Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N$^3$LL

Markus A. Ebert; Johannes K. L. Michel; Iain W. Stewart; Frank J. Tackmann

Paper

Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N$^3$LL

Abstract

We consider Drell-Yan production

at small

. Experimental measurements require fiducial cuts on the leptonic state

, which introduce enhanced, linear power corrections in

. We show that they can be unambiguously predicted from factorization, and resummed to the same order as the leading-power contribution. We thus obtain predictions for the fiducial

spectrum to N3LL and next-to-leading-power in

. Matching to full NNLO (

), we find that the linear power corrections are indeed the dominant ones, and the remaining fixed-order corrections become almost negligible below

GeV. We also discuss the implications for more complicated observables, and provide predictions for the fiducial

spectrum at N3LL+NNLO. We find excellent agreement with ATLAS and CMS measurements of

and

. We also consider the

spectrum. We show that it develops leptonic power corrections in

, which diverge near the Jacobian peak

and must be kept to all powers to obtain a meaningful result there. Doing so, we obtain for the first time an analytically resummed result for the

spectrum around the Jacobian peak at N3LL+NNLO. Our method is based on performing a complete tensor decomposition for hadronic and leptonic tensors. In practice this is equivalent to often-used recoil prescriptions, for which our results now provide rigorous, formal justification. Our tensor decomposition yields nine Lorentz-scalar hadronic structure functions, which directly map onto the commonly used angular coefficients, but also holds for arbitrary leptonic final states. In particular, for suitably defined Born-projected leptons it still yields a LO-like angular decomposition even when including QED final-state radiation. We also discuss the application to

subtractions.