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The elastic $I=1/2$, $s$- and $p$-wave kaon-pion scattering amplitudes arecalculated using a single ensemble of anisotropic lattice QCD gauge fieldconfigurations with $N_{\mathrm{f}} = 2+1$ flavors of dynamical Wilson-cloverfermions 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 dueto 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 $m_{\pi}a_0 = -0.353(25)$.

Determination of $s$- and $p$-wave $I=1/2$ $K\pi$ scattering amplitudes in $N_{\mathrm{f}}=2+1$ lattice QCD