the demonstration of the method for calculating master integrals described in detail, let us consider the time-like q → g splitting function at NLO. Where M (3) and M (4) are amplitudes for the processes depicted in figures 1(a) and 1(b) respectively, l is a loop momentum, and dPS(n) denotes a n-particle phase-space integral dPS(n) =. Find master integrals solving differential equations in x-space as described
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