On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses

We study the pole trajectory of the recently established subthreshold negative parity nucleon pole, namely the $N^{\ast }(920)$, with varying pion masses, in the scheme of linear $\sigma$ model with nucleons using the $N\mathrm{/}D$ unitarization method. We find that as the pion mass increases, the pole moves toward the real axis. For larger pion masses, at tree level, the pole falls to a specific point on $u$-channel cut and crosses to the adjacent Riemann sheet defined by the logarithmic $u$ channel cut. At one-loop level, the pole does not meet the $u$-cut up to $m_{\pi }=0.36$GeV. We also re-examined the $\sigma$ pole trajectory and find it in good agreement with Roy equation analysis result.