 Solution

For the asymptotically free beta function, separation of variables givesThe anomalous-dimension integral is elementary:For a reference two-point factor regular and nonzero at the free coupling, $C(r,g(t))\to C(r,0)$, so the large-momentum correction is a power $c/b$ of $\log (p^2/{\mu }^2)$. These are asymptotic freedom and logarithmic two-point scaling from a cubic beta function. If the supplied beta and gamma expressions are leading small-coupling terms rather than exact functions, they fix the leading logarithmic exponent, while subleading corrections and the prefactor depend on higher orders.