Decays of an exotic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mn>1</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math> hybrid meson resonance in QCD
Antoni J. Woss, Jo Dudek, Robert G. Edwards, Christopher E. Thomas, David J. Wilson
Abstract
We present the first determination of the hadronic decays of the lightest exotic ${J}^{PC}={1}^{\ensuremath{-}+}$ 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 ${m}_{\ensuremath{\pi}}\ensuremath{\sim}700\text{ }\text{ }\mathrm{MeV}$, 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 ${\ensuremath{\pi}}_{1}$ resonance decaying dominantly through the ${b}_{1}\ensuremath{\pi}$ mode with much smaller decays into ${f}_{1}\ensuremath{\pi}$, $\ensuremath{\rho}\ensuremath{\pi}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}$ and $\ensuremath{\eta}\ensuremath{\pi}$. A large total width is potentially in agreement with the experimental ${\ensuremath{\pi}}_{1}(1564)$ candidate state observed in $\ensuremath{\eta}\ensuremath{\pi}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}$, which we suggest may be heavily suppressed decay channels.