标题： 介子-重子散射长度在重子手征微扰理论中不包含湮灭图的$p^4$阶情况 显示英文标题

标题： Meson-baryon scattering lengths without annihilation diagrams to order $p^4$ in heavy baryon chiral perturbation theory

摘要： 我们计算了没有湮灭图的介子和重子过程的阈值 $T$矩阵： $\pi^{+}\Sigma^{+}$, $\pi^{+}\Xi^0$, $K^+p$, $K^+n$, 和 $\bar{K}^0\Xi^0$在重子有效理论的手征微扰理论的四阶。 通过将最小二乘法和贝叶斯拟合应用于非物理格点QCD数据，我们通过微扰和非微扰迭代方法确定了低能常数。 通过使用这些低能常数，我们在这些拟合中得到了物理散射长度。 在微扰方法中，散射长度的值在四阶时趋于收敛。 五种通道的散射长度是通过取四种不同拟合方法的中位数得到的，分别为$a_{\pi^+\Sigma^+}=-0.16\pm 0.07\,\text{fm}$，$a_{\pi^+\Xi^0}=-0.04\pm0.04\,\text{fm}$，$a_{K^+p}=-0.41\pm 0.11\,\text{fm}$，$a_{K^+n}=-0.19\pm 0.10\,\text{fm}$，和$a_{\bar{K}^0\Xi^0}=-0.30\pm 0.07\,\text{fm}$，其中不确定度是通过取中位数与统计误差极端值之间的最大偏差来保守估计的。 显示英文摘要

摘要： We calculate the threshold $T$ matrices of the meson and baryon processes that have no annihilation diagrams: $\pi^{+}\Sigma^{+}$, $\pi^{+}\Xi^0$, $K^+p$, $K^+n$, and $\bar{K}^0\Xi^0$ to the fourth order in heavy baryon chiral perturbation theory. By performing least squares and Bayesian fits to the non-physical lattice QCD data, we determine the low-energy constants through both perturbative and non-perturbative iterative methods. By using these low-energy constants, we obtain the physical scattering lengths in these fits. The values of the scattering lengths tend to be convergent at the fourth order in the perturbative method. The scattering lengths for the five channels, obtained by taking the median values from four different fitting approaches, are $a_{\pi^+\Sigma^+}=-0.16\pm 0.07\,\text{fm}$, $a_{\pi^+\Xi^0}=-0.04\pm0.04\,\text{fm}$, $a_{K^+p}=-0.41\pm 0.11\,\text{fm}$, $a_{K^+n}=-0.19\pm 0.10\,\text{fm}$, and $a_{\bar{K}^0\Xi^0}=-0.30\pm 0.07\,\text{fm}$, where the uncertainties are conservatively estimated by taking the maximum deviation between the median and extreme values of the statistical errors.