Abstract
Within the nonrelativistic QCD (NRQCD) factorization framework, we have computed the \( \mathcal{O}\left({\alpha}_s^2\right) \) corrections to the exclusive production of P-wave spin-triplet charmonia χcJ (J = 0, 1, 2) accompanied with a hard photon at B factory. For the first time, we have explicitly verified the validity of NRQCD factorization for exclusive P-wave quarkonium production to two-loop order. Unlike the χcJ electromagnetic decays, the \( \mathcal{O}\left({\alpha}_s^2\right) \) corrections are found to be smaller than the \( \mathcal{O} \)(αs) corrections in all three channels e+e− → χc0,1,2 + γ. In particular, the \( \mathcal{O}\left({\alpha}_s^2\right) \) corrections appear moderate for χc1 + γ case, and marginal for χc0 + γ. Moreover, the predictions in next-to-next-to-leading order (NNLO) accuracy for the production rates of χc0,1 + γ are insensitive to the renormalization and factorization scales. All these features may indicate that perturbative expansion in these two channels exhibits a decent convergence behavior. By contrast, both the \( \mathcal{O} \)(αs) and \( \mathcal{O}\left({\alpha}_s^2\right) \) corrections to the χc2 + γ production rate are sizable, which reduce the Born order cross section by one order of magnitude after including the NNLO perturbative corrections. Taking the values of the long-distance NRQCD matrix elements from nonrelativistic potential model, our prediction to χc1 + γ production rate is consistent with the recent Belle measurement. The NNLO predictions to the χc0,2 + γ production rates are much smaller than that for χc1 + γ, which seems to naturally explain why the e+e− → χc0,2 + γ channels have escaped experimental detection to date.
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Sang, WL., Feng, F. & Jia, Y. Next-to-next-to-leading-order radiative corrections to e+e− → χcJ + γ at B factory. J. High Energ. Phys. 2020, 98 (2020). https://doi.org/10.1007/JHEP10(2020)098
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DOI: https://doi.org/10.1007/JHEP10(2020)098