A study of $ρ-ω$ mixing in resonance chiral theory

Abstract

The strong and electromagnetic corrections to $ρ-ω$ mixing are calculated using a SU(2) version of resonance chiral theory up to next-to-leading orders in $1/N_C$ expansion, respectively. Up to our accuracy, the effect of the momentum dependence of $ρ-ω$ mixing is incorporated due to the inclusion of loop contributions. We analyze the impact of $ρ-ω$ mixing on the pion vector form factor by performing numerical fit to the data extracted from $e^+e^-\rightarrow π^+π^-$ and $τ\rightarrow ν_τ2π$, while the decay width of $ω\rightarrow π^+π^-$ is taken into account as a constraint. It is found that the momentum dependence is significant in a good description of the experimental data. In addition, based on the fitted values of the involved parameters, we analyze the decay width of $ω\rightarrow π^+π^-$, which turns out to be highly dominated by the $ρ-ω$ mixing effect.