U(2)_{L}\times U(2)_{R} Chiral Theory of Mesons

Abstract

A $U(2)_{L}\times U(2)_{R}$ chiral theory of pseudoscalar, vector, and axial-vector mesons has been proposed. VMD has been revealed from this theory. The physical processes of normal parity and abnormal parity have been studied by using the same lagrangian and the universality of coupling has been revealed. Two new mass relations between vector and axial-vector mesons have been found. Weinberg's first sum rule and new relations about the amplitude of $a_{1}$ decay are satisfied. KSFR sum rule is satisfied pretty well. The $\rho$ pole in pion form factor has been achieved. The theoretical results of $\rho\rightarrow\pi\pi$, $\omega\rightarrow \pi\pi$, $a_{1}\rightarrow\rho\pi$ and $\pi\gamma$, $\tau\rightarrow \rho\nu$, $\tau\rightarrow a_{1}\nu$, $\pi^{0}\rightarrow \gamma\gamma$, $\omega \rightarrow\pi\gamma$, $\rho\rightarrow\pi\gamma$, $f_{1} \rightarrow\rho\pi\pi$, $f_{1}\rightarrow\eta\pi\pi$, $\rho\rightarrow\eta\gamma$, $\omega \rightarrow\eta\gamma$ are in good agreement with data. Weinberg's $\pi\pi$ scattering lengths and slopes and $a^{0}_{2}$, $a^{2}_{2}$, and $b^{1}_{1}$ have been obtained. Especially, the $\rho$ resonance in the amplitude $T^{1}_{1}$ of $\pi\pi$ scattering has been revealed from this theory. Two coefficients of chiral perturbation theory have been determined and they are close to the values used by chiral perturbation theory.