Monte Carlo Solution to the Balitsky-Fadin-Kuraev-Lipatov Equation for Resummation in Perturbative QCD

A simple solution to the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation is obtained as a series in the number of real gluons emitted with transverse momentum greater than some small cutoff μ. This solution reveals physics inside the BFKL ladder which is hidden in the standard inclusive solution, and lends itself to a straightforward Monte Carlo implementation. With this approach one can explore new useful physical observables, which are shown to be independent of the cutoff μ. In addition, this approach allows the imposition of kinematic constraints (such as energy conservation) which are important at finite energies. The distribution of $\Sigma E_{\perp }$ of particles in a central rapidity bin between two widely spaced jets is presented as an example.