$q$ given by $$\begin{aligned}
q = \frac{\lambda^{1/2}(s,m^2_l,M^2_l)}{2\sqrt{s}}\, ,\, \textrm{and Im(q)}>0\, .\end{aligned}$$

In addition, we evaluate the couplings $g_i$ of the states obtained to the different channels defined such that, close to the pole $M_R$ we have $$T_{ij} = \frac{g_i g_j}{\sqrt{s}-M_R} \, ,$$ and we also evaluate $g_iG_i$, which for $s$-wave gives the strength of the wave function at the origin [@gamermann].

In Table \[res2\] we show the poles that we obtain for the $J^P={1/2}^-$ sector for different values of the cutoff $q_{max}$. We only show the results with the pseudoscalar-baryon interaction. This sector decouples from the vector-baryon one, where the states are obtained degenerate in $J^P=1/2^-, 3/2^-$ . We will come back to this sector later on.

   $q_{max}$         600                  650                  700               750               800
  ----------- ----------------- ----------------------- ----------------- ----------------- ------------------
                $3065.4+i0.1$    ${\bf 3054.05+i0.44}$   $3038.13+i1.78$   $3016.21+i6.02$   $2989.69+i16.24$
               $3114.22+i3.75$   ${\bf 3091.28+i5.12}$   $3067.71+i4.12$   $3046.24+i3.83$   $3027.75+i2.19$

  : Poles in $J^P={1/2}^-$ sector from pseudoscalar-baryon interaction. (Units: MeV).

\[res2\]

We can see that we always get two states in the range of the masses observed experimentally. The strategy followed in these calculations is to fine tune the cutoff to adjust the pole position to some experimental data. We see that if we take $q_{max}=650$ MeV the results 