arXiv 2006.140352020-06hep-lathep-ph

格点量子色动力学的$S$波和$P$波$Kπ$散射和$κ$和$K^*$共振

$I=1/2$ $S$-wave and $P$-wave $Kπ$ scattering and the $κ$ and $K^*$ resonances from lattice QCD

Gumaro Rendon, Luka Leskovec, Stefan Meinel, John Negele, Srijit Paul, Marcus Petschlies, Andrew Pochinsky, Giorgio Silvi, Sergey Syritsyn

备注：: 25 pages, 10 figures
发表信息：: Phys. Rev. D 102, 114520 (2020)
DOI：: 10.1103/PhysRevD.102.114520

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摘要：

本文利用Lüscher方法，用晶格QCD方法确定了弹性同位旋- $1/2$-$S$ -波和$P$ -波的$Kπ$散射振幅随质心能量的变化.我们进行全球适合的$K$矩阵参数化的有限体积能谱的所有不可约表示与总动量高达$\sqrt{3}\frac{2π}{L}$，这包括混合的$S$和$P$波的不代表。几种不同的参数化的能量依赖的$K$矩阵被认为是。我们还确定了散射振幅中最近极点的位置，它们对应于$S$波中的宽$κ$共振和$P$波中的窄$K^*(892)$共振。我们的计算进行了$2+1$动力三叶草费米子两个不同的π介子质量的$317.2(2.2)$和$175.9(1.8)$ MeV。我们首选的$S$波参数化是基于一个共形映射，包括阿德勒零;对于$P$波，我们使用一个标准的极点参数化，包括布拉特-韦斯科普夫障碍因素。发现在较重的π介子质量下，$S$波的$κ$共振极点位置为$\left[0.86(12) - 0.309(50)\,i\right]\:{\rm GeV}$，在较轻的π介子质量下，为$\left[0.499(55)- 0.379(66)\,i\right]\:{\rm GeV}$.发现在较重的π介子质量下，$P$波的$K^*$共振极点位置为$\left[ 0.8951(64) - 0.00250(21)\,i \right]\:{\rm GeV}$，在较轻的π介子质量下为$\left[0.8718(82) - 0.0130(11)\,i\right]\:{\rm GeV}$，分别对应于$g_{K^* Kπ}=5.02(26)$和$g_{K^* Kπ}=4.99(22)$的耦合.

英文摘要：

We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $Kπ$ scattering amplitudes as a function of the center-of-mass energy using Lüscher's method. We perform global fits of $K$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $\sqrt{3}\frac{2π}{L}$; this includes irreps that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the $K$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $κ$ 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 $κ$-resonance pole positions are found to be $\left[0.86(12) - 0.309(50)\,i\right]\:{\rm GeV}$ at the heavier pion mass and $\left[0.499(55)- 0.379(66)\,i\right]\:{\rm GeV}$ at the lighter pion mass. The $P$-wave $K^*$-resonance pole positions are found to be $\left[ 0.8951(64) - 0.00250(21)\,i \right]\:{\rm GeV}$ at the heavier pion mass and $\left[0.8718(82) - 0.0130(11)\,i\right]\:{\rm GeV}$ at the lighter pion mass, which corresponds to couplings of $g_{K^* Kπ}=5.02(26)$ and $g_{K^* Kπ}=4.99(22)$, respectively.

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