Lattice Seminar

# Leading isospin breaking effects in the HVP contribution to $a_{\mu}$ and to the running of $\alpha_{\mathrm{em}}$

## by Andreas Risch (Z_ZPPT (Zeuthen Particle PhysicsTheory))

Europe/Berlin
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Description

The anomalous magnetic moment of the muon $a_{\mu}$ and the running of the electromagnetic coupling $\alpha_{\mathrm{em}}$ play a fundamental role in beyond Standard Model (SM) physics searches. Non-perturbative hadronic contributions to both quantities, which are related to the hadronic vacuum polarisation (HVP) function consisting of two electromagnetic quark currents, are a main source of uncertainty in their SM predictions. I will introduce the setup used to perform lattice QCD+QED computations based on $N_{\mathrm{f}}=2+1$ QCD$_{\mathrm{iso}}$ gauge ensembles generated by the CLS initiative with non-perturbatively $O(a)$-improved Wilson fermions and on a leading order perturbative expansion around the isosymmetric limit. I will discuss the hadronic renormalisation scheme suitable for QCD+QED and provide an insight into the methods applied to evaluate the quark-connected contributions of the relevant correlation functions. The renormalisation procedure of the local vector current in QCD+QED, relevant for the renormalised HVP function, will be introduced. The renormalised HVP function is then computed applying the time-momentum representation method from which leading isospin breaking effects in the HVP contribution to $a_{\mu}$ and to the running of $\alpha_{\mathrm{em}}$ are derived.