1/N_c and 1/n preasymptotic corrections to Current-Current correlators

TL;DR

This paper calculates preasymptotic corrections to decay constants of scalar and pseudoscalar currents in large N_c theories, using operator product expansion and models, confirming results with numerical solutions and exploring finite N_c effects.

Contribution

It provides model-independent corrections in 1/n and 1/ln n for decay constants, and analyzes the impact of perturbative and finite N_c effects on Regge trajectories.

Findings

Corrections are model-independent in 2D case.

Numerical solutions confirm the analytical corrections.

Finite N_c effects do not fix Regge slope.

Abstract

We obtain the corrections in $1/n$ and in $1/\ln n$ ($n$ is the principal quantum number of the bound state) of the decay constants of scalar and pseudoscalar currents in two and four dimensions in the large $N_c$. We obtain them from the operator product expansion provided a model for the large $n$ mass spectrum is given. In the two-dimensional case the spectrum is known and the corrections obtained in this paper are model independent. We confirm these results by confronting them with the numerical solution of the 't Hooft model. We also consider a model at finite $N_c$ and obtain the associated decay constants that are consistent with perturbation theory. This example shows that that the inclusion of perturbative corrections, or finite $N_c$ effects, to the OPE does not constrain the slope of the Regge trajectories, which remain a free parameter for each different channel.