Analysis on heavy quarkonia transitions with pion emission in terms of the QCD multipole expansion and determination of mass spectra of hybrids
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Abstract
One of the most important tasks in high energy physics is the search for the exotic states, such as glueball, hybrid, and multiquark states. The transitions $\ensuremath{\psi}(ns)\ensuremath{\rightarrow}\ensuremath{\psi}(ms)+\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\Upsilon}(ns)\ensuremath{\rightarrow}\ensuremath{\Upsilon}(ms)+\ensuremath{\pi}\ensuremath{\pi}$ attract great attention 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.