Analysis of the coupling constants $g_{a_0\eta {\pi }^0}$ and $g_{a_0{\eta }^{\prime }{\pi }^0}$ with light-cone QCD sum rules

Abstract

In this article, we take the point of view that the light scalar meson $a_0(980)$ is a conventional $q\bar{q}$ state, and calculate the coupling constants $g_{a_0\eta {\pi }^0}$ and $g_{a_0{\eta }^{\prime }{\pi }^0}$ with the light-cone QCD sum rules. The central value of the coupling constant $g_{a_0\eta {\pi }^0}$ is consistent with the one extracted from the radiative decay $\varphi (1020)\to a_0(980)\gamma \to \eta {\pi }^0\gamma$. The central value and lower bound of the decay width ${\Gamma }_{a_0\to \eta {\pi }^0}=127_{-48}^{+84}\mathrm{MeV}$ are compatible with the experimental data of the total decay width ${\Gamma }_{a_0(980)}=(50-100)\mathrm{MeV}$ from the Particle Data Group with very model dependent estimation (the decay width can be much larger), while the upper bound is too large. We give possible explanation for the discrepancy between the theoretical calculation and experimental data.

Comments: 17 pages, 3 figures, revised version, add some technical details