In this paper (https://arxiv.org/abs/1701.07081), they study the effect of a four-fermion perturbation $H'$ on the SYK model, and they take the form of the perturbation to be $H' = \frac{u}{2}C_{ij}C_{kl}\psi_{i}\psi_{j}\psi_{k}\psi_{l}$, where $C_{ij}$ is also an anti-symmetric Gaussian-distributed random matrix.
They then compute the beta function of $u$ (equation 13)
$$ \beta(u) = \frac{2J^{2}}{\sqrt{\pi}J_{4}}u^{2} $$ where $J$ and $J_{4}$ are positive constants which determine the variances of $C_{ij}$ and $J_{ijkl}$.
From this beta function, they then claim that $H'$ is marginally relevant when $u > 0$ and marginally irrelevant when $u < 0$. But I am confused as to why this is the case. Since $\beta(u) \sim u^{2}$, why would the RG flows depend on the sign of $u$? Shouldn't $H'$ grow for all nonzero values of $u$? How does its sign affect its relevance?
