Pomeron with a Running Coupling Constant: Intercept and Slope

Abstract

The equation for two reggeized gluons with a running QCD coupling constant, proposed earlier on the basis of the bootstrap condition, is investigated by the variational technique in the vacuum channel. The pomeron intercept and slope are calculated as a function of the infrared cutoff parameter $m$ ("the gluon mass"). The intercept depends weakly on $m$ staying in the region $0.3--0.5$ for values of $m$ in the range $0.3--1.0\ GeV$. The slope goes down from $5.0\ GeV^{-2}$ to $0.08\ GeV^{-2}$ in this range. The optimal value of $m$ seems to lie in the region $0.6--0.8\ GeV$ with the intercept $0.35$ and slope $0.35--0.15$. The character of the pomeron singularity: pole or cut, is also discussed.