Higher-order QCD corrections to triple collinear splitting functions

TL;DR

This paper computes next-to-leading order triple collinear splitting functions in massless QCD+QED, providing compact results for photon-involving processes and confirming the IR divergence structure aligns with established theoretical predictions.

Contribution

It introduces the first NLO triple collinear splitting functions in massless QCD+QED, including photon processes, with simplified expressions and consistency checks.

Findings

IR divergence structure matches Catani's formula

Compact expressions for photon-involved splitting functions

Cross-checked results with symmetry considerations

Abstract

We present splitting functions in the triple collinear limit at next-to-leading order in the strong coupling. We performed the computation in the context of massless QCD+QED, and consider first collinear processes which include at least one photon. The IR divergent structure of the multi-partonic splitting functions agrees with the Catani's formula. Consistency checks based on symmetry arguments have been implemented and results for different configurations have been cross-checked. Studying photon-started processes, we obtained very compact results: this allowed us to simplify the expressions for the remaining splitting functions.