The $q_T$ subtraction method: electroweak corrections and power suppressed contributions

TL;DR

This paper applies the $q_T$ subtraction method to calculate electroweak corrections for Drell-Yan lepton pair production, analyzing power-suppressed contributions and their impact on the subtraction's efficiency.

Contribution

It presents the first application of the $q_T$ subtraction formalism to electroweak corrections and analytically computes leading power corrections from initial and final-state radiation.

Findings

Power correction from initial-state radiation is quadratic in $r_{cut}$.

Final-state radiation produces linear power corrections.

Linear corrections may affect the efficiency of the $q_T$ subtraction method.

Abstract

Building upon the formulation of transverse-momentum resummation for heavy-quark hadroproduction, we present the first application of the $q_T$ subtraction formalism to the computation of electroweak corrections to massive lepton pairs through the Drell-Yan mechanism. We then study the power suppressed contributions to the $q_T$ subtraction formula in the parameter $r_{cut}$, defined as the minimum transverse momentum of the lepton pair normalised to its invariant mass. We analytically compute the leading power correction from initial and final-state radiation to the inclusive cross section. In the case of initial-state radiation the power correction is quadratic in $r_{cut}$ and our analytic result is consistent with results previously obtained in the literature. Final-state radiation produces linear contributions in $r_{cut}$ that may challenge the efficiency of the $q_T$ subtraction procedure. We explicitly compute the linear power correction in the case of the inclusive cross section and we discuss the extension of our calculation to differential distributions.