Decays of an exotic $1^{-+}$ hybrid meson resonance in QCD

TL;DR

This study uses lattice QCD to determine the decay properties of the lightest exotic $1^{-+}$ hybrid meson, revealing a narrow resonance with specific decay channels and implications for experimental observations.

Contribution

First lattice QCD calculation of the decay patterns of the exotic $1^{-+}$ hybrid meson, including coupled-channel analysis and resonance pole identification.

Findings

Identified a narrow resonance with weak coupling to open channels.

Predicted a broad $ ext{pi}_1$ resonance decaying mainly into $b_1 ext{pi}$.

Suggested compatibility with the experimental $ ext{pi}_1(1564)$ state.

Abstract

We present the first determination of the hadronic decays of the lightest exotic $J^{PC}=1^{-+}$ resonance in lattice QCD. Working with SU(3) flavor symmetry, where the up, down and strange quark masses approximately match the physical strange-quark mass giving $m_\pi \sim 700$ MeV, we compute finite-volume spectra on six lattice volumes which constrain a scattering system featuring eight coupled channels. Analytically continuing the scattering amplitudes into the complex energy plane, we find a pole singularity corresponding to a narrow resonance which shows relatively weak coupling to the open pseudoscalar--pseudoscalar, vector--pseudoscalar and vector--vector decay channels, but large couplings to at least one kinematically-closed axial-vector--pseudoscalar channel. Attempting a simple extrapolation of the couplings to physical light-quark mass suggests a broad $\pi_1$ resonance decaying dominantly through the $b_1 \pi$ mode with much smaller decays into $f_1 \pi$, $\rho \pi$, $\eta' \pi$ and $\eta \pi$. A large total width is potentially in agreement with the experimental $\pi_1(1564)$ candidate state, observed in $\eta \pi$, $\eta' \pi$, which we suggest may be heavily suppressed decay channels.