Hadronic Spectrum in the Chiral Large $N_c$ Extension of Quantum Chromodynamics

Abstract

We study Quantum Chromodynamics in the chiral large $N_c$ limit which contains a left-handed Weyl fermion in the fundamental representation, a left-handed Weyl fermion in the two index antisymmetric representation and $(N_c-3)$ left-handed Weyl fermions in the antifundamental representation of the $SU(N_c)$ gauge group. We construct gauge singlet composite operators and study their masses and correlation functions at large $N_c$. It is shown that all hadron masses scale as $\sim N_c^0{n}_q$ where $n_q$ is the number of constituent quarks in the hadron. In addition by simple gluon exchange considerations it is seen that scattering amplitudes between hadrons have the same $N_c$ scaling as the mass of the lightest hadron involved. This is the case provided the hadrons in the scattering amplitude share a sufficiently large number of constituent quarks. The chiral large $N_c$ extension also allows for other non-trivial processes. For instance we consider two different baryonium states that are unique to this extension and that decay via emissions of two- and three-quark hadrons. Also other non-trivial scattering processes are considered. Finally, we study composites made of a mix of left- and right-handed fields. We categorize multiple groups of hadrons within the full spectrum according to their flavor structure. Within these groups all $n$-point functions scale the same.