Abstract
We calculate the strong isospin breaking and QED corrections to meson masses and the hadronic vacuum polarization in an exploratory study on a 64 × 243 lattice with an inverse lattice spacing of a−1 = 1.78 GeV and an isospin symmetric pion mass of mπ = 340 MeV. We include QED in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. We find that the electromagnetic correction to the leading hadronic contribution to the anomalous magnetic moment of the muon is smaller than 1% for the up quark and 0.1% for the strange quark, although it should be noted that this is obtained using unphysical light quark masses. In addition to the results themselves, we compare the precision which can be reached for the same computational cost using each method. Such a comparison is also made for the meson electromagnetic mass-splittings.
Highlights
In recent years, lattice QCD has made remarkable progress in calculating quantities relevant to Standard Model phenomenology
We find that the electromagnetic correction to the leading hadronic contribution to the anomalous magnetic moment of the muon is smaller than 1% for the up quark and 0.1% for the strange quark, it should be noted that this is obtained using unphysical light quark masses
We find the correlated difference between both datasets to be non-zero at the level of ≈ 1.5σ and of the order of 1% of the QED correction itself, which can be attributed to O(α2) effects
Summary
Since the electromagnetic coupling α is small in the low-energy regime, QED can be treated perturbatively. The photon propagator in the Coulomb gauge is given in the appendix in equation (D.2). For mesonic two-point functions one obtains from equation (2.16) at leading order in α three different types of quark-connected Wick contractions: a photon exchange diagram, a quark self-energy diagram and a tadpole diagram. These diagrams are shown in figure 1. We neglect diagrams that correspond to photons coupling to sea quarks. In the perturbative method working in unquenched QED is possible by calculating the appropriate quark-disconnected diagrams. For the stochastic method unquenched QED requires the generation of combined QCD+QED gauge configurations at substantial extra cost
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