Trouble on the horizon?

Well I have been busy with marking and stuff, but between all of that I have managed to get some work done on my phd project.

After spending a whole month on a calculation for the 1 loop correction to the non-abelian rho propagator I discovered something interesting. The diagrams must be added in pairs. a loop and a tadpole diagram go together in making up the contribution to the order g^2 calculation and it is because the these diagrams come in pairs that the self energy is transverse. This was an interesting thing to learn on my own. Whats more troubling though is that the when computing the amplitudes for these diagrams we resorted to the standard technique of dimensional regularization, where we compute the 4 dimensional integral in d dimensions then take the limit where d approaches 4 from below. When we take this limit we find the divergent part of the amplitude. At this stage we adopt a renormalization scheme and this is usually the “MS bar” scheme and we ignore the divergences. Whats troubling about this practice in the case that I am working on is the that divergent term carries a functional dependence, through its coefficient, of the incoming 4-momentum squared.