Parity doubling from Weinberg sum rules

TL;DR

This paper explores the relationships between Regge trajectories of mesons with different parities using large N_c QCD arguments, proving conditions for their slopes and intercepts to satisfy Weinberg sum rules and analyzing their behavior as N_c increases.

Contribution

It provides a theoretical proof that the slopes of Regge trajectories for mesons of opposite parity must coincide to satisfy Weinberg sum rules, and discusses the behavior of their intercepts and the scale separation in large N_c QCD.

Findings

Slopes of Regge trajectories for opposite parity mesons must be equal.

Intercept differences relate to the scale separation between resonance and perturbative regions.

The scale mbda^{(V,A)} grows as mbda^{(V,A)}  with N_c, and intercept differences tend to zero as N_c .

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.