Comments on the 2nd order bootstrap relation

TL;DR

This note defends the 2nd order bootstrap relation within the BFKL framework by clarifying the formalism and demonstrating that the strong bootstrap condition and the η(q)-based solving ansatz are valid at least for the quark component of the next-to-leading contribution. It shows that the LO and NLO bootstrap conditions can be satisfied, clarifies the relation between the bootstrap formalism and the irreducible kernel Kr, and confirms that the quark part of the NLO trajectory and kernel derived from the ansatz agrees with independent calculations. The work thus strengthens the consistency of the Reggeized-gluon picture at NLO and supports the proposed potential underlying the BFKL dynamics. The findings bolster confidence in the completeness of the NLO potential and its compatibility with unitarity-based approaches.

Abstract

The 2nd order bootstrap relation is discussed in view of the recent critics by F.Fadin, R.Fiore y A.Papa. It is shown that the strong bootstrap condition and the anzatz to solve it used in our earlier paper are valid at least for the quark part of the next-to-leading contribution.