Scale Anomaly and "Soft" Pomeron in QCD

TL;DR

This paper introduces a non-perturbative QCD approach based on the scale anomaly, explaining the 'soft' Pomeron as a consequence of vacuum energy density, and predicts the Pomeron intercept's value and dependence on N_c and N_f.

Contribution

It presents a novel non-perturbative framework linking the scale anomaly to Regge behavior and the soft Pomeron in high-energy hadronic scattering.

Findings

The Pomeron intercept Delta is approximately 0.08-0.1.

Delta is proportional to (N_f/N_c)^2 for arbitrary N_c and N_f.

In the large N_c limit, Delta remains finite and independent of N_c.

Abstract

We propose a new non-perturbative approach to hadronic interactions at high energies and small momentum transfer, which is based on the scale anomaly of QCD and emphasizes the role of semi-classical vacuum fields. We find that the hadron scattering amplitudes exhibit Regge behavior and evaluate the intercept alpha(0) of the corresponding trajectory. Both the intercept and the scale for the slope of the trajectory appear to be determined by the energy density of non-perturbative QCD vacuum (the gluon condensate). Numerically, we find Delta = alpha(0) - 1 = 0.08 -0.1, consistent with the values ascribed phenomenologically to the ``soft'' Pomeron. For arbitrary numbers of colors N_c and flavors N_f, Delta is found to be proportional to (N_f/N_c)^2; however, in the large N_c (N_f fixed) limit, Delta \sim N_c^0.