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4

The main point that you have to always keep in mind is that relevant/irrelevant coupling constants are defined with respect to a fixed point. The standard/naive power counting is done assuming that the fixed point controlling the RG flow is the gaussian. This is true for massless QED and $\phi^4$ theories in four dimensions in the infrared, and for QCD in ...

2

This is a special case of a more general phenomena. Conserved currents never acquire anomalous dimensions, they are protected by the symmetry. If you have a conserved current, you have a symmetry algebra for the theory $$[Q^a,Q^b]=if^{abc}Q_c$$ For this to hold, the charges need to be dimensionless. But the charges are given by ...

2

The renormalization factor $1/Z_S$ that Manohar and Wise discuss in their book is not the renormalization of the coupling constant. It is there to remove divergences that come from the fact that we have inserted an operator that is a product of fields. As I understand their line of reasoning, this is before we discuss a coupling constant at all, so if we add ...

1

In general, derivative couplings lead to momentum-dependencies in scattering amplitudes. This can be seen from the fact that the Fourier transform of a derivative operator corresponds to a multiplication by the relevant momentum. A mass dependence is implicit through by having a momentum, since the momentum of a fermion depends on its mass. In this case, ...

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