Electromagnetic mass splittings of π,a1,K,K1(1400),andK*(892)

Abstract

To one-loop order and $O({\ensuremath{\alpha}}_{\mathrm{EM}}),$ the electromagnetic mass splittings of \ensuremath{\pi}, ${a}_{1},$ $K,$ ${K}_{1}(1400),$ and ${K}^{*}(892)$ are calculated in the framework of $\mathrm{U}{(3)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(3)}_{R}$ chiral field theory. The logarithmic divergences emerging in the Feynman integrations of the mesonic loops are factorized by using an intrinsic parameter $g$ of this theory. No other additional parameters or counterterms are introduced to absorb the mesonic loop divergences. When ${f}_{\ensuremath{\pi}},$ ${m}_{\ensuremath{\rho}},$ and ${m}_{a}$ are taken as inputs, the parameter $g$ will be determined and all the physical results are finite and fixed. Dashen's theorem is satisfied in the chiral SU(3) limit of this theory and a rather large violation of the theorem is revealed at the order of ${m}_{s}$ or ${m}_{K}^{2}.$ Mass ratios of light quarks have been determined. A relation for electromagnetic corrections to masses of axial-vector mesons is obtained. It could be regarded as a generalization of Dashen's theorem. Comparing with data, it is found that the nonelectromagnetic mass difference of ${K}^{*}$ is in agreement with the estimation of Schechter, Subbaraman, and Weigel.