Decay properties of light $1^{-+}$ hybrids

Abstract

We explore the decay properties of the isovector and isoscalar $1^{-+}$ light hybrids, ${\pi }_1$ and ${\eta }_1$, in $N_f=2$ lattice QCD at a pion mass $m_{\pi }\approx 417\mathrm{MeV}$. The McNeile and Michael method is adopted to extract the effective couplings for individual decay modes, which are used to estimate the partial decay widths of ${\pi }_1(1600)$ and ${\eta }_1(1855)$ by assuming SU(3) symmetry. The partial decay widths of ${\pi }_1(1600)$ are predicted to be $({\Gamma }_{b_1\pi },{\Gamma }_{f_1(1285)\pi },{\Gamma }_{\rho \pi },{\Gamma }_{K^{\ast }\bar{K}})=(325\pm 75,\mathcal{O}(10),52\pm 7,8.6\pm 1.3)\mathrm{MeV}$, and the total width is estimated to be $396\pm 90\mathrm{MeV}$, considering only statistical errors. If ${\eta }_1(1855)$ and the $4.4\sigma$ signal observed by BESIII (labeled as ${\eta }_1(2200)$) are taken as the two mass eigenstates of the isoscalar $1^{-+}$ light hybrids in SU(3), then the dominant decay channel(s) of ${\eta }_1(1855)$ (${\eta }_1(2200)$) is $K_1(1270)\bar{K}$ ($K_1(1270)\bar{K}$ and $K_1(1400)\bar{K}$) through the $1^{+(-)}{0}^{-(+)}$ mode. The vector-vector decay modes are also significant for the two ${\eta }_1$ states. Using the mixing angle $\alpha \approx 22.7^{\circ }$ obtained from lattice QCD for the two ${\eta }_1$ states, the total widths are estimated to be ${\Gamma }_{{\eta }_1(1855)}=282(85)\mathrm{MeV}$ and ${\Gamma }_{{\eta }_1(2200)}=455(143)\mathrm{MeV}$. The former is compatible with the experimental width of ${\eta }_1(1855)$. Although many systematic uncertainties are not well controlled, these results are qualitatively informative for the experimental search for light hybrids.