A study of $\rho-\omega$ mixing in resonance chiral theory

TL;DR

This paper investigates the momentum-dependent $ ho- ext{omega}$ mixing effects within resonance chiral theory, analyzing their impact on pion form factors and decay widths through numerical fits to experimental data.

Contribution

It introduces a detailed calculation of $ ho- ext{omega}$ mixing including momentum dependence using resonance chiral theory up to next-to-leading order in $1/N_C$ expansion.

Findings

Momentum dependence significantly improves data description.

$ ho- ext{omega}$ mixing dominates the $ ext{omega} ightarrow ext{pi}^+ ext{pi}^-$ decay width.

Theoretical calculations align well with experimental measurements.

Abstract

The strong and electromagnetic corrections to $\rho-\omega$ 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 $\rho-\omega$ mixing is incorporated due to the inclusion of loop contributions. We analyze the impact of $\rho-\omega$ mixing on the pion vector form factor by performing numerical fit to the data extracted from $e^+e^-\rightarrow \pi^+\pi^-$ and $\tau\rightarrow \nu_{\tau}2\pi$, while the decay width of $\omega\rightarrow \pi^+\pi^-$ 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 $\omega \rightarrow \pi^+\pi^-$, which turns out to be highly dominated by the $\rho-\omega$ mixing effect.