We calculate the $T$-matrices of elastic pion-nucleon ($\pi N$) scattering up to fourth order in SU(3) heavy baryon chiral perturbation theory. The baryon mass in the chiral limit $M_0$ and the pertinent low-energy constants are determined by fitting to empirical $\pi N$ phase shifts below 200 MeV pion laboratory momentum in the physical region. The scattering lengths and scattering volumes are also extracted from the chiral amplitudes, and turn out to be in good agreement with those of other approaches and the available experimental values. On the basis of the various phase shifts and the threshold parameters, the convergence of the chiral expansion is analyzed in detail. A good convergence for $\pi N$ scattering observables is obtained when working up to fourth order. In addition, we extend the fit to 250 MeV pion laboratory momentum, and obtain also a good description of the empirical $S$- and $P$-wave phase shifts.

中文翻译：

---

在 SU(3) 重重子手征扰动理论中，π-核子散射到 p4 阶

我们计算了在 SU(3) 重重子手征扰动理论中散射到四阶的弹性π-核子 ($\pi N$) 的 $T$-矩阵。手性极限 $M_0$ 中的重子质量和相关的低能量常数是通过拟合经验 $\pi N$ 相移来确定的，该相移低于物理区域中低于 200 MeV 的 pion 实验室动量。散射长度和散射体积也从手征振幅中提取，结果与其他方法和可用实验值非常吻合。在各种相移和阈值参数的基础上，详细分析了手征展开的收敛性。当工作到四阶时，可以获得 $\pi N$ 散射可观测量的良好收敛。此外，我们将拟合扩展到 250 MeV pion 实验室动量，