My course on QFT follows Srednicki's book. He derives the running of coupling constants in different theories in the following way: When he uses dimesional regularization (going to [itex]x-\epsilon[/itex] dimensions), he has to introduce a parameter [itex]\mu[/itex] with dimensions of mass in oder to keep the coupling, let's call it [itex]\alpha[/itex], dimensionless. Later, the running of the coupling is determined by demanding that no measurable quantity can depend on [itex]\mu[/itex]. We get a function [itex]\alpha(\mu)[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

Consider now a process. I want to know the coupling strength in that process. Apparently, [itex]\mu[/itex] is linked to the center of mass energy of the process considered. That's how I determine the coupling. My question is now the following: Why is [itex]\mu[/itex] linked to the energy scale of the process I am considering? In the derivation the magnitude of the parameter [itex]\mu[/itex] is completely arbitrary. I asked my professor the same question and he answered that [itex]\mu[/itex] must be linked to the center of mass energy, since this is the only parameter with dimesion of mass, that the considered process can depend on. Since ist depends on [itex]\mu[/itex] and the center of mass energy, these two quantities must be linked. I do not understand that argument: Didn't we demand earlier that physical processes must be independent of the unphysical parameter [itex]\mu[/itex]? So the considered process cannot depend on [itex]\mu[/itex].

I would be very thankful if someone could clear that up for me.

Best regards, physicus

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# Running of the coupling

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