Studies on quark-mass dependence of the $N^{\ast }(920)$ pole from $\pi N$ $\chi$PT amplitudes

Abstract

The quark-mass dependence of the $N^{\ast }(920)$ pole is analyzed using $K$-matrix method, with the $\pi N$ scattering amplitude calculated up to $O(p^3)$ order in chiral perturbation theory. As the quark mass increases, the $N^{\ast }(920)$ pole gradually approaches the real axis in the complex $w$-plane (where $w=\sqrt{s}$). Eventually, in the $O(p^2)$ case, it crosses the $u$-cut on the real axis and enters the adjacent Riemann sheet when the pion mass reaches $526\mathrm{MeV}$. At order $O(p^3)$, the rate at which it approaches the real axis slows down; however, we argue that it will ultimately cross the $u$-cut and enter the adjacent Riemann sheet as well. Additionally, the trajectory of the \(N^*(920)\) pole is in qualitative agreement with the results from the linear $\sigma$ model calculation.