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

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 $f_1\pi$, $\rho \pi$, ${\eta }^{\prime }\pi$ and $\eta \pi$. A large total width is potentially in agreement with the experimental ${\pi }_1(1564)$ candidate state, observed in $\eta \pi$, ${\eta }^{\prime }\pi$, which we suggest may be heavily suppressed decay channels.

Comments: 33 pages, 20 figures, small changes to match published version