  We apply the QCD sum rule method to study the light single-gluon hybrid
states with various (exotic) quantum numbers. We construct twenty-four
single-gluon hybrid currents, and use eighteen of them to calculate the masses
of forty-four single-gluon hybrid states with the quark-gluon contents $\bar q
q g$ ($q=u/d$) and $\bar s s g$. We concentrate on the hybrid states with the
exotic quantum number $J^{PC} = 1^{-+}$, whose masses and widths are calculated
to be $M_{|\bar q q g;1^-1^{-+}\rangle} =1.67^{+0.15}_{-0.17}$ GeV,
$\Gamma_{|\bar q q g;1^-1^{-+}\rangle} = 530^{+540}_{-330}$ MeV, $M_{|\bar q q
g;0^+1^{-+}\rangle} = 1.67^{+0.15}_{-0.17}$ GeV, $\Gamma_{|\bar q q
g;0^+1^{-+}\rangle} = 120^{+160}_{-110}$ MeV, $M_{|\bar s s g;0^+1^{-+}\rangle}
= 1.84^{+0.14}_{-0.15}$ GeV, and $\Gamma_{|\bar s s g;0^+1^{-+}\rangle} =
100^{+110}_{-~80}$ MeV. Our results support the interpretations of the
$\pi_1(1600)$ and $\eta_1(1855)$ as the hybrid states $|\bar q q
g;1^-1^{-+}\rangle$ and $|\bar s s g;0^+1^{-+}\rangle$, respectively.
Considering the uncertainties, our results suggest that the $\pi_1(1600)$ and
$\eta_1(1855)$ may also be interpreted as the hybrid states $|\bar q q
g;1^-1^{-+}\rangle$ and $|\bar q q g;0^+1^{-+}\rangle$, respectively. To
differentiate these two assignments and to verify whether they are hybrid
states or not, we propose to examine the $a_1(1260) \pi$ decay channel in
future experiments.
