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

Abstract

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 $m_{K^{\ast }}/m_{\pi }=3.808(18)$ and $g_{K^{\ast }K\pi }^{\mathrm{BW}}=5.33(20)$ 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 $m_{\pi }{a}_0=-0.353(25)$.

Comments: 27 pages, 12 figures. Mistake corrected in Fig. 4, plus minor changes to the text. Agrees with published version