The BFKL Pomeron Calculus in zero transverse dimensions: summation of Pomeron loops and generating functional for the multiparticle production processes

Abstract

In this paper we address two problems in the BFKL Pomeron calculus in zero transverse dimensions: the summation of the Pomeron loops and the calculation of the processes of multiparticle generation. We introduce a new generating functional for these processes and obtain the evolution equation for it. We argue that in the kinematic range given by $1\ll \ln (1/{\text{as}}^2)\ll \text{as}Y\ll \frac{1}{\text{as}}$, we can reduce the Pomeron calculus to exchange of non-interacting Pomerons with the renormalized amplitude of their interaction with the target. Therefore, the summation of the Pomeron loops can be performed using Mueller, Patel, Salam and Iancu approximation.

Comments: 20 pp. 8 figures