Semiclassical solution to the BFKL equation with massive gluons

TL;DR

This paper develops a semiclassical method to analyze the high energy behavior of scattering amplitudes in a Yang-Mills theory with massive gluons, simplifying previous numerical approaches and aiding in understanding impact parameter effects.

Contribution

It introduces a semiclassical approach to the BFKL equation with massive gluons, providing analytical solutions that match earlier numerical results and facilitate impact parameter analysis.

Findings

Semiclassical solutions reproduce previous numerical results.

Impact parameter exponential decrease influences high energy asymptotics.

Method can be applied to electroweak theory for experimental predictions.

Abstract

In this paper we proceed to study the high energy behavior of a scattering amplitudes in the Yang-Mills theory with the Higgs mechanism for the gauge boson mass. The spectrum of the $j$-plane singularities of the $t$-channel partial waves, and corresponding eigenfunctions of the BFKL equation in leading log approximation (LLA), were previously calculated by us numerically in arXiv:1401.4671 . Here we develop a semiclassical approach and investigate the influence of the impact parameter exponential decrease, existing in this model, on the high energy asymptotic behaviour of the scattering amplitude. This approach is much simpler than the numerical calculations, and reproduces our earlier numerical results. The analytical (semianalytical) solutions which have been found in this paper, can be used to incorporate correctly the large impact parameter behavior in the framework of CGC/saturation approach. This behaviour is interesting as provides the high energy amplitude for the electroweak theory, which can be measured experimentally.