Reggeized Gluons with a Running Coupling Constant

TL;DR

This paper develops a running-coupling generalization of the two-reggeized-gluon (pomeron) equation in the vacuum channel by enforcing the bootstrap condition for gluon reggeization. The analysis introduces a generalized kernel K and trajectory ω tied together through nonlinear integral relations via a single momentum-dependent function η(q); asymptotics in the ultraviolet yield a ω and an interaction that scale like $\log\log q^2$, while confinement is modeled by an effective gluon mass m. A key finding is that the pomeron intercept is strongly reduced relative to the fixed-c coupling BFKL result, with Δ in the range $0.15 \lesssim Δ \lesssim 0.17$ for reasonable $m/\Lambda$ values, and the limit $m=\Lambda$ reproducing the BFKL behavior in a formal sense. These results suggest the running coupling framework can preserve essential infrared robustness while producing a softer high-energy behavior, potentially aligning with phenomenological soft-pomeron descriptions. The work highlights the sensitivity of high-energy QCD Regge behavior to confinement-scale modeling and provides a variational method to estimate the intercept in the presence of a running coupling.

Abstract

The equation for two reggeized gluons in the vacuum channel is generalized to take into account the running QCD coupling constant on the basis of the bootstrap condition for gluon reggeization. Both the gluon trajectory as a function of momentum and the interaction as a function of distance grow like $\log\log$ in the ultraviolet. The resulting equation depends on the confinement region. With a simple parametrization of its influence by an effective gluon mass the pomeron intercept turns out much smaller than for a fixed coupling constant (the BFKL pomeron).