Probing the weak mixing angle at high energy

TL;DR

This paper proposes using high-energy Drell-Yan measurements at the LHC to determine the energy dependence of the weak mixing angle, testing Standard Model predictions and constraining new physics at TeV scales.

Contribution

It introduces a method to measure the running of the weak mixing angle at high energies using LHC data, with an implementation in the POWHEG-BOX Monte Carlo generator.

Findings

Potential to test Standard Model predictions at TeV scales.

Assessment of higher order correction impacts.

Evaluation of uncertainties from parton distribution functions.

Abstract

The weak mixing angle is a probe of the vector-axial coupling structure of electroweak interactions. It has been measured precisely at the $Z$-pole by experiments at the LEP and SLD colliders, but its energy dependence above $M_Z$ remains unconstrained. In this contribution we propose to exploit measurements of Neutral-Current Drell Yan at large invariant dilepton masses at the Large Hadron Collider, to determine the scale dependence of the weak mixing angle in the $\overline{MS}$ renormalisation scheme, $\sin^2 \theta_w^{\overline{MS}}(\mu)$. Such a measurement can be used to test the Standard Model predictions for the $\overline{MS}$ running at TeV scales, and to set model-independent constraints on new states with electroweak quantum numbers. To this end, we present an implementation of $\sin^2 \theta_w^{\overline{MS}}(\mu)$ in the POWHEG-BOX Monte Carlo event generator, which we use to explore the potential of future analyses with the LHC Run~3 and High-Luminosity datasets. In particular, the impact of the higher order corrections and of the uncertainties due to the knowledge of parton distribution functions are studied.