Lattice QCD study of the $K^*(892)$ resonance at the physical point

Abstract

We present a lattice QCD study of the $K^*(892)$ resonance using a set of $N_f=2+1$ 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 $Kπ$ 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 $K^*(892)$ 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 $K^*(892)$ 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-principle QCD determination of the $K^*(892)$ mass and width with controlled systematic uncertainties.

Figures (12)

• Figure 1: The Wick contractions corresponding to the elements $\langle (K\pi) (K\pi)^\dagger\rangle = A + \frac{1}{2} X - \frac{3}{2} H$ and $\langle K_i (K\pi)^\dagger \rangle = - \sqrt{ \frac{3}{2} } T$ for the correlation matrix $C^{\Lambda,\boldsymbol P}(t)$.
• Figure 2: Upper: The effective masses of the GEVP eigenvalues for $(O_h,A_1^+)$ and $(O_h,T_1^-)$ irreps for the F48P30 ensemble. The $\omega^l$-weighted histograms of the energy level results from the fit to a double exponential form are shown with same colors. The central values and error bands are calculated using Eq. \ref{['sigmome']}. Lower: The first row shows the effective mass of the eigenvalues and central values of the energy levels with total error bands. The second and third rows display the $\chi^2/d.o.f$ and energy levels over several fit ranges, respectively. The $x-$axises in the third row denote the initial times $t_{min}$ (the end times are the max times of the error band covering the eigenvalues in the corresponding figure in the first row). The three bands denote the statistical uncertainties, systematic uncertainties and total uncertainties in the third row. The red points are chosen as the central values for each energy level.
• Figure 3: The finite-volume spectra with total errors for F48P30 and F32P30 ensembles. The red points are used in the minimization described in the following. The gray dashed lines present the free energy levels and pink bands are the inelastic threshold. The blue bands denote the solutions of the Lüshcer equations with model "PR". The more details are given in the following section.
• Figure 4: The same as in Fig. \ref{['fig:spectra1']}, but for F48P21 and F32P21 ensembles spectrum.
• Figure 5: The same as in Fig. \ref{['fig:spectra1']}, but for C32P29 ensemble spectrum.