U(2)L×U(2)Rchiral theory of mesons

A U(2${)}_{\mathit{L}}$×U(2${)}_{\mathit{R}}$ chiral theory of pseudoscalar, vector, and axial-vector mesons is proposed and studied at the tree level. VMD is a natural result of this theory. The physical processes of normal parity and abnormal parity have been studied by using the same Lagrangian leading to a universality of coupling. 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 ${\mathit{a}}_1$ decay are satisfied. The KSFR sum rule is satisfied reasonably well. The ρ pole in the pion form factor has been achieved. The theoretical results for the processes ρ→ππ, ω→ππ, ${\mathit{a}}_1$→ρπ, and πγ, τ→ρν, τ→${\mathit{a}}_1$ν, ${\mathrm{\pi }}^0$→γγ, ω→πγ, ρ→πγ, ${\mathit{f}}_1$→ρππ, ${\mathit{f}}_1$→ηππ, ρ→ηγ, ω→ηγ are in good agreement with the data. The ππ scattering lengths and slopes have been found to be the same as obtained by Weinberg. In particular, the ρ resonance in the amplitude ${\mathit{T}}_1^1$ of ππ scattering has been obtained from this theory. Two coefficients of chiral perturbation theory have been determiend and they are close to the values used in chiral perturbation theory. This theory has dynamical chiral symmetry breaking.