The preliminary lattice QCD calculation of $κ$ meson decay width

We present a direct lattice QCD calculation of the $κ$ meson decay width with the s-wave scattering phase shift for the isospin $I=1/2$ pion-kaon ($πK$) system. We employ a special finite size formula, which is the extension of the Rummukainen-Gottlieb formula for the $πK$ system in the moving frame, to calculate the scattering phase, which indicates a resonance around $κ$ meson mass. Through the effective range formula, we extract the effective $κ\to πK$ coupling constant $g_{κπK} = 4.54(76)$ GeV and decay width $Γ= 293 \pm 101$ 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 $16^3\times48$ lattice at $(m_π+ m_K) / m_κ\approx 0.8$ and lattice spacing $a \approx 0.15$ fm.

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