BFKL Pomeron with massive gluons

Abstract

We solve the BFKL equation in the leading logarithmic approximation numerically in the Yang-Mills theory with the Higgs mechanism for the vector boson mass generation. It can be considered as a model for the amplitude with the correct behavior of the $s$-channel partial waves at large impact parameters. The Pomeron spectrum of the massive BFKL kernel in the $\ensuremath{\omega}$ space for $t=0$ coincides with the continuous spectrum for the massless case although the density of its eigenvalues is 2 times smaller for $\ensuremath{\omega}>{\ensuremath{\omega}}_{0}$, where ${\ensuremath{\omega}}_{0}$ is a negative number. We find a simple parametrization for the corresponding eigenfunctions. Because the leading singularity in the $\ensuremath{\omega}$ plane in this Higgs model for $t=0$ is a fixed cut, the Regge pole contributions could be only for nonphysical positive $t$. Hence we can state that the correct behavior at large $b$ does not influence the main properties of the BFKL equation.