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A recent study indicates that the $\alpha^2\alpha_s^2$ order QED processes of$\Upsilon \to \jpsi + X$ decay are compatible with those of QCD processes.However, in the endpoint region, the Non-relativistic QED (NRQED) calculationbreaks down since the collinear degrees of freedom are missing under theframework of this effective theory.  In this paper we apply the soft collinear effective theory (SCET) to studythe color-singlet QED process at the kinematic limit. Within this approach weare able to sum the kinematic logarithms by running operators using therenormalization group equations of SCET, which will lead to a dramatic changein the momentum distribution near the endpoint and the spectrum shapeconsistent with the experimental results.

QED Contribution to the Color-Singlet $\jpsi$ Production in $\Upsilon$ Decay Near the Endpoint