Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Deciphering the mechanism of $J/ψ$-nucleon scattering

Bing Wu, Xiang-Kun Dong, Meng-Lin Du, Feng-Kun Guo, Bing-Song Zou

Abstract

The low-energy $J/ψN$ scattering is important for various reasons: it is related to the hidden-charm $P_c$ pentaquark states, provides insights into the role of gluons in nucleon structures, and is relevant to the $J/ψ$ properties in nuclear medium. The scattering can happen through two distinct mechanisms: the coupled-channel mechanism via open-charm meson-baryon intermediate states, and the soft-gluon exchange mechanism. We investigate the $J/ψN$ $S$-wave scattering length through both mechanisms, and find that the soft-gluon exchange mechanism leads to a scattering length at least one order of magnitude larger than that from the coupled-channel mechanism and thus is the predominant one. The findings can be verified by lattice calculations and will enhance our understanding of the scattering processes breaking the Okubo-Zweig-Iizuka rule.

Deciphering the mechanism of $J/ψ$-nucleon scattering

Abstract

The low-energy scattering is important for various reasons: it is related to the hidden-charm pentaquark states, provides insights into the role of gluons in nucleon structures, and is relevant to the properties in nuclear medium. The scattering can happen through two distinct mechanisms: the coupled-channel mechanism via open-charm meson-baryon intermediate states, and the soft-gluon exchange mechanism. We investigate the -wave scattering length through both mechanisms, and find that the soft-gluon exchange mechanism leads to a scattering length at least one order of magnitude larger than that from the coupled-channel mechanism and thus is the predominant one. The findings can be verified by lattice calculations and will enhance our understanding of the scattering processes breaking the Okubo-Zweig-Iizuka rule.

Paper Structure

This paper contains 6 sections, 23 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Coupled-channel mechanism
  3. Gluon exchange mechanism
  4. Charmonium-nucleon scattering lengths
  5. Summary
  6. Chiral Lagrangians and amplitudes

Figures (4)

  • Figure 1: Feynman diagrams illustrating key steps in the calculation. (a) Soft-gluon exchange between $J/\psi$ and nucleon, which is equivalent to the exchange of $\pi\pi$, $K\bar{K}$ and other heavier hadrons. (b) Crossing symmetry between $J/\psi N$ scattering and $J/\psi J/\psi\to N\bar{N}$. (c) $A\bar{A}\to\mathcal{P}\bar{\mathcal{P}}$ ($A=N,J/\psi$, and $\mathcal{P}=\pi,K$) amplitude with the $\pi\pi$-$K\bar{K}$ coupled-channel rescattering, where the black dot represents the full $A\bar{A}\to\mathcal{P}\bar{\mathcal{P}}$ amplitude, and the black square denotes the $\pi\pi$-$K\bar{K}$ coupled-channel rescattering.
  • Figure 2: Tree-level Feynman diagrams for the $N\bar{N}\to\pi\pi$ and $N\bar{N}\to K\bar{K}$ processes.
  • Figure 3: Fit to the BESII data BES:2006eer and ATLAS data ATLAS:2016kwu for the $\psi(2S)\to J/\psi\pi^+\pi^-$ transition: dipion invariant mass distribution (left) and the helicity angular distribution (right). The "Best fit--DP" and "Best fit--HD" represent the fitting results obtained using the Omnès matrix from Ref. Ropertz:2018stk and Ref. Hoferichter:2012wf, respectively.
  • Figure 4: Dependence of the $S$-wave $J/\psi N$ scattering length on the cutoff $\Lambda$, evaluated assuming $c^{(11)}_{1,2,m}=c^{(21)}_{1,2,m}$.