Rapidity renormalized TMD soft and beam functions at two loops

TL;DR

This paper calculates the TMD soft and beam functions at two loops within the rapidity renormalization group framework, enabling more precise predictions of transverse momentum distributions at the LHC.

Contribution

It provides the first NNLO computation of TMD soft and beam functions in the RRG scheme, including recurrence relations and verification of non-Abelian exponentiation.

Findings

Computed TMD soft function at NNLO in RRG framework.

Extracted universal TMD beam functions at the same order.

Confirmed non-Abelian exponentiation at two loops.

Abstract

We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of pT-differential cross sections at NNLL' in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and to assess the associated perturbative uncertainties.