BFKL ansatz for BK equation in conformal basis

TL;DR

This paper proposes an analytical ansatz for solving the BK equation in the conformal basis at high energies, simplifying the equation and describing the transition between low and high rapidities.

Contribution

It introduces a new analytical ansatz for the BK equation in the conformal basis that captures high-energy behavior and transition regions.

Findings

The ansatz satisfies initial conditions at low energy.

It becomes independent of initial conditions at high energy.

The transition region between small and large rapidities is characterized.

Abstract

The BK equation in the conformal basis is considered and analyzed. It is shown that at high energy a factorization of the coordinate and rapidity dependence should hold. This allows to simplify significantly the from of the equation under discussion. An analytical ansatz for the solution to the BK equation at high energies is proposed and analyzed. This analytical ansatz satisfies the initial condition at low energy and does not depend on both rapidity and the initial condition in the high energy limit. The case of the final rapidity being not too large is discussed and the properties of the transition region between small and large final rapidities have been studied.