Analysis on Heavy Quarkonia Transitions with Pion Emission in Terms of the QCD Multipole Expansion and Determination of Mass Spectra of Hybrids

TL;DR

This paper analyzes heavy quarkonia transitions involving pions using QCD multipole expansion, predicts hybrid mass spectra, and compares theoretical potentials with lattice results, providing insights into hybrid states and their mixing with quarkonia.

Contribution

It introduces a method to determine hybrid mass spectra from transition data and compares hybrid potentials with lattice QCD results.

Findings

Predicted hybrid masses: 4.23 GeV for charmonium and 10.79 GeV for bottomonium.

Hybrid states may mix with regular quarkonia, affecting observed spectra.

Potential models for hybrids align with lattice QCD results.

Abstract

One of the most important tasks in high energy physics is search for the exotic states, such as glueball, hybrid and multi-quark states. The transitions $\psi(ns)\to \psi(ms)+\pi\pi$ and $\Upsilon(ns)\to \Upsilon(ms)+\pi\pi$ attract great attentions because they may reveal characteristics of hybrids. In this work, we analyze those transition modes in terms of the theoretical framework established by Yan and Kuang. It is interesting to notice that the intermediate states between the two gluon-emissions are hybrids, therefore by fitting the data, we are able to determine the mass spectra of hybrids. The ground hybrid states are predicted as 4.23 GeV (for charmonium) and 10.79 GeV (for bottonium) which do not correspond to any states measured in recent experiments, thus it may imply that very possibly, hybrids mix with regular quarkonia to constitute physical states. Comprehensive comparisons of the potentials for hybrids whose parameters are obtained in this scenario with the lattice results are presented.