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Light cone perturbation theory has become an essential tool to calculatecross sections for various small-$x$ dilute-dense processes such as deepinelastic scattering and forward proton-proton and proton-nucleus collisions.Here we set out to do one loop calculations in an explicit helicity basis inthe four dimensional helicity scheme. As a first process we calculate lightcone wave function for one gluon emission to one-loop order in Hamiltonianperturbation theory on the light front. We regulate ultraviolet divergenceswith transverse dimensional regularization and soft divergences with using acut-off on longitudinal momentum. We show that when all the renormalizationconstants are combined, the ultraviolet divergences can be absorbed into thestandard QCD running coupling constant, and give an explicit expression for theremaining finite part.

The one loop gluon emission light cone wave function