Leading isospin breaking effects in the HVP contribution to $a_μ$ and to the running of $α$

Abstract

The anomalous magnetic moment of the muon 𝑎 𝜇 and the running of the electromagnetic coupling 𝛼 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 polarization (HVP) function consisting of two electromagnetic currents, are a main source of uncertainty in the SM prediction. We compute the HVP function in lattice QCD+QED applying the timemomentum representation method. We expand the relevant correlation functions around the isosymmetric limit. In particular, we focus on leading isospin breaking effects taking quarkconnected contributions into account, which we evaluate on isosymmetric 𝑁 f = 2 + 1 QCD gauge ensembles generated by the CLS initiative with non-perturbatively 𝑂 (𝑎)-improved Wilson fermions.

The hadronic running of the electromagnetic coupling and the electroweak mixing angle from lattice QCD

“…Since the renormalization procedure of the local vector current in our QCD+QED computation [ 121 , 122 ] differs from the purely isosymmetric QCD calculation [ 65 ] we determine the relative correction by isospin breaking in the QCD+QED setup. We observe that the size of the relative first-order corrections for Πγγ [ 121 ] and ΠZγ is largest on D450. To rate the systematic error of disregarding isospin-breaking corrections, which is added to the error budget of the final result, we multiply the obtained relative correction on D450 by the final results obtained from the isosymmetric QCD calculation.…”

“…These conditions are compatible with the definition of the "physical" point of isosymmetric QCD in Section 4 . We extend this scheme by the corresponding proxy for the light quark mass splitting [ 121 ] and set it to its physical value. As we consider leading-order effects, the electromagnetic coupling does not renormalize and, hence, is fixed via the fine-structure constant e 2 = 4πα [ 119 ].…”

HVP contribution to Running Coupling and Electroweak Precision Science

“…Our gauge configurations do not include isospin breaking (IB) effects (up/down quark mass difference and QED interaction). We have perturbatively estimated them based on QED approach [11] using some of our ensembles [12] and taken account the result into one of systematic errors.…”

Hadronic vacuum polarization with C* boundary conditions

“…To determine the vector mass and amplitude in Eq. (10) we select a fit range and a cutoff 𝑥 0,cut . We estimate the error due to that choice by varying the cutoff and the fit range around our chosen value.…”

“…[1] for an overview) at the isospin-symmetric point, the systematic uncertainty due to neglecting isospinbreaking effects becomes crucial. Several collaborations have started to take these effects into account for the anomalous magnetic moment [4][5][6][7][8][9][10].…”