Monte Carlo studies of BFKL Physics

Abstract

We study the properties of the BFKL evolution of a (-channel gluon exchange in the high-energy limit. In particular we formulate a solution to the BFKL evolution equation in terms of an explicit sum over emitted gluons, which allows for a Monte Carlo integration of the resulting rapidity ordered multi-gluon phase space. This formulation allows for an introduction of the running of the coupling to the BFKL evolution. More importantly, the Monte Carlo implementation of the solution to the BFKL evolution equation allows for studies of the exclusive final states resulting from the exchange. The full control over the gluon radiation allows for energy and momentum conservation to be observed when calculating the hadronic cross sections. This is in contrast to the standard analytic approach to BFKL physics, which solves the BFKL equation by effectively summing over any number of gluons emitted and integrating over the full rapidity ordered allowed phase space. It is therefore impossible to reconstruct the parton momentum fractions exactly, and thus energy and longitudinal momentum conservation is violated. Although the effect is indeed formally subleading, we show that the numerical impact at present and planned collider energies is very significant. The reduction in parton flux due to the increased energy consumption by the BFKL evolution is sufficient to change the parton level result of an exponential rise of the dijet cross section as a function of the rapidity separation of the leading dijets to a situation much like the LO case. However, we identify the azimuthal correlation between the dijets as an observable sensitive to BFKL effects but more stable under the observation of energy and momentum conservation. We also apply the BFKL MC to a study of dijets at the Tevatron. Finally we consider W + 2-jet production, a process which in the limit of large rapidity separation between the two jets exhibit the same factorisation into two impact factors and a (-channel gluon exchange as dijet production. We identify observables in this setup, for which BFKL effects could be important.