$\omega$ meson from lattice QCD

Abstract

Many excited states in the hadron spectrum have large branching ratios to three-hadron final states. Understanding such particles from first principles QCD requires input from lattice QCD with one-, two-, and three-meson interpolators as well as a reliable three-body formalism relating finite-volume spectra at unphysical pion mass values to the scattering amplitudes at the physical point. In this work, we provide the first-ever calculation of the resonance parameters of the $\omega$ meson from lattice QCD, including an update of the formalism through matching to effective field theories. The main result of this pioneering study, the pole position of the $\omega$ meson at $\sqrt{s_{\omega }}=(778.0(11.2)-i3.0(5))\mathrm{MeV}$, agrees reasonably well with experiment. In addition we provide an estimate of the $\omega -\rho$ mass difference as $29(15)\mathrm{MeV}$.

Comments: 14 pages, 11 figures, 3 tables. v2: version published in PRL