We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $K\pi$ scattering amplitudes as a function of the center-of-mass energy using L"uscher’s method. We perform global fits of parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $\sqrt{3}\frac{2\pi }{L}$; this includes irreps that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $\kappa$ resonance in the $S$-wave and the narrow $K^{*}(892)$ resonance in the $P$-wave. Our calculations are performed with $2+1$ dynamical clover fermions for two different pion masses of $317.2(2.2)$ and $175.9(1.8)$ MeV. Our preferred $S$-wave parametrization is based on a conformal map and includes an Adler zero; for the $P$-wave we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The $S$-wave $\kappa$-resonance pole positions are found to be $\left[0.84(14)- 0.338(55)\,\I\right]\:{\rm GeV}$ at the heavier pion mass and $\left[0.662(88)- 0.368(44)\,\I\right]\:{\rm GeV}$ at the lighter pion mass. The $P$-wave $K^{*}$-resonance pole positions are found to be $\left[0.8951(64)- 0.00249(21)\,\I \right]\:{\rm GeV}$ at the heavier pion mass and $\left[0.8719(82)- 0.0132(11)\,\I\right]\:{\rm GeV}$ at the lighter pion mass, which corresponds to couplings of $g_{K^{*}K\pi }=5.02(26)$ and $g_{K^{*}K\pi }=5.03(22)$, respectively.

中文翻译：

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I = 1 / 2S波和P波的Kπ散射以及来自晶格QCD的κ和K *共振

我们提出了弹性同位旋的格子QCD测定$\mathrm{1个}/2$ $\mathrm{小号}$波和 $P$-波 $ķ\pi$ 使用L“ uscher方法将散射振幅作为质心能量的函数。我们对所有不可约表示的总不可动表示进行参数化对有限体积能谱的全局拟合。 $\sqrt{3}\frac{2\pi }{\mathrm{大号}}$; 这包括混合了$\mathrm{小号}$-和 $P$-波浪。考虑了用于能量依赖的几种不同的参数化。我们还确定了散射幅度中最接近的极点的位置，这对应于宽$\kappa$ 共振 $\mathrm{小号}$波和狭窄 ${ķ}^{*}（892）$ 共振 $P$-波。我们的计算是通过$2+\mathrm{1个}$ 两个不同介子质量的动态三叶草费米子 $317.2（2.2）$ 和 $175.9（1.8）$MeV。我们的首选$\mathrm{小号}$-波参数化基于共形图并且包括阿德勒零点；为了$P$对于波，我们使用包括Blatt-Weisskopf势垒因子的标准极点参数化。的$\mathrm{小号}$-波 $\kappa$-共振极位置为$ \ left [0.84（14）-0.338（55）\ ,, \ I \ right] \：{\ rm GeV} $，重质子质量和$ \ left [0.662（88） -0.368（44）\，\ I \ right] \：{\ rm GeV} $（较轻的介子质量）。的$P$-波 ${ķ}^{*}$-共振极位置为$ \ left [0.8951（64）-0.00249（21）\ ,, \ I \ right] \：{\ rm GeV} $，重质子质量和$ \ left [0.8719（82） -0.0132（11）\，\ I \ right] \：{\ rm GeV} $在较轻的介子质量处，它对应于$G_{{ķ}^{*}ķ\pi }=5.02（26）$ 和 $G_{{ķ}^{*}ķ\pi }=5.03（22）$， 分别。