  We explore the Mellin representation of correlation functions in conformal
field theories in the weak coupling regime. We provide a complete proof for a
set of Feynman rules to write the Mellin amplitude for a general tree level
Feynman diagram involving only scalar operators. We find a factorised form
involving beta functions associated to the propagators, similar to tree level
Feynman rules in momentum space for ordinary QFTs. We also briefly consider the
case where a generic scalar perturbation of the free CFT breaks conformal
invariance. Mellin space still has some utility and one can consider
non-conformal Mellin representations. In this context, we find that the beta
function corresponding to conformal propagator uplifts to a hypergeometric
function.
