Charged Current $\nu_\mu+e^-$ interaction?

Basically I want to know if there is something that forbids an interaction like $$\nu_\mu+e^-\rightarrow\mu^-+\nu_e$$ Having a look at the effective fermi interaction charged current lagrangian $$\mathcal{L}=-\sum_{\alpha,\beta}\frac{G_F}{\sqrt{2}} \left[\overline{\nu}_\alpha\gamma^\mu (1-\gamma^5)l_\alpha\right] \left[\overline{\nu}_\beta\gamma_\mu(1-\gamma^5)l_\beta\right]+\text{h.c.}$$ it should allow such an interaction? However in my textbook (Fundamentals of neutrino physics by Giunti) only electron charged current interactions are displayed. Is this only due to the larger energy needed to produce a muon or is there something I forgot that forbids this interaction?

• @Katermickie Yes. Even lower, really. For instance, the threshold for muon production via $\rm \nu_\mu e\rightarrow\mu\nu_e$ is around $10~\rm GeV$ in vacuum, and CC interactions in matter can occur at energies as low as $m_\mu$ in general. – Chris Aug 16 '18 at 16:18