Comprehensive study of light axial vector mesons with the presence of triangle singularity

TL;DR

This paper systematically studies light axial vector mesons in charmonium decays, highlighting the role of triangle singularities and meson loop transitions in their production and decay processes.

Contribution

It introduces the impact of triangle singularities and meson loop transitions on axial vector meson behaviors, providing new insights into their production and decay mechanisms.

Findings

Triangle singularities significantly influence meson decay patterns.

Meson loop transitions explain puzzling production phenomena.

Strong coupling to $K^*ar{K}$ channels is crucial for understanding axial mesons.

Abstract

We present a systematic study of the productions and decays of light axial vector mesons with $J^{PC}=1^{+\pm}$ in charmonium decays. In the quark model scenario, the two axial vector nonets are connected with each other by the Gell-Mann-Okubo mass relation through the mixing between two $K_1$ states (i.e. $K_1(1270)$ and $K_1(1400)$) with configurations of $^3P_1$ and $^1P_1$. The mixing angles between $f_1$ and $f_1'$ (i.e. $f_1(1285)$ and $f_1(1420)$), and between $h_1$ and $h_1'$ (i.e. $h_1(1170)$ and $h_1(1415)$) can be reliably constrained. We then introduce the intermediate $K^*\bar{K}+c.c.$ meson loop transitions in the description of the productions and decays of these axial vector mesons. The presence of the nearby $S$-wave $K^*\bar{K}+c.c.$ to which these axial vector mesons have strong coupling strengths, turns out to be crucial for understanding many puzzling questions related to their productions and decays. This is because that the $S$-wave $K^*\bar{K}+c.c.$ rescatterings by the kaon exchange satisfy the triangle singularity (TS) condition in some of these cases and the TS mechanism can introduce special interference effects in the exclusive decays of these light axial vector mesons.