Negative parity baryons in the 1/Nc expansion: the three towers of states revisited.

We discuss the compatibility between the quark-shell picture and the meson-nucleon scattering picture
in large $N_c$ QCD for mixed symmetric $\ell$ = 1 states previously analyzed by using a simple Hamiltonian
including operators up to order $\mathcal{O}(N^0_c)$ defined in the standard ground state symmetric core + excited quark
procedure. Here we introduce a Hamiltonian of order $\mathcal{O}(N^0_c)$ defined in a new approach where
the separation of the system into two parts is not required. Three degenerate sets of states (towers) with the same
quantum numbers as in the scattering picture and in the standard procedure are obtained. Thus the compatibility is equally achieved.
The eigenvalues of the presently chosen Hamiltonian also
have simple analytic expressions, depending linearly on the three dynamical coefficients
entering the Hamiltonian.
This reinforces the validity of the new approach
which had already successfully described excited negative parity baryons in a large energy range.