Effects of isospin symmetry breaking in light mesons and application to the anomalous magnetic moment of the muon

Abstract

In this work, we investigate the effect of a modified QCD/QED model for a functional DSE/BSE framework. The applied model lifts the current quark mass degeneracy and in a second step includes charge dependency to the calculation of quark propagator, meson mass and amplitudes and the quark-photon vertex. We confirmed that the expected dominance of electromagnetic corrections to the pion mass splitting is uphold in the DSE/BSE framework. Even with a maximum value for a quark current mass splitting of delta mq = 6.6 MeV, the observed pion masses varied only by a value of Mpi_pm - Mpi_0 = 0.2 MeV which can be considered to be in a range of numerical uncertainty.The truncation of the quark-photon vertex, used to implement QED corrections, models a 1BC-like vertex with additional strengthening factor. This treatment allowed us to find a quark mass set of m_u = 2.45 MeV, m_d = 4.61 MeV and m_s = 84.88 MeV which reproduces physical masses for Mpi_pm, Mpi_0, MK_pm and MK_0 simultaneously.The first results using the model is the hadronic vacuum polarization (HVP) as a part of the anomalous magnetic moments of muon and tau. For the hadronic vacuum polarization part of the muon anomalous magnetic moment in the isospin limit and with isospin symmetry breaking model, we find a^HVP_(mu,isospin symm.) = 687.7·10^-10 and a^HVP_(mu,isospin broken) = 695.1·10^-10, For the tau lepton, we report a^HVP_(tau,isospin symm.) = 348.46·10^-8 and a^HVP_(tau,isospin broken) = 350.18·10^-8.The model uncertainty is estimated to be around 10%.As a second application, the hadronic polarization function is used to calculate the correction to the electromagnetic coupling alphaQED and the weak mixing angle. Our results for both observables agree reasonably well with lattice calculations and experiment.