Inside looking out: Probing JIMWLK wave functions with BFKL calculations

Tolga Altinoluk*, Alex Kovner, Eugene Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We investigate the relation between the eigenvalues and eigenfunctions of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) and Jalilian-Marian-Iancu-McLerran- Weigert-Leonidov-Kovner (JIMWLK/KLWMIJ) Hamiltonians. We show that the eigenvalues of the BFKL Hamiltonians are also 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.

Original languageEnglish
Article number074016
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number7
StatePublished - 19 Oct 2010


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