Gluon production in the Color Glass Condensate from BCFW recursion

Abstract

In the Color Glass Condensate framework, the colliding projectiles are described as classical color currents. Gluon production at leading order in the coupling is obtained from the retarded solution of the classical Yang-Mills equations, with these currents acting as sources. However, while the final gluon spectrum is gauge invariant, the classical color field $A^μ$ from which it is obtained is gauge dependent. This makes the intermediate steps of this approach unnecessarily complicated, as some effort is spent to also determine the gauge dependent part of $A^μ$, which is then discarded when one calculates a gauge invariant observable. In this work, we use a generalization of BCFW recursion applicable to off-shell gluons in order to calculate directly the gauge independent gluon production amplitude. This approach allows all manipulations to be performed in terms of gauge invariant amplitudes instead of gauge dependent Feynman diagrams, and therefore provides a gauge agnostic way to obtain the result.