Question

If neutrino oscillations do occur, will they violate conservation of the various lepton family numbers (\({{\rm{L}}_{\rm{e}}}\),\({{\rm{L}}_{\rm{\mu }}}\), and \({{\rm{L}}_{\rm{T}}}\))? Will neutrino oscillations violate conservation of the total number of leptons?

Short answer

Neutrino oscillations will deviate from the conservation of lepton family numbers but not from the total number.

Step-by-step solution

Definition of Neutrino oscillations.

In case of Neutrino oscillation process neutrino can change itself into any other form spontaneously.

Conservation of the total number of leptons.

The oscillations will violate conservation of lepton family numbers\({{\rm{L}}_{\rm{e}}}\),\({{\rm{L}}_{\rm{\mu }}}\),\({{\rm{L}}_{\rm{\tau }}}\). This is because in neutrino oscillations, a neutrino oscillates between lepton families. For example, a neutrino could oscillate between an electron neutrino\({{\rm{\nu }}_{\rm{e}}}\)that has\({{\rm{L}}_{\rm{e}}}{\rm{ = 1}}\),\({L_\mu } = 0\),\({{\rm{L}}_{\rm{\tau }}}{\rm{ = 0}}\)and a muon neutrino\({{\rm{\nu }}_{\rm{\mu }}}\)that has\({{\rm{L}}_{\rm{e}}}{\rm{ = 0}}\),\({{\rm{L}}_{\rm{\mu }}}{\rm{ = 1}}\),\({{\rm{L}}_{\rm{\tau }}}{\rm{ = 0}}\)which obviously violates conservation of lepton family numbers.

On the other hand, because a lepton is never formed or annihilated during an oscillation - a single neutrino is merely changing lepton families - there will be no violation of the total number of leptons conservation law.