Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation

TL;DR

This paper computes the quark beam function matching coefficient at N$^3$LO in perturbative QCD within a generalized large-$N_c$ approximation, advancing the precision of theoretical predictions for collider processes.

Contribution

It provides the first N$^3$LO calculation of the quark beam function in the generalized large-$N_c$ limit, a key step toward fully differential collider predictions.

Findings

N$^3$LO matching coefficient computed in the large-$N_c$ limit.

Shows potential for N$^3$LO fully differential predictions at colliders.

Highlights need for further refinements for phenomenological use.

Abstract

We present the matching coefficient for the quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large $N_c$-approximation, $N_c \sim N_f \gg 1$. Although several refinements are still needed to make this result interesting for phenomenological applications, our computation shows that a fully-differential description of simple color singlet production processes at a hadron collider at N$^3$LO in perturbative QCD is within reach.