On the mass and decay constant of the P-wave ground and radially excited $h_{c}$ and $h_{b}$ axial-vector mesons

The mass and decay constant of the heavy quarkonia $h_{Q}(1P)$ and $h_{Q}(2P)$ (Q = b, c) with quantum numbers $J^{PC} =1^{+-}$ are calculated in the framework of the two-point QCD sum rule method by taking into account the vacuum condensates up to eight dimensions. We compare our results for parameters of the $h_{b}(1P)$ and $h_{c}(1P)$ quarkonia, and their first radially excited states $h_{b}(2P)$ and $h_{c}(2P)$ with available experimental data as well as predictions of other theoretical studies existing in the literature. The results of present work may shed light on experimental searches for the $h_{c}(2P)$ state.