A massive variable flavour number scheme for the Drell-Yan process

TL;DR

This paper introduces a novel variable flavour number scheme for the Drell-Yan process that combines massive and massless approaches, improving the accuracy of differential cross-section predictions at the LHC.

Contribution

A new method to isolate and combine power corrections involving heavy-quark masses with massless computations for better Drell-Yan process predictions.

Findings

Validated the scheme with LHCb data for lepton pair distributions.

Recovered the massless N³LO coefficient from the massive scheme.

Provided differential predictions for the Drell-Yan process.

Abstract

The prediction of differential cross-sections in hadron-hadron scattering processes is typically performed in a scheme where the heavy-flavour quarks ($c, b, t$) are treated either as massless or massive partons. In this work, a method to describe the production of colour-singlet processes which combines these two approaches is presented. The core idea is that the contribution from power corrections involving the heavy-quark mass can be numerically isolated from the rest of the massive computation. These power corrections can then be combined with a massless computation (where they are absent), enabling the construction of differential cross-section predictions in a massive variable flavour number scheme. As an example, the procedure is applied to the low-mass Drell-Yan process within the LHCb fiducial region, where predictions for the rapidity and transverse-momentum distributions of the lepton pair are provided. To validate the procedure, it is shown how the $n_f$-dependent coefficient of a massless computation can be recovered from the massless limit of the massive one. This feature is also used to differentially extract the massless $\text{N}^3\text{LO}$ coefficient of the Drell-Yan process in the gluon-fusion channel.