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

## TL;DR

This paper calculates complex three-loop integrals essential for advancing the precision of quark beam function predictions in QCD at N$^3$LO, focusing on the triple-real emission process.

## Contribution

It provides the first computation of three-loop master integrals for the triple-real contribution to the quark beam function at N$^3$LO in QCD.

## Key findings

- Computed three-loop master integrals for triple-real emission
- Enabled next-to-next-to-next-to-leading order (N$^3$LO) calculations of the quark beam function
- Contributed to precision QCD predictions for collider physics

## Abstract

We compute the three-loop master integrals required for the calculation of the triple-real contribution to the N$^3$LO quark beam function due to the splitting of a quark into a virtual quark and three collinear gluons, $q \to q^*+ggg$. This provides an important ingredient for the calculation of the leading-color contribution to the quark beam function at N$^3$LO.