QCD Reggeon Calculus From KLWMIJ/JIMWLK Evolution: Vertices, Reggeization and All

TL;DR

This paper derives a QCD Reggeon Field Theory Hamiltonian from the KLWMIJ evolution, clarifying the reggeization process and providing explicit operators and equations for Reggeons in high-energy QCD.

Contribution

It explicitly connects the KLWMIJ Hamiltonian to QCD Reggeon Field Theory, defining Reggeons and deriving their evolution equations, including the triple Pomeron vertex.

Findings

Derived the RFT Hamiltonian from KLWMIJ evolution.

Provided explicit expressions for Reggeon operators.

Included evolution equations for all Reggeons in dilute-dense scattering.

Abstract

We show explicitly how the high energy QCD evolution generated by the KLWMIJ Hamiltonian can be cast in the form of the QCD Reggeon Field Theory. We show how to reduce the KLWMIJ Hamitonian to physical color singlet degrees of freedom. We suggest a natural way of defining the Pomeron and other Reggeons in the framework of the KLWMIJ evolution and derive the QCD Reggeon Field Theory Hamiltonian which includes several lowest Reggeon operators. This Hamiltonian generates evolution equations for all Reggeons in the case of dilute-dense scattering, including the nonlinear Balitsky-Kovchegov equation for the Pomeron. We also find explicit expressions for the Reggeon conjugate operators in terms of QCD operators, and derive their evolution equations. This provides a natural and unambiguous framework for reggeization procedure introduced in \cite{BW, BE}. The Bartels triple Pomeron vertex is inherited directly from the RFT Hamiltonian. For simplicity in the bulk of the paper we work in the large $N_c$ limit.