QCD analysis of the P -wave charmonium electromagnetic Dalitz decays hc→η(′)<mml…

The P-wave charmonium electromagnetic Dalitz decays hc→η^(')⁺^- (=e,μ) with large recoil momentum are investigated in the framework of perturbative QCD, and the contributions from the small-recoil-momentum region are described by the overlap of soft wave functions. The transition form factors f_hcη^(')(q²) and the normalized transition form factors F_hcη^(')(q²) in full kinematic region are derived for the first time. It is noticed that there are no IR divergences at the one-loop level, and the transition form factors with the relativistic corrections from the internal momentum of hc are insensitive to both the shapes of η^(') distribution amplitudes and the invariant mass of the lepton pair in the large-recoil-momentum region. Intriguingly, unlike the situation in the S-wave charmonium decays J/ψ→η^(')⁺^-, we find that the contributions from the small-recoil-momentum region are comparable with those from the large-recoil-momentum region in the P-wave charmonium decays hc→η^(')⁺^-. By employing the obtained F_hcη^(')(q²), we give predictions of the branching ratios B(hc→η^(')⁺^-), which may come within the range of measurement of present or near-future experiments.