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

TL;DR

This paper applies soft collinear effective theory (SCET) to analyze the color-singlet QED contribution to $$J/psi production in $$Upsilon decay near the endpoint, improving the theoretical description of the spectrum shape.

Contribution

It introduces SCET to study the endpoint region of $$J/psi production in $$Upsilon decay, enabling resummation of logarithms and better agreement with experimental data.

Findings

Resummation of kinematic logarithms significantly alters the momentum distribution.

The spectrum shape near the endpoint matches experimental observations.

SCET provides a consistent framework where NRQED fails.

Abstract

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) calculation breaks down since the collinear degrees of freedom are missing under the framework of this effective theory. In this paper we apply the soft collinear effective theory (SCET) to study the color-singlet QED process at the kinematic limit. Within this approach we are able to sum the kinematic logarithms by running operators using the renormalization group equations of SCET, which will lead to a dramatic change in the momentum distribution near the endpoint and the spectrum shape consistent with the experimental results.