The elastic $I=1/2$, $s$- and $p$-wave kaon-pion scattering amplitudes are calculated using a single ensemble of anisotropic lattice QCD gauge field configurations with $N_{ \mathrm{ f}} = 2+1$ flavors of dynamical Wilson-clover fermions at $m_{ \pi} = 230\mathrm{ MeV}$. A large spatial extent of $L = 3.7\mathrm{ fm}$ enables a good energy resolution while partial wave mixing due to the reduced symmetries of the finite volume is treated explicitly.The $p$-wave amplitude is well described by a Breit-Wigner shape with parameters $m_{ K^{ *}}/m_{ \pi} = 3.808(18)$ and $g^{ \mathrm{ BW}}_{ K^{ *}K\pi} = 5.33(20)$ which are insensitive to the inclusion of $d$-wave mixing and variation of the $s$-wave parametrization. An effective range description of the near-threshold $s$-wave amplitude yields $m_{ \pi}a_0 = -0.353(25)$.
Categories: hep-lat hep-ph nucl-th