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Dimensional regularization is a method of isolating divergencies in scattering amplitudes.
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Explicit computation of singular part of two-loop sunrise diagram
For $\phi^4$, there is two-loop self-energy contribution from sunrise (sunset) diagram.
The integration is
$$
I(p)=\int\frac{d^D p_1}{(2\pi)^D}\frac{d^Dp_2}{(2\pi)^D}\frac{1}{(p_1^2+m^2)(p_2+m^2 …