Pomeron loops in zero transverse dimensions
  We analyze a toy model which has a structure similar to that of the recently found QCD evolution equations, but without transverse dimensions. We develop two different but equivalent methods in order to compute the leading-order and next-to-leading order Pomeron loop diagrams. In addition to the leading-order result which has been derived from Mueller's toy model~\cite% {Mueller:1994gb}, we can also calculate the next-to-leading order contribution which provides the $(\alpha_{s}^{2}\alpha Y)$ correction. We interpret this result and discuss its possible implications for the four-dimensional QCD evolution. 
Arif I. Shoshi and Bo-Wen Xiao