Parity doubling from Weinberg sum rules

Abstract

We investigate the relation among slopes and intercepts of Regge trajectories for mesons of a given spin and different parities using large N_c arguments and the matching to perturbative QCD in the deep-Minkowski region. For spin-1 mesons of opposite parities we prove that: a) for large and increasing N_c, the scale \Lambda^{(V,A)} separating the resonance-dominated and the perturbative-saturated region in the channels V,A grows as \sqrt{N_c}; b) to satisfy the Weinberg sum rules the slopes of Regge trajectories for mesons of opposite parities must coincide; c) their intercepts may differ and their difference corresponds to the difference between \Lambda^V and \Lambda^A. Some arguments indicate that this difference should tend to zero as N_c\to\infty.