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Leading power SCET analysis of $e^+ e^- \to J/ψg g$

Zhi-Hai Lin, Guohuai Zhu

TL;DR

This paper investigates the endpoint behavior of the color-singlet $J/\psi gg$ production in $e^+e^-$ annihilation. It employs a leading-power SCET framework matched to NRQCD, factorizes the rate into hard, jet, and ultrasoft functions, and performs Sudakov resummation to obtain a suppressed endpoint $J/\psi$ momentum spectrum. A surprising finding is a large discrepancy between NRQCD and tree-level SCET in the endpoint region even before resummation, mirroring observations in radiative $\Upsilon$ decays and suggesting missing power-suppressed contributions or limitations of the leading SCET expansion. To address the full kinematic range, the authors propose an interpolation between NRQCD and resummed SCET and discuss the implications for angular distributions and future refinements.

Abstract

Recently, Belle and BaBar Collaborations observed surprising suppression in the endpoint $J/ψ$ spectrum, which stimulates us to examine the endpoint behaviors of the $e^+ e^- \to J/ψgg$ production. We calculate the $J/ψ$ momentum and angular distributions for this process within the framework of the soft-collinear effective theory (SCET). The decreasing spectrum in the endpoint region is obtained by summing the Sudakov logarithms. We also find a large discrepancy between the NRQCD and SCET spectrum in the endpoint region even before the large logarithms are summed, which is probably due to the fact that only the scalar structure of the two-gluon system is picked out in the leading power expansion. A comparison with the process $Υ\to γgg$ is made.

Leading power SCET analysis of $e^+ e^- \to J/ψg g$

TL;DR

This paper investigates the endpoint behavior of the color-singlet production in annihilation. It employs a leading-power SCET framework matched to NRQCD, factorizes the rate into hard, jet, and ultrasoft functions, and performs Sudakov resummation to obtain a suppressed endpoint momentum spectrum. A surprising finding is a large discrepancy between NRQCD and tree-level SCET in the endpoint region even before resummation, mirroring observations in radiative decays and suggesting missing power-suppressed contributions or limitations of the leading SCET expansion. To address the full kinematic range, the authors propose an interpolation between NRQCD and resummed SCET and discuss the implications for angular distributions and future refinements.

Abstract

Recently, Belle and BaBar Collaborations observed surprising suppression in the endpoint spectrum, which stimulates us to examine the endpoint behaviors of the production. We calculate the momentum and angular distributions for this process within the framework of the soft-collinear effective theory (SCET). The decreasing spectrum in the endpoint region is obtained by summing the Sudakov logarithms. We also find a large discrepancy between the NRQCD and SCET spectrum in the endpoint region even before the large logarithms are summed, which is probably due to the fact that only the scalar structure of the two-gluon system is picked out in the leading power expansion. A comparison with the process is made.

Paper Structure

This paper contains 3 sections, 22 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Leading order SCET calculation
  3. Results and Discussions

Figures (3)

  • Figure 1: Matching the amplitude for $\gamma^\ast \rightarrow J/\psi gg$ process in QCD and SCET.
  • Figure 2: The momentum distribution (a) and angular coefficient $\alpha(z)$ (b) for $e^+ e^- \rightarrow J/\psi gg$ process. The dashed, dotted and dot-dashed curves correspond to the NRQCD, tree-level SCET and resummed SCET calculations, respectively. The solid curve is for the interpolated resummed results.
  • Figure 3: The momentum distribution (a) and angular coefficient $\alpha(z)$ (b) for $e^+ e^- \rightarrow \Upsilon \rightarrow \gamma gg$ process. The dashed, dotted and dot-dashed curves correspond to the NRQCD, tree-level SCET and resummed SCET calculations, respectively. The solid curve is for the interpolated resummed results.