The hadronic contribution to the running of the electromagnetic coupling and the electroweak mixing angle

TL;DR

This paper presents a lattice QCD study of the hadronic contributions to the running of the electromagnetic coupling and the electroweak mixing angle, reducing uncertainties in Standard Model precision tests.

Contribution

It introduces a lattice computation of the leading hadronic effects on the running of key electroweak parameters using the time-momentum representation method with $N_{f}=2+1$ Wilson fermions.

Findings

Computed hadronic vacuum polarization contributions on multiple lattice ensembles.

Performed reliable extrapolation to physical quark masses and continuum limit.

Provides improved estimates of hadronic effects on electroweak parameters.

Abstract

The electromagnetic coupling $\alpha$ and the electroweak mixing angle $\theta_{\mathrm{W}}$ are parameters of the Standard Model (SM) that enter precision SM tests and play a fundamental r\^ole in beyond SM physics searches. Their values are energy dependent, and non-perturbative hadronic contributions are the main source of uncertainty to the theoretical knowledge of the running with energy. We present a lattice study of the leading hadronic contribution to the running of $\alpha$ and $\sin^2\theta_{\mathrm{W}}$. The former is related to the hadronic vacuum polarization (HVP) function of electromagnetic currents, and the latter to the HVP mixing of the electromagnetic current with the vector part of the weak neutral currents. We use the time-momentum representation (TMR) method to compute the HVP on the lattice, estimating both connected and disconnected contributions on $N_{\mathrm{f}}=2+1$ non-perturbatively $O(a)$-improved Wilson fermions ensembles from the Coordinated Lattice Simulations (CLS) initiative. The use of different lattice spacings and quark masses allows us to reliably extrapolate the results to the physical point.