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$$ \pi^{-} \to \tau^{-}+\overline{\nu}_{\tau} $$

So, this interaction (reaction) is supposed to be forbidden. But, can not see what should be wrong here.

Charge is conserved. Baryon number is fine. Even if I check the lepton numbers, everything works.

Do I see something wrong, or I forgot some conservation law?

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There simply isn't enough energy. A tau lepton is heavier than a proton ($1777\,\mathrm{MeV}$), so it can't be a decay product of a pion which only has a mass of about $140 \,\mathrm{MeV}$.

And you can't fix it by boosting the meson to high speed because the same consideration still applies in the rest frame of the pion.

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  • $\begingroup$ Thanks for the reply.@dmckee I see that I need to pay more attention to energies. I thought that barion, charge and lepton numbers could always tell me surely is the interaction possible, Is it then the same if there is kaon going to pion? $$ K^{-} \to \pi^{-} $$ Then, here it should be the same? Kaon has too much energy to decay only to negative pion? $\endgroup$ – solidbastard Jul 3 at 23:56
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    $\begingroup$ Just so you know... it’s “baryon”, not “barion”. (I fixed it in your question, and in your previous question.) $\endgroup$ – G. Smith Jul 4 at 0:10
  • $\begingroup$ My mistake, thanks! @G.Smith :) $\endgroup$ – solidbastard Jul 4 at 0:15
  • $\begingroup$ A single particle of one mass cannot become a single particle of a different mass, because energy would not be conserved. $\endgroup$ – G. Smith Jul 4 at 0:17
  • $\begingroup$ By the way, there are some other conserved or mostly-conserved quantum numbers, like weak isospin. $\endgroup$ – G. Smith Jul 4 at 0:18

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