Zero-jettiness beam functions at N$^3$LO

TL;DR

This paper discusses the ongoing calculation of zero-jettiness beam functions at N$^3$LO in QCD, which are crucial for precise predictions of color-singlet production at hadron colliders.

Contribution

It presents the first steps towards computing zero-jettiness beam functions at N$^3$LO, focusing on partial fraction relations and master integral calculations.

Findings

Advances in calculating N$^3$LO$ zero-jettiness$ beam functions.

Insights into partial fraction relations in high-order QCD calculations.

Progress on master integral evaluations for N$^3$LO$ processes.

Abstract

The zero-jettiness beam functions describe collinear emissions from initial state legs and appear in the factorisation theorem for cross sections in the limit of small zero-jettiness. They are an important building block for slicing schemes for colour-singlet production at hadron colliders. We report on our ongoing calculation of this quantity at next-to-next-to-next-to-leading order (N$^3$LO) in QCD, highlighting in particular the aspects of partial fraction relations and the calculation of master integrals.