Radiative vertex $VP\gamma$ and $\eta-\eta'$ mixing in light-cone sum rules

TL;DR

This paper calculates radiative vertex functions involving vector and pseudoscalar mesons using light-cone sum rules, extracting the eta-eta' mixing angle consistent with experimental data.

Contribution

It introduces a method combining $ ho- ho'$ mixing and three-particle twist-4 photon distribution amplitudes to determine the $ heta_{ ext{mix}}$ angle.

Findings

The $ heta_{ ext{mix}}$ angle is determined to be approximately 41°.

The approach aligns well with experimental decay data.

It provides a refined theoretical framework for meson mixing analysis.

Abstract

In this work, we calculate radiative vertex $VP\gamma$ ($V=\phi,\omega,\rho$ and $P=\eta,\eta'$) by utilizing $\omega-\phi$ mixing scheme and taking into account the contributions of the three-particle twist-4 distribution amplitudes of the photon in QCD sum rules on light cone. According to experimental data of $V\rightarrow P\gamma$ and $P\rightarrow V\gamma$ from PDG, a value of the $\eta-\eta^\prime$ mixing angle, $\phi=(40.9\pm0.5)^\circ$, is extracted in the framework of the quark-flavor basis to describe the $\eta-\eta^\prime$ system.