The color-singlet contribution to e^+ e^- ->J/psi + X at the endpoint

TL;DR

This paper addressing $e^+e^-\to J/\psi+X$ near the kinematic endpoint ($z\to 1$) uses a NRQCD+SCET framework to provide a consistent color-singlet endpoint resummation. It derives a factorization theorem into a hard, jet, and usoft sector for the color-singlet ${}^3S_1^{(1)}$ contribution, and performs renormalization-group evolution to sum single Sudakov logarithms of $1-z$. The authors show that the resummed color-singlet cross section is suppressed near the endpoint relative to fixed-order NRQCD, but that the color-octet contributions (previously treated) remain essential to describe the data, including open-charm channels; thus a complete description requires both sectors. The work provides an interpolation to connect endpoint-resummed and bulk regions, yielding a consistent prediction across the full kinematic range and clarifying the limited impact of endpoint resummation on the overall rate. These results refine the theoretical understanding of quarkonium production and reinforce the need for color-octet mechanisms to explain experimental observations.

Abstract

Recent observations of the J/psi spectrum produced in e^+e^- collisions at the Upsilon(4S) resonance are in conflict with fixed-order calculations using Non-Relativsitic QCD effective theory (NRQCD). One problem is an enhancement in the cross section when the J/psi has maximal energy, due to large perturbative corrections (Sudakov logarithms). In a recent paper, the Sudakov logarithms in the color-octet contribution were summed by combining NRQCD with the Soft-Collinear Effective Theory. However to be consistent, the color-singlet contributions must also be summed in the endpoint region which was not done in that paper. In this paper, we sum the leading and next-to-leading logarithms in the color-singlet contribution to the J/psi production cross section. We find that the color-singlet cross section is suppressed near endpoint compared to the fixed order NRQCD prediction.

Figures (7)

• Figure 1: Matching the production amplitude for $e^+ e^- \rightarrow c\bar{c}+gg$ in QCD and SCET. Collinear gluons are represented by a spring with a line through it.
• Figure 2: Feynman diagram for the leading order jet function.
• Figure 3: The difference between mixing and non-mixing $d\sigma_{\rm{resum}}/dz$, normalized to the mixing result, calculated at the scale $\mu_c = \sqrt{1-z} \mu_H$.
• Figure 4: The color-singlet differential cross section . The dot-dashed curve is the leading-order NRQCD preciction. The solid curve is the interpolated result, Eq. (\ref{['fulleq']}) prediction at calculated at the scale $\mu_c = \sqrt{(1-z)} \mu_H$. The dashed curve is the interpolated result at the scale $\mu_c = 2\sqrt{(1-z)} \mu_H$, and the dotted curve is the interpolated result using the scale $\mu_c = \sqrt{(1-z)} \mu_H/2$.
• Figure 5: The difference of the leading-order NRQCD $e^+e^-\to J/\psi gg$ differential cross section and the interpolated result, Eq. (\ref{['fulleq']}), normalized to the leading-order result. The interpolated result was calculated at the scale $\mu_c = \sqrt{(1-z)} \mu_H$.