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Strong Decays of the Light Exotic $0^{+-}$ and $2^{+-}$ Hybrid Mesons

Christian Farina, Eric S. Swanson

TL;DR

The paper develops a Coulomb-gauge QCD Hamiltonian framework with a single axial quasigluon to describe light exotic hybrids. It couples a $q\bar{q}$ pair to a gluon and uses a gluon-dissociation decay mechanism to compute strong decays for the $0^{+-}$ and $2^{+-}$ states, predicting notably narrow isovector hybrids. Lattice-informed mass inputs are interpolated to ground the decay predictions and reveal a crucial suppression of the $0^{+-}\rightarrow 2^1S_0+1^1S_0$ channel, explaining the unexpectedly small width of the $0^{+-}$ state. The study highlights how mixing, mass choices, and wavefunction parameters influence decay patterns and offers guidance for upcoming experimental searches at facilities like GlueX and BESIII. It also suggests directions for extending the model to additional hybrid states and incorporating spin-dependent contributions for mass spectra.

Abstract

A model of hybrid meson structure based on the QCD Hamiltonian in Coulomb gauge and the use of a single constituent quasigluon is applied compute hadronic decays of mesons with exotic quantum numbers, $0^{+-}$ and $2^{+-}$. These correspond to hybrid mesons in which the gluon couples to a $q\bar{q}$ pair in an $P$-wave and can therefore be identified as orbital excitations of the exotic $1^{-+}$ state. Interestingly, we find $0^{+-}$ states to be narrow, contrary to what was found by previous calculations. This is primarily due to the suppression of the decay mode $0^{+-}\rightarrow 2^1S_0+1^1S_0$, which is unique to our model. The $2^{+-}$ states are found to be narrow, as expected.

Strong Decays of the Light Exotic $0^{+-}$ and $2^{+-}$ Hybrid Mesons

TL;DR

The paper develops a Coulomb-gauge QCD Hamiltonian framework with a single axial quasigluon to describe light exotic hybrids. It couples a pair to a gluon and uses a gluon-dissociation decay mechanism to compute strong decays for the and states, predicting notably narrow isovector hybrids. Lattice-informed mass inputs are interpolated to ground the decay predictions and reveal a crucial suppression of the channel, explaining the unexpectedly small width of the state. The study highlights how mixing, mass choices, and wavefunction parameters influence decay patterns and offers guidance for upcoming experimental searches at facilities like GlueX and BESIII. It also suggests directions for extending the model to additional hybrid states and incorporating spin-dependent contributions for mass spectra.

Abstract

A model of hybrid meson structure based on the QCD Hamiltonian in Coulomb gauge and the use of a single constituent quasigluon is applied compute hadronic decays of mesons with exotic quantum numbers, and . These correspond to hybrid mesons in which the gluon couples to a pair in an -wave and can therefore be identified as orbital excitations of the exotic state. Interestingly, we find states to be narrow, contrary to what was found by previous calculations. This is primarily due to the suppression of the decay mode , which is unique to our model. The states are found to be narrow, as expected.

Paper Structure

This paper contains 11 sections, 17 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Constituent-Gluon Model of Hybrids
  3. QCD Hamiltonian In Coulomb Gauge
  4. Light Hybrids
  5. Model Parameters
  6. Decay Model
  7. Light Hybrid Decays
  8. Hybrid Masses
  9. Isovectors
  10. Isoscalars
  11. Summary and Conclusions

Figures (2)

  • Figure 1: Schematic diagram of the hybrid decay model, in which the hybrid meson decays into two conventional mesons through gluon dissociation into a $q\bar{q}$ pair.
  • Figure 2: Plot of $\Gamma(0^{+-}\rightarrow\pi(1300)\pi)$ as a function of the $\pi(1300)$$\beta$ parameter. The asterisk corresponds to the value of $\Gamma$ at $\beta_{\pi(1300)}=0.167$, which is what we obtain from the spin dependent model in Eq. \ref{['eq:SDmodel']} and report in Table \ref{['tab:IsovectorDecays']} above.