Proper constituent gluon mass as the final piece to construct hybrid mesons

Abstract

In this letter, we propose that a proper constituent gluon mass $m_g$=450 MeV can be applied to identify the hybrids composed of quarks and gluons. By investigating the spectra and decay widths of the light hybrids $(q\bar{q}g)$ with $J^P=1^{-+}$, we find the $\ddot{I}{€}_1(1600)$ and $\hat{I}{\cdot }_1(1855)$ may not be explained as $1^{-+}$ hybrids, simultaneously, and the $\hat{I}{\cdot }_1(1855)$ observed by BESIII may not be a hybrid. In addition, we predict an existence of a hybrid $\hat{I}{\cdot }_1(1640)$, which can be verified by searching the $a_1(1260)\ddot{I}€$ channel. Moreover, we suggest the $K_1(1270)\bar{K}$ and $K_1(1270)\ddot{I}€$ as the golden channels to search for an isospin-0 and an isospin-$\frac{1}{2}$ hybrids, respectively.