Leading isospin-breaking corrections to meson masses on the lattice

We present a study of the isospin-breaking (IB) corrections to pseudoscalar (PS) meson masses using the gauge configurations produced by the ETM Collaboration with $N_f=2+1+1$ dynamical quarks at three lattice spacings varying from 0.089 to 0.062 fm. Our method is based on a combined expansion of the path integral in powers of the small parameters $(\widehat{m}d - \widehat{m}u)/\Lambda{QCD}$and$\alpha{em}$,where$\widehat{m}_f$ is the renormalized quark mass and ${\alpha }_{em}$ the renormalized fine structure constant. We obtain results for the pion, kaon and $D$-meson mass splitting; for the Dashen’s theorem violation parameters ${ϵ}_{\gamma }(\overline{\mathrm{M}\mathrm{S}},2GeV)$, ${ϵ}_{{\pi }^0}$, ${ϵ}_{K^0}(\overline{\mathrm{M}\mathrm{S}},2GeV)$; for the light quark masses $({\widehat{m}}_d-{\widehat{m}}_u)(\overline{\mathrm{M}\mathrm{S}},2GeV)$, $({\widehat{m}}_u\mathrm{/}{\widehat{m}}_d)(\overline{\mathrm{M}\mathrm{S}},2GeV)$; for the flavour symmetry breaking parameters $R(\overline{$\mathrm{M}\mathrm{S}$}, 2~\mbox{GeV})$and$Q(\overline{$\mathrm{M}\mathrm{S}$}, 2~\mbox{GeV})$ and for the strong IB effects on the kaon decay constants.