Field-renormalization anomalous dimension (${\gamma }_{\varphi }=\frac{1}{2}\mu d\log Z_{\varphi }/d\mu$)

If ${\varphi }_B=Z_{\varphi }^{1/2}{\varphi }_R$, differentiating a renormalized $n$-point function at fixed bare parameters gives $(\mu {\partial }_{\mu }+\beta {\partial }_g+n{\gamma }_{\varphi })G_{n,R}=0$. With this convention the field scaling dimension at a fixed point is its engineering dimension plus ${\gamma }_{\varphi }$. The critical exponent $\eta$ for scalar two-point decay is $2{\gamma }_{\varphi }$.