Abstract
We obtain analytic results for integrated triple-collinear splitting functions that emerge as collinear counter-terms in the context of the nested soft-collinear subtraction scheme [1]. With these results, all integrated subtraction terms required for NNLO QCD computations within this scheme are known analytically. In addition to improving efficiency and numerical stability of practical computations, the availability of these results will contribute towards establishing a general NNLO QCD subtraction formula for generic hard scattering processes in hadron collisions, similar to Catani-Seymour and FKS subtractions at NLO.
Highlights
An overview of the nested subtraction scheme and its modificationThe calculation of NNLO QCD corrections to any scattering process requires three ingredients — two-loop virtual corrections, one-loop virtual corrections to a process with an additional final-state parton and the double-real emission contribution
Amplitudes rather than to individual Feynman diagrams and if the subtraction of soft singularities is performed first
In addition to improving efficiency and numerical stability of practical computations, the availability of these results will contribute towards establishing a general NNLO QCD subtraction formula for generic hard scattering processes in hadron collisions, similar to Catani-Seymour and FKS subtractions at NLO
Summary
The calculation of NNLO QCD corrections to any scattering process requires three ingredients — two-loop virtual corrections, one-loop virtual corrections to a process with an additional final-state parton and the double-real emission contribution. Formally correct and practically stable, this procedure impacts properties of the unresolved phase space in a way that makes further analytic integrations very difficult To overcome this problem, it is useful to re-define the triple-collinear operators CC1,2, making them independent of the sector parametrization. It is easy to see that this reformulation leads to significant simplifications In this case, the triple-collinear subtraction term is integrated over the full unresolved phase-space of two gluons with additional constraint on the sum of their energies. The advantage in this procedure is that the integrand remains a rotationally invariant function in d−1 spatial dimensions. In the remaining sections of this paper, we will describe our computation in detail and present the results for the integrated collinear counter-terms for a variety of triple-collinear splitting functions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
