As far as I have understood, the mass $m$ of a fermion causes a coupling of the both chiralities $\psi_L$ and $\psi_R$. This coupling would induce an oscillation of the chirality within a time scale determined by $\frac 1 m$.
Furthermore, it is known that the weak interaction only couples to the left-handed particles, i.e. only to $\psi_L$.
Combining these two statements, one would have to conclude that the weak interaction of a massive fermion is time dependent, i.e. it is stronger when $\psi_L$ dominates and vanishes completely half an oscillation period later. However, I have never heard about such a strange phenomenon and I conjecture that there's a mistake in my reasoning somewhere.
I'd be grateful if someone could help me find it.