Electromagnetic Mass Difference of Heavy Mesons

Using the Cottingham formula, we give an estimate of the electromagnetic mass splitting of pseudoscalar heavy mesons in the beauty and charm sector. We include in the dispersion relation the Born term, the $1^-$ resonance and the positive parity $1^+$ resonance. We also evaluate the contribution to the mass difference from the isospin breaking quark mass differences. Our results: $m_{B^+}-m_{B^0} = - 0.83\pm 0.34$ MeV and $m_{D^+}-m_{D^0} = + 4.33\pm 0.37$ MeV, are in agreement with the experimental measurements: $m_{B^+}-m_{B^0} = - 0.35\pm 0.29$ MeV and $m_{D^+}-m_{D^0} = + 4.78\pm 0.10$ MeV. We also compute the mass differences in the infinite heavy quark mass limit, which show small deviations from the finite mass results for the $B$ case and 30% effects in the charm case