Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study

Understand

We calculate the strong isospin breaking and QED corrections to meson masses and the hadronic vacuum polarization in an exploratory study on a $64\times24^3$ lattice with an inverse lattice spacing of $a^{-1}=1.78$ GeV and an isospin symmetric pion mass of $m_\pi=340$ 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.