## Determination of auxiliary scale in dimensional regularization

My questions are in italics. In the article [1] a dimensional regularization is presented on an electrostatic example of an infinite wire with constant linear charge density λ. It is shown that the direct computation of the scalar potential gives infinity: ϕ(x)=λ4πϵ0∫∞−∞dl|x−l|=λ4πϵ0∫∞−∞dl(x2+y2+(z−l)2)12= =λ4πϵ0∫∞−∞du√x2+y2+u2=∞ But with dimensional regularization in the modified minimal subtraction scheme we get … Read more