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.
Highlights
The constituent quark model has proved to be successful in describing many qualitative features of low-lying hadrons
In this work we show that the S-wave KÃKþ c:c: interactions cut into the problem via the introduction of the triangle singularity (TS) mechanism into the axial vector meson decays
In this work we present a comprehensive study of the C 1⁄4 Æ1 light axial vector mesons
Summary
The constituent quark model has proved to be successful in describing many qualitative features of low-lying hadrons. [18], and it was clarified that, apart from the width effects, the TS enhanced a0ð980Þπ production should be explicitly included This provides another important isospin-breaking source from the TS mechanism in ηð1405=1475Þ → 3π and makes it possible to coherently investigate those three decay channels in a self-consistent framework. Concerning the observation of a1ð1420Þ by the COMPASS Collaboration [13] listed above, it is explained as a tetraquark state in some studies based on the QCD sum rule [22,23] and the AdS=CFT method [24] It can be regarded as a natural consequence of the presence of the TS mechanism in this kinematic region caused by the S-wave isovector coupling between KÃKþ c:c: in the 3π spectrum [25].
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