Past exam of the particle physics course of the University of Oxford / 2015 / 7 / c / i / Solution

In ${\tau }^{-}\to {\ell }^{-}{\bar{\nu }}_{\ell }{\nu }_{\tau }$, charge and missing four-momentum show an invisible neutral component beyond the visible charged lepton. The distributions are consistent with three-body V-A interaction decay; hadronic modes such as ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$ instead have two-body missing-mass kinematics. Production and decay accounting assigns $L_{\tau }({\tau }^{-})=L_{\tau }({\nu }_{\tau })=1$ and their antiparticles minus one. Searches for wrong-flavour and neutrinoless channels constrain violations. These observations establish a useful approximately conserved tau-family number in ordinary interactions, rather than proving an exact law from missing energy alone.

To establish that the invisible particle is distinct from ${\nu }_e$ and ${\nu }_{\mu }$, combine decay evidence with the absence of unsuppressed tau production by conventional electron- and muon-flavour beams, and direct tau neutrino charged current interactions. DONUT observed the short displaced tau lepton decay in nuclear emulsion after a neutrino interaction. ^[ref] Neutrino oscillation means individual family numbers are not exact conserved quantities during propagation, even though they are an excellent approximation for these local decay assignments.