Permutation group S_N and hadron spectroscopy

We discuss the application of the permutation group S_N to a few problems in hadron physics. In Ref. [11] a method was proposed for matching a quark model Hamiltonian onto the effective Hamiltonian of the 1/N_c expansion, which makes use of the transformation properties of the states and operators under S_N. This method is used in [13] to obtain information about the spin-flavor structure of the quark interaction Hamiltonian from the spectrum of the negative parity L = 1 excited baryons. Assuming the most general 2-body quark Hamiltonian, we derive two correlations among the masses and mixing angles of these states which should hold in any quark model. These correlations constrain the mixing angles, and can be used to test for the presence of 3-body quark interactions. We find that the pure gluon-exchange model is disfavored by data, independently of any assumptions about the hadronic wave functions.