The Quark Beam Function at NNLL

TL;DR

This paper develops a field-theoretic framework for quark beam functions at NNLL order, enabling more precise descriptions of initial states in hadron collider processes with specific final state measurements.

Contribution

It introduces a detailed derivation of the quark beam function's one-loop matching onto PDFs and provides the NNLL resummed Drell-Yan cross section expression.

Findings

Derived the one-loop matching of quark beam functions onto PDFs.

Computed NLO Wilson coefficients and verified IR cancellation.

Presented the NNLL resummed Drell-Yan beam thrust cross section.

Abstract

In hard collisions at a hadron collider the most appropriate description of the initial state depends on what is measured in the final state. Parton distribution functions (PDFs) evolved to the hard collision scale Q are appropriate for inclusive observables, but not for measurements with a specific number of hard jets, leptons, and photons. Here the incoming protons are probed and lose their identity to an incoming jet at a scale \mu_B << Q, and the initial state is described by universal beam functions. We discuss the field-theoretic treatment of beam functions, and show that the beam function has the same RG evolution as the jet function to all orders in perturbation theory. In contrast to PDF evolution, the beam function evolution does not mix quarks and gluons and changes the virtuality of the colliding parton at fixed momentum fraction. At \mu_B, the incoming jet can be described perturbatively, and we give a detailed derivation of the one-loop matching of the quark beam function onto quark and gluon PDFs. We compute the associated NLO Wilson coefficients and explicitly verify the cancellation of IR singularities. As an application, we give an expression for the next-to-next-to-leading logarithmic order (NNLL) resummed Drell-Yan beam thrust cross section.