Isospin breaking corrections to the hadronic vacuum polarization with stochastic coordinate sampling

Abstract

In the recent Muon g-2 Theory Initiative white paper update, the hadronic vacuum polarization (HVP) contribution -- which dominates the theoretical uncertainty -- is evaluated as an average of different lattice QCD calculations. Since lattice simulations are mostly carried out in isospin symmetric QCD, corrections due to the mass difference of the up and down quarks and the coupling to photons have to be accounted for. These isospin breaking effects are of order 1\% and can be treated as corrections to the result for the HVP contribution in isospin symmetric QCD. In the current estimate of the HVP contribution, these effects are a large source of uncertainty due to the extensive computational cost to compute all occurring Wick contractions and degrading signal-to-noise behaviour especially for quark disconnected diagrams. We present the current status of the calculation of isospin breaking corrections in the HVP contribution for the RBC/UKQCD collaborations. We use a dataset of propagators computed using stochastic coordinate sampling (SCS) to construct all necessary Wick contractions for the electromagnetic and strong isospin breaking effects. We employ different versions of QED on the lattice, such as QED$_L$, QED$_r$ and QED$_\infty$ to improve our estimate of finite-volume uncertainties.

Figures (4)

• Figure 1: QED corrections to the HVP contribution, taken from Ref. Gulpers:2018mim. Gluons are not depicted, so that for example all quark- disconnected diagrams are connected by gluons.
• Figure 2: Strong isospin breaking diagrams, taken from Ref. Gulpers:2018mim
• Figure 3: Integrands for several diagrams, contributing to Eq. \ref{['eq:G1gamma_star']}. For each plot, we normalize the y-axis by the value of the peak of the contribution from the diagram (V) in QED$_L$ on the ensemble 4.
• Figure 4: (a): Integrand for the SIB diagrams. The y-axis is normalized to the absolute height of the peak of diagram M. (b): Correlator ratios for the diagrams (V), (S), (T), and (M) contributing to $\Delta(m_{K^0}-m_{K^\pm})$ on the ensemble 48I.