Lattice calculation of the pion mass difference Mπ+−Mπ0 at order O(αem)

We present a lattice calculation of the charged/neutral pion mass difference Mπ+−Mπ0 at order O(αem) using the gauge configurations produced by the Extended Twisted Mass Collaboration with Nf=2+1+1 dynamical quark flavors at three values of the lattice spacing (a≃0.062,0.082,0.089  fm) and pion masses in the range Mπ≃250–500  MeV. We employ the RM123 method and expand the path integral around the isospin symmetric point at leading order in the electromagnetic coupling αem. Making use of the recently proposed rotated twisted-mass scheme, we evaluate the full O(αem) contribution, with the inclusion of the disconnected diagram. At the physical point, after performing the continuum and infinite volume extrapolation, we obtain the value Mπ+−Mπ0=4.622(95)  MeV which is in good agreement with the experimental result [Mπ+−Mπ0]exp=4.5936(5)  MeV.