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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?

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It's as you assume. Nothing forbids this, but in many cases neutrinos are at too low of energy to produce a muon, much less a tau, and so low energy muon and tau neutrinos effectively only participate in the neutral current interaction.

In principle, this can be the case for electron neutrinos as well, but electrons are sufficiently light that it is not unusual for electron neutrinos to have enough energy to produce electrons.

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  • $\begingroup$ Thank's for the fast answer. So for high energy TeV to PeV neutrinos this interaction might become relevant in detectors like SK or IceCube? $\endgroup$ – Katermickie Aug 16 '18 at 15:13
  • $\begingroup$ @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. $\endgroup$ – Chris Aug 16 '18 at 16:18

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