I am considering the following one loop virtual correction in the DIS process.(adsbygoogle = window.adsbygoogle || []).push({});

where I have a quark of momentum ##p## coming in, emitting a gluon before interacting with a photon of momentum ##q## to produce a fermionic propagator with momentum ##p+q##. My question is, in the red box, I have an on shell initial or final state quark ##p^2=0## but in the green box I have an off shell fermionic quark propagator ##p^2 \neq 0##.

So, in my equations, in particular upon evaluation of the loop integral $$\int d^D l \frac{\text{Tr}( \not p \gamma^{\nu} (\not p + \not q) \dots)}{p^2 (p+q)^2 (p-l)^2}$$ where the denominators are all off shell terms, in simplifying the numerator (the trace results in dot products of all the momenta scales in the problem) would I use ##p^2=0## or ##p^2 \neq 0##?

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# On shell and off shell simultaneously?

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