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 $\omega$-space for $t=0$ coincides with the continuous spectrum for the massless case although the density of its eigenvalues is two times smaller for $\omega >{\omega }_0$, where ${\omega }_0$ is a negative number. We find a simple parametrization for the corresponding eigenfunctions. Because the leading singularity in the $\omega$-plane in this Higgs model for $t=0$ is a fixed cut, the Regge pole contributions could be only for non-physical positive $t$. Hence we can state that the correct behaviour at large $b$ does not influence the main properties of the BFKL equation.

35 pages, 21 figures

References in corpus (1)

• The Pomeranchuk Singularity and Vector Boson Reggeization in Electroweak Theory

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