<Asymptotic freedom> means that the gauge <running coupling> tends to zero as the renormalization scale tends to infinity. In the stated convention this occurs when $b_0>0$, namely
$$
\boxed{11N_c-N_f-\frac12N_s>0}.
$$
The high-energy theory then approaches the <Gaussian fixed point> and perturbation theory becomes increasingly accurate.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 305 / 2 / i / Solution

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An asymptotically free theory has a <running coupling> that tends to zero at arbitrarily high energy. Its negative weak-coupling beta function makes short-distance perturbation theory increasingly accurate.

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