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.