$\rho^0-\omega$ mixing in ${\rm U(3)}_L\times {\rm U(3)}_R$ chiral theory of mesons

Dao-Neng Gao; Mu-Lin Yan

doi:doi:10.1007/s100500050180

EPJ

$\rho^0-\omega$ mixing in ${\rm U(3)}_L\times {\rm U(3)}_R$ chiral theory of mesons

Dao-Neng Gao¹ - Mu-Lin Yan^2,3

¹ Center for Fundamental Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
² Chinese Center for Advanced Science and Technology (World Lab), P.O.Box 8730, Beijing, 100080, People's Republic of China - Mailing adress: Center for Fundamental Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China

Received: 30 January 1998 / Revised version: 3 June 1998 Communicated by W. Weise

Abstract
In this paper, U(3) $_L\times$ U(3)_R chiral theory of mesons is extended to the leading order in quark mass expansion in order to evaluate the $\rho^0-\omega$ mixing. It is shown that the use of path integral method to integrate out the quark fields naturally leads to the $\rho^0-\omega$ mixing vertices, and this mixing is entirely from the quark loop in this theory. The off-shell behaviour of the mixing amplitude is analyzed. The on-shell mixing amplitude is obtained from the decay $\omega\rightarrow \pi^+\pi^-$ . Furthermore, the constraints on the light quark mass parameters are extracted from the $\rho^0-\omega$ mixing and the mesons masses, and the mass splitting of K^*(892)-mesons is predicted.

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