Next-to-leading-order QCD corrections to S- and P-wave heavy quarkonium decay to l+l−γ

A bstract In this work, we comprehensively study the total and differential decay widths of the radiative Dalitz decays H → l + l − γ up to QCD next-to-leading order (NLO) accuracy within the framework of NRQCD factorization. Our calculation includes the decays of S -wave states ( η c , η b ) and the P -wave triplets ( χ cJ , χ bJ for J = 0 , 1 , 2) to both electron ( l = e ) and muon ( l = μ ) final states. To match realistic experimental detection thresholds, systematic kinematic cuts are implemented on the final-state photon energy. Our analysis of the lepton-pair invariant mass distribution shows distinct singular behaviors across the multiplets originating from the lepton-pair threshold region, which is regularized by the lepton mass, and the soft-photon region, respectively. For the S -wave states, there is only one peak near the lepton-pair threshold region, while for the J = 0 and J = 2 P -wave states, the peaks show up in both regions. However, for the J = 1 P -wave states, the peak only appears in the soft-photon region. Such features provide a rich venue to probe the γ * → l + l − form factor in heavy quarkonium decay. Integrating over the bounded phase spaces reveals a distinct hierarchy among the χ QJ states in the sensitivity of our theoretical predictions to the soft-photon energy cuts, ordered as χ Q 1 > χ Q 2 > χ Q 0 . In the χ cJ → l + l − γ cases, as the energy cut increases from 100 MeV to 500 MeV the theoretical predictions at QCD NLO are reduced by 6%( χ c 0 ), 66%( χ c 1 ), and 21%( χ c 2 ) for l = e , and by 17%( χ c 0 ), 66%( χ c 1 ), and 39%( χ c 2 ) for l = μ . Comparing our predictions with the upcoming high-precision experimental tests at BESIII will definitely deepen our understanding of the predictive power of perturbative calculations.