QCD analysis of the P -wave charmonium electromagnetic Dalitz decays hc→η(′)ℓ+ℓ−

Abstract

The P-wave charmonium electromagnetic Dalitz decays hc→η(′)ℓ+ℓ− (ℓ=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 fhcη(′)(q2) and the normalized transition form factors Fhcη(′)(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(′)ℓ+ℓ−, 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(′)ℓ+ℓ−. By employing the obtained Fhcη(′)(q2), we give predictions of the branching ratios B(hc→η(′)ℓ+ℓ−), which may come within the range of measurement of present or near-future experiments. Published by the American Physical Society 2024