KLWMIJ Reggeon Field Theory beyond the large $N_c$ limit

Abstract: We extend the analysis of KLWMIJ evolution in terms of QCD Reggeon fields beyond leading order in the $1/N_c$ expansion. We show that there is only one type of corrections to the leading order Hamiltonian discussed in \cite{last}. These are terms linear in original Reggeons and quadratic in conjugate Reggeon operators. All of these have the interpretation as vertices of the "`merging"' type $2\rightarrow 1$, where two Reggeons merge into one. Importantly, the triple Pomeron merging vertex does not emerge from the KLWMIJ Hamiltonian. We show that, although in the range of applicability of the KLWMIJ Hamiltonian these merging terms are subleading in $N_c$, in the dense-dense regime they all become of the same (leading) order in $N_c$. In this regime vertices involving higher Reggeons are enhanced by inverse powers of the coupling constant.