- #1

Elmo

- 38

- 6

- TL;DR Summary
- Should the renormalization scale in loop amplitudes be assigned a value or should it be removed via an on-shell subtraction scheme counterterm ?

I want some clarification on what is done about the ##\mu^{2\epsilon}## renormalization scale parameter in loop amplitudes. I am under the impression that it shows up to restore the mass dimension of an amplitude when the loop momentum integral is reduced from 4 to ##4-2\epsilon## dimensions. As such upon expanding in powers of the regulator, one ends up with ##\ln(\mu/m)##.

I also know that physical observables should be independent of ##\mu## but its unclear to me how this is achieved. Some texts say that you simply choose a value for ##\mu## while others like MD Schwartz (Ch 19) imply that adding an on-shell subtraction scheme counterterm diagram to the loop diagram gets rid of both the divergence AND the renormalization scale term.

But this is not a feature of every subtraction scheme like MS or MSbar.

I am confused as to what approach should one take, are there any specific requirements or conditions when choosing a value for the renormalization scale or any particular subtraction scheme ?

I also know that physical observables should be independent of ##\mu## but its unclear to me how this is achieved. Some texts say that you simply choose a value for ##\mu## while others like MD Schwartz (Ch 19) imply that adding an on-shell subtraction scheme counterterm diagram to the loop diagram gets rid of both the divergence AND the renormalization scale term.

But this is not a feature of every subtraction scheme like MS or MSbar.

I am confused as to what approach should one take, are there any specific requirements or conditions when choosing a value for the renormalization scale or any particular subtraction scheme ?