Chromopolarizability of Charmonium and ππ Final State Interaction Revisited

Yun-Hua Chen

doi:10.1155/2019/7650678

Abstract

The chromopolarizability of a quarkonium describes the quarkonium’s interaction with soft gluonic fields and can be measured in the heavy quarkonium decay. Within the framework of dispersion theory which considers the ππ final state interaction (FSI) model-independently, we analyze the transition ψ′→J/ψπ+π- and obtain the chromopolarizability αψ′ψ and the parameter κ. It is found that the ππ FSI plays an important role in extracting the chromopolarizability from the experimental data. The obtained chromopolarizability with the FSI is reduced to about 1/2 of that without the FSI. With the FSI, we determine the chromopolarizability αψ′ψ=(1.44±0.02) GeV-3 and the parameter κ=0.139±0.005. Our results could be useful in studying the interactions of charmonium with light hadrons.

Highlights

The chromopolarizability α of a quarkonium parametrizes the quarkonium’s effective interaction with soft gluons, and it is an important quantity in the heavy quark effective theory
We have used dispersion theory to study the ππ final state interaction (FSI) in the decay ψ耠 󳨀→ J/ψπ+π−
It is found that the effect of the ππ FSI is quite sizeable in the chromopolarizability α휓󸀠휓, and the one with FSI is almost 1/2 of that without FSI

Summary

Introduction

The chromopolarizability α of a quarkonium parametrizes the quarkonium’s effective interaction with soft gluons, and it is an important quantity in the heavy quark effective theory. Within a quarkoniumnucleon effective field theory, the chromopolarizability of the J/ψ is determined through fitting the lattice QCD data [12] of the J/ψ-nucleon potential, and the result is α퐽/휓 = 0.24 GeV−3 [13, 14]. Instead of the chiral unitary approach [18, 19], in which the scalar mesons (σ, f0(980), and a0(980)) are dynamically generated, in the dispersion theory the ππ FSI is treated in a modelindependent way consistent with ππ scattering data. Another update of our calculation is that we consider the FSIs of separate partial waves, namely, the S- and D-waves, instead.

Theoretical Framework

Phenomenological Discussion

Conclusions