Theory Uncertainties in the Extraction of $\alpha_s$ from Drell-Yan at Small Transverse Momentum

TL;DR

This paper assesses the theoretical uncertainties in extracting the strong coupling constant from Drell-Yan transverse momentum data, introducing a new approach with theory nuisance parameters to improve accuracy and reliability.

Contribution

It introduces a novel method using theory nuisance parameters to better account for correlations in perturbative uncertainties during $oldsymbol{ ext{α}_s}$ extraction from Drell-Yan data.

Findings

Traditional scale variation methods are insufficient for this analysis.

The new TNP approach correctly encodes theory correlations.

Including nonperturbative effects and lattice QCD constraints can improve $oldsymbol{ ext{α}_s}$ precision.

Abstract

We perform a detailed pseudodata study to estimate the expected theory uncertainty in the extraction of the strong coupling constant, $\alpha_s(m_Z)$, from a fit to the measured Drell-Yan transverse momentum ($q_T$) spectrum at small $q_T \ll m_Z$. We consider two approaches to estimate the dominant perturbative uncertainties. We first discuss that the traditional approach based on varying unphysical scales is insufficient here because it cannot correctly account for bin-by-bin theory correlations in the $q_T$ spectrum, which are critically important in this case. We then use this case as a nontrivial application of a new approach based on theory nuisance parameters (TNPs), which encodes the correct theory correlations by construction. Moreover, the TNPs can be profiled in the fit thereby allowing the data to constrain the theory uncertainties in a consistent manner. We furthermore discuss the interplay with nonperturbative effects in the peak region $q_T \lesssim 10$ GeV, from where most of the $\alpha_s$ sensitivity originates. The associated nonperturbative uncertainties on $\alpha_s$ when fitting only the $q_T$ spectrum are large. They can in principle be reduced by including additional constraints on the nonperturbative Collins-Soper kernel from lattice QCD calculations. We find that these improvements in the treatment of perturbative and nonperturbative uncertainties and their correlations will enable a competitive $\alpha_s$ extraction from Drell-Yan data at small $q_T$. We also discuss the implications of our findings, calling into question a recent $\alpha_s$ extraction from the $Z$ $q_T$ spectrum by the ATLAS experiment.