= Tau-pair electron-muon missing-energy signature
{title2=$e^+e^-\to\tau^+\tau^-\to e^\pm\mu^\mp+\text{invisible recoil}$}
In the modern <weak charged current> interpretation, one allowed assignment is
$$
e^+e^-\to\tau^-\tau^+,\qquad
\tau^-\to e^-\bar\nu_e\nu_\tau,\qquad
\tau^+\to\mu^+\nu_\mu\bar\nu_\tau.
$$
The <electron antineutrino>, <tau neutrino>, <muon neutrino> and <antineutrino> of the <tau neutrino> carry away <energy> and <momentum>. There are four undetected <particles> in this decay assignment. Interchanging which parent decays electronically gives the opposite <electric charge> assignment. Each parent conserves <electric charge> and, in this approximation, total <lepton number>; <four-momentum conservation> applies separately to production and to each <particle decay>.
If $B_e$ and $B_\mu$ denote the corresponding <branching fractions>, independent parent decays give an inclusive mixed-flavour fraction $2B_eB_\mu$. The factor two counts the two assignments to opposite parent charges. For chosen $B_e=B_\mu=1/5$, the mixed fraction is $2/25$, before acceptance and <detection efficiency>. Correlations between the parents' <spins> can affect angular selection even when the fully inclusive <branching fractions> factorize.
The <neutrinos> in that equation are a physical interpretation to test. Neither a deficit in visible <energy> nor two unusual tracks alone establishes their identities or uniquely counts them. Even a compatible <invariant mass> and an angular distribution require <particle identification>, background checks and agreement across further <particle decay> channels. The direct detection milestone for the <tau neutrino> was in 2000, separate from the charged <tau lepton> discovery.
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