The hadronic contribution to the running of the electroweak gauge couplings

TL;DR

This paper provides an improved lattice QCD calculation of the hadronic vacuum polarization contribution to the running of the electromagnetic coupling and electroweak mixing angle, enhancing precision for future collider tests.

Contribution

It introduces a refined analysis strategy and kernel functions that better separate Euclidean regions, reducing cutoff effects and chiral dependence in lattice calculations.

Findings

Achieved significantly enhanced precision over previous results.

Converted lattice data into an ab initio estimate of eltalpha_{ ext{had}}^{(5)}(M_Z^2).

Compared results with other lattice and phenomenological determinations.

Abstract

We present an updated determination of the hadronic vacuum polarization contribution to the running of the electromagnetic coupling $\Delta\alpha_{\mathrm{had}}^{(5)}(-Q^2)$, and of the electroweak mixing angle in the space-like momentum range up to $12 \ \mathrm{GeV}^2$. Using $N_f=2+1$ CLS ensembles at five values of the lattice spacing and several pion masses, including the physical point, we achieve a significantly enhanced precision over our previous result. A refined analysis strategy based on telescopic series and a new family of kernel functions enables a clean separation of distinct Euclidean regions, disentangling strong cutoff effects at short distances from the pronounced chiral dependence at larger ones. Employing the Euclidean split technique, we convert our lattice results into an ab initio estimate of $\Delta\alpha_{\mathrm{had}}^{(5)}(M_Z^2)$. A comparison with results from other lattice calculations and phenomenology is performed. We also analyze improvement scenarios required to match the projected precision of future electroweak measurements at next-generation colliders.