Precise predictions for the angular coefficients in Z-boson production at the LHC

TL;DR

This paper provides precise theoretical predictions for angular coefficients in Z-boson production at the LHC, addressing recent experimental anomalies and proposing new observables to better understand QCD dynamics.

Contribution

It performs a next-to-next-to-leading order QCD calculation of angular coefficients, improving agreement with experimental data and introducing a new observable for testing the Lam-Tung relation.

Findings

N3LO corrections significantly impact angular coefficient distributions.

The new observable $ riangle^{LT}$ enhances sensitivity to Lam-Tung violation.

Theoretical predictions align better with ATLAS and CMS data at N3LO.

Abstract

The angular distributions of lepton pairs in the Drell-Yan process can provide rich information on the underlying QCD production mechanisms. These dynamics can be parameterised in terms of a set of frame dependent angular coefficients, $A_{i=0,\ldots,7}$, which depend on the invariant mass, transverse momentum, and rapidity of the lepton pair. Motivated by recent measurements of these coefficients by ATLAS and CMS, and in particular by the apparent violation of the Lam-Tung relation $A_0-A_2=0$, we perform a precision study of the angular coefficients at $\mathcal{O}(\alpha_s^3)$ in perturbative QCD. We make predictions relevant for $pp$ collisions at $\sqrt{s} = 8$ TeV, and perform comparisons with the available ATLAS and CMS data as well as providing predictions for a prospective measurement at LHCb. To expose the violation of the Lam-Tung relationship we propose a new observable $\Delta^\mathrm{LT} = 1-A_2/A_0$ that is more sensitive to the dynamics in the region where $A_0$ and $A_2$ are both small. We find that the $\mathcal{O}(\alpha_s^3)$ corrections have an important impact on the $p_{T,Z}$ distributions for several of the angular coefficients, and are essential to provide an adequate description of the data. The compatibility of the available ATLAS and CMS data is reassessed by performing a partial $\chi^2$ test with respect to the central theoretical prediction which shows that $\chi^2/N_\mathrm{data}$ is significantly reduced by going from $\mathcal{O}(\alpha_s^2)$ to $\mathcal{O}(\alpha_s^3)$.