Lattice QCD study of the $K^{\ast }(892)$ resonance at the physical point

Abstract

We present a lattice QCD study of the $K^{\ast }(892)$ resonance using eight $N_f=2+1$ Wilson-Clover ensembles with three lattice spacings and six pion masses ranging from 135 to 320 MeV. For each ensemble, a large number of finite volume energy levels in the $P$-wave $K\ddot{I}€$ channel are determined. The energy dependence of the scattering phase shift is then obtained from Lüscher's finite-volume method. To systematically assess parametrization dependence, the amplitude is described using three different models, which yield consistent results. The resulting phase shifts show a clear resonant behavior for all ensembles, and the corresponding $K^{\ast }(892)$ resonance pole is identified on the second Riemann sheet in the complex energy plane. The pole positions are extrapolated to the physical pion mass and the continuum limit, yielding a $K^{\ast }(892)$ resonance located at $\sqrt{s_0}=[883(22)-i20(13)]\mathrm{MeV}$, which is in excellent agreement with the experimental value. This study provides a first-principles QCD determination of the $K^{\ast }(892)$ mass and width with controlled systematic uncertainties.

25 pages, 12 figures; Appendix improved