 Renormalization-group characteristic solution for a two-point function

For $t=\log (|p|/\mu )$ and $d\bar{g}/dt=\beta (\bar{g})$, the displayed characteristic solution follows from $(-{\partial }_t+\beta {\partial }_g+2{\gamma }_{\varphi })d=0$. It separates the running coupling from the accumulated field-renormalization anomalous dimension. The exponent sign is determined by the precise Callan-Symanzik equation convention.