Inside looking out: probing JIMWLK with BFKL calculations

TL;DR

This paper explores the relationship between BFKL and JIMWLK/KLWMIJ Hamiltonians, showing that BFKL eigenvalues are also eigenvalues of the latter, and investigates implications for reggeized gluon exchange and bootstrap conditions.

Contribution

It demonstrates the exact correspondence of BFKL eigenvalues with those of KLWMIJ/JIMWLK Hamiltonians and analyzes the impact on reggeized gluon exchange and bootstrap conditions.

Findings

BFKL eigenvalues are also eigenvalues of KLWMIJ/JIMWLK Hamiltonians.

First correction to BFKL wave function identified as impact factor for shadowing.

Bootstrap condition is automatically satisfied within the KLWMIJ framework.

Abstract

We investigate the relation between the eigenvalues and eigenfunctions of the BFKL and JIMWLK/KLWMIJ Hamiltonians. We show that the eigenvalues of the BFKL Hamiltonians are also {\it exact} eigenvalues of the KLWMIJ (and JIMWLK) Hamiltonian, albeit corresponding to possibly non normalizable eigenfunctions. The question whether a given eigenfunction of BFKL corresponds to a normalizable eigenfunction of KLWMIJ is rather complicated, except in some obvious cases, and requires independent investigation. As an example to illustrate this relation we concentrate on the color octet exchange in the framework of KLWMIJ Hamiltonian. We show that it corresponds to the reggeized gluon exchange of BFKL, and find first correction to the BFKL wave function, which has the meaning of the impact factor for shadowing correction to the reggeized gluon. We also show that the bootstrap condition in the KLWMIJ framework is satisfied automatically and does not carry any additional information to that contained in the second quantized structure of the KLWMIJ Hamiltonian. This is an example of how the bootstrap condition inherent in the t-channel unitarity, arises in the s-channel picture.