$\mathcal O(α^{3}α_s)$ Study on the yields and polarizations of $J/ψ(Υ)$ within the framework of non-relativistic QCD via $γγ\to J/ψ(Υ)+γ+X$ at CEPC
Within the framework of the non-relativistic QCD (NRQCD), we make a systematical study of the yields and polarizations of $J/ψ$ and $Υ$ via $γγ\to J/ψ(Υ)+γ+X$ in photon-photon collisions at the Circular Electron Positron Collider (CEPC), up to $\mathcal O(α^{3}α_s)$. We find that this process at CEPC is quite "clean", namely the direct photoproduction absolutely dominate over the single- and double- resolved processes, at least 2 orders of magnitude larger. It is found that the next-to-leading order (NLO) QCD corrections will significantly reduce the results due to that the virtual corrections to $^3S_1^1$ is large and negative. For $J/ψ$, as $p_t$ increases, the color octet (CO) processes will provide increasingly important contributions to the total NLO results. Moreover the inclusion of CO contributions will dramatically change the polarizations of $J/ψ$ from toally transverse to longitudinal, which can be regarded as a distinct signal for the CO mechanism. However, for the case of $Υ$, the effects of the CO processes are negligible, both for yields and polarizations. For $J/ψ$, the dependence of the yields on the value of the renormalization scale $μ_r$ is moderate, while significant for the polarization. The impact of the variation of $μ_λ$ is found to be relatively slight. As for the case of $Υ$, the uncertainties of $μ_{r}$ and $μ_λ$ just bring about negligible effects. The future measurements on this semi-inclusive photoproductions of $J/ψ(Υ)+γ+X$, especially on the polarization parameters of $J/ψ$, will be a good laboratory for the study of heavy quarkonium production mechanism and helpful to clarify the problems of the $J/ψ$ polarization puzzle.