We present an effective-field-theory calculation of QCD axion emissivity from dense matter beyond the first quark generation
in the context of core-collapse supernovae.
By including the full meson and baryon octets, we evaluate all additive contributions from 134 Compton-like processes
$B_i M \to B_f a$, with $B$ octet baryons and $M$ octet mesons, as well as 7 baryon decays $B_i \to B_f a$, obtaining robust order-of-magnitude bounds on various axial couplings of the axion to light quarks $i,j$, $(\boldsymbol{k}_A)_{ij}$.
Our results reveal strong correlations among diagonal axial couplings ($(\boldsymbol{k}_A)_{11}, (\boldsymbol{k}_A)_{22}, (\boldsymbol{k}_A)_{33}$) and provide stringent direct constraints on flavour violation induced by the axial $a$-$d$-$s$ coupling: $|(\boldsymbol{k}_A)_{23}| \lesssim 10^{-1} - 10^{-2}$. The material presented here is based on Ref. [1].