Electromagnetic mass splittings of $\pi ,a_1,K,K_1(1400)$ and $K^{\ast }(892)$

Abstract

To one-loop order and $O({\alpha }_{em})$, the electromagnetic mass splittings of $\pi$, $a_1$, $K$, $K_1(1400)$, and $K^{\ast }(892)$ are calculated in the framework of $U(3{)}_L\times U(3{)}_R$ 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 $f_{\pi }$,$m_{\rho }$ 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 non-electromagnetic mass difference of $K^{\ast }$ is in agreement with the estimation of Schechter, Subbaraman, Weigel.

Comments: LateX, 40 pages and five PS files. Final version will appear in Phys. Rev. D56