# Dropping yukawa contributions to beta functions when corresponding fermion is inactive?

Consider the two loop beta function for the strong coupling $g_3$, schematically (see eq.98 in https://arxiv.org/pdf/1307.3536.pdf): $$\frac{dg^2_3}{d \ln\mu^2} = O(g_3^4) + O(g_3^6) + O(g_3^4\:g_2^2)+ O(g_3^4\:g_1^2)+ O(g_3^4\:y_t^2) + O(g_3^4\:y_b^2),$$ where $g_1$,$g_2$ are the electroweak couplings and $y_b$, $y_t$ are the bottom and top quark yukawas (other contributions are neglected).

The 1 loop contribution is $O(g_3^4)=(\frac{2}{3}n_f - 11)g_3^4$, where $n_f$ is the number of 'active' quarks. I know that if I was integrating the beta function at scale $m_b<\mu<m_t$ I would have $n_f=5$ as the top is not active. My question is however: for $\mu<m_t$ should I also drop all contributions involving $y_t$ in the beta functions for $\{g_1,g_2,g_3,y_b\}$, e.g. the $O(g_3^4\:y_t^2)$ term above?