Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 304 / 3 / b / Solution

Put $d=6-ϵ$. The one-loop two-point bubble has symmetry factor $1/2$ and, after a Feynman parameter and momentum shift, its pole is proportional toCancelling the pole in the minimal subtraction scheme gives, with $ϵ=6-d$,If one defines dimensional regularization by $d=6-2ϵ$, these same poles are written with $2ϵ$ in place of $ϵ$.