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We present a systematic study of the productions and decays of light axialvector mesons with $J^{PC}=1^{+\pm}$ in charmonium decays. In the quark modelscenario, the two axial vector nonets are connected with each other by theGell-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 $^1P_1$. Themixing angles between $f_1$ and $f_1'$ (i.e. $f_1(1285)$ and $f_1(1420)$), andbetween $h_1$ and $h_1'$ (i.e. $h_1(1170)$ and $h_1(1415)$) can be reliablyconstrained. We then introduce the intermediate $K^*\bar{K}+c.c.$ meson looptransitions in the description of the productions and decays of these axialvector mesons. The presence of the nearby $S$-wave $K^*\bar{K}+c.c.$ to whichthese axial vector mesons have strong coupling strengths, turns out to becrucial for understanding many puzzling questions related to their productionsand decays. This is because that the $S$-wave $K^*\bar{K}+c.c.$ rescatteringsby the kaon exchange satisfy the triangle singularity (TS) condition in some ofthese cases and the TS mechanism can introduce special interference effects inthe exclusive decays of these light axial vector mesons.

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