Speaker
Description
The Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation ['75-78; 98], describing the rapidity evolution of the pomeron in linear regime, is the cornerstone for entire field of small-$x$ physics. Knowing the kernel at next${}^N$-to-leading order (N${}^N$LO, ${\cal O}(\bar\alpha_s^{N + 1})$), one access the next${}^N$-to-leading-logarithmic resummation (N${}^N$LL $\propto \bar\alpha^{N + l} Y^l$) by solving this equation. At LO, the equation is solved by conformal eigenfunctions, diagonalizing the kernel, which is not true beyond the LO due to running coupling (RC) effects. A great progress has been made towards understanding the properties of the solutions with the RC at NLO [E. Levin '98; Y. Kovchegov, A. Mueller '98; S. Forte et.al. '07; A. Chirilli, Y. Kovchegov '13; A. Grabovsky '13], but still the overall picture seem to be not transparent. The goal of this talk is to demonstrate the consistency of these solutions and construct an ansatz for solving the BFKL equation at any order, preserving hermicity and renormalization group invariance at a fixed order.
