Leading isospin breaking effects in the hadronic vacuum polarisation with open boundaries

TL;DR

This paper investigates the leading isospin breaking effects in the hadronic vacuum polarization relevant for the muon g-2, using lattice QCD with open boundaries and including quark-disconnected diagrams.

Contribution

It introduces a detailed lattice QCD calculation of isospin breaking effects in the hadronic vacuum polarization, emphasizing the treatment of quark-disconnected diagrams and vector current renormalization.

Findings

Quantitative estimates of isospin breaking effects in the hadronic vacuum polarization.

Methodology for including quark-disconnected diagrams in such calculations.

Analysis of vector current renormalization in QCD+QED.

Abstract

We discuss leading isospin breaking effects in the hadronic vacuum polarisation required for the investigation of the hadronic contribution to $(g-2)_{\mu}$. The calculation proceeds by expanding the relevant correlation functions around the isosymmetric limit. Isosymmetric observables are evaluated on gauge ensembles with $N_{f}=2+1$, $O(a)$ improved Wilson fermions and open boundary conditions generated by the CLS effort. Particular emphasis is placed on the relevant quark-disconnected diagrams required for a complete treatment of leading isospin breaking effects in the valence quark sector. We provide a detailed discussion of the renormalisation of the vector current in QCD+QED taking operator mixing into account.