Electromagnetic Splittings and Light Quark Masses in Lattice QCD

Abstract

A method for computing electromagnetic properties of hadrons in lattice QCD is described and preliminary numerical results are presented. The electromagnetic field is introduced dynamically, using a noncompact formulation. Employing enhanced electric charges, the dependence of the pseudoscalar meson mass on the (anti)quark charges and masses can be accurately calculated. At $\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5.7$ with Wilson action, the ${\ensuremath{\pi}}^{+}\ensuremath{-}{\ensuremath{\pi}}^{0}$ splitting is found to be 4.9(3) MeV. Using the measured ${K}^{0}\ensuremath{-}{K}^{+}$ splitting, we also find ${m}_{u}/{m}_{d}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.512(6)$. Systematic errors are discussed.