The preliminary lattice QCD calculation of $\kappa$ meson decay width

Abstract

We present a direct lattice QCD calculation of the $\kappa$ meson decay width with the s-wave scattering phase shift for the isospin $I=1/2$ pion-kaon ($\pi K$) system. We employ a special finite size formula, which is the extension of the Rummukainen-Gottlieb formula for the $\pi K$ system in the moving frame, to calculate the scattering phase, which indicates a resonance around $\kappa$ meson mass. Through the effective range formula, we extract the effective $\kappa \to \pi K$ coupling constant $g_{\kappa \pi K}=4.54(76)$ GeV and decay width $\Gamma =293\pm 101$ MeV. Our simulations are done with the MILC gauge configurations with $N_f=2+1$ flavors of the "Asqtad" improved staggered dynamical sea quarks on a $16^3\times 48$ lattice at $(m_{\pi }+m_K)/m_{\kappa }\approx 0.8$ and lattice spacing $a\approx 0.15$ fm.

To make it concise. arXiv admin note: text overlap with arXiv:1110.1422, but much of v1 text overlap with articles by same and other authors removed

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• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• Lattice study on $\pi K$ scattering with moving wall source
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• Lattice QCD study on $K^{\ast }(892)$ meson decay width
• $I=1/2$ $S$-wave and $P$-wave $K\pi$ scattering and the $\kappa$ and $K^{\ast }$ resonances from lattice QCD
• $I=0$ $\pi \pi$ $s$-wave scattering length from lattice QCD
• Preliminary lattice study of $\sigma$ meson decay width
• Preliminary lattice study of the I=1 $K\bar{K}$ scattering length
• I=1/2 low-lying mesons in lattice QCD
• Bubble contributions to scalar correlators with mixed actions