Leading isospin-breaking corrections to pion, kaon, and charmed-meson masses with twisted-mass fermions

We present a lattice computation of the isospin-breaking corrections to pseudoscalar meson masses using the gauge configurations produced by the European Twisted Mass Collaboration with Nf=2+1+1 dynamical quarks at three values of the lattice spacing (a≃0.062, 0.082, and 0.089 fm) with pion masses in the range Mπ≃210–450 MeV. The strange and charm quark masses are tuned at their physical values. We adopt the RM123 method based on the combined expansion of the path integral in powers of the d- and u-quark mass difference (m^d−m^u) and of the electromagnetic coupling αem. Within the quenched QED approximation, which neglects the effects of the sea-quark charges, and after the extrapolations to the physical pion mass and to the continuum and infinite volume limits, we provide results for the pion, kaon, and (for the first time) charmed-meson mass splittings, for the prescription-dependent parameters επ0, εγ(MS¯,2 GeV), εK0(MS¯,2 GeV), related to the violations of the Dashen’s theorem, and for the light quark mass difference (m^d−m^u)(MS¯,2 GeV).