Automated Calculation of Beam Functions at NNLO

TL;DR

This paper introduces an automated computational framework for calculating beam functions at NNLO, enabling precise predictions of initial-state radiation effects in collider physics.

Contribution

It provides a novel automated method for NNLO beam function calculations applicable to various collider observables, validated against known analytical results.

Findings

Accurate numerical computation of quark beam functions at NNLO.

Excellent agreement with known analytical results for transverse-momentum resummation and N-jettiness.

Framework applicable to a broad class of collider observables.

Abstract

We present an automated framework for the calculation of beam functions that describe collinear initial-state radiation at hadron colliders at next-to-next-to leading order (NNLO) in perturbation theory. By exploiting the infrared behaviour of the collinear matrix elements, we factorise the phase-space singularities with suitable observable-independent parametrisations. Our numerical approach applies to a large class of collider observables, and as a check of its validity, we compute the quark beam functions for transverse-momentum resummation and N-jettiness, which are known analytically at this order, finding excellent agreement.