A charged pion (π), an unstable particle of mass 140 MeV/c", is known to decay into a muon (µ‡, mass 106 MeV/c²) and a neutrino (μ; we can treat it as massless here). In this decay of pion (→ μ± + V), typically only the muon is detected, the neutrino being an electrically neutral particle that rarely interact with other matter. Properties of neutrinos in this decay are inferred from measured properties of pion and muon. Explain, as conceptually as possible, why it is not possible for a pion to simply decay into a muon, without an associated neutrino. That is, why is this decay, π‡ → µ‡, impossible? (Note: If you happen to know about lepton numbers and neutrino flavors, please give an explanation that does not make use of concepts we have not yet covered.)

A charged pion (π), an unstable particle of mass 140 MeV/c", is known to decay into a muon (µ‡, mass 106 MeV/c²) and a neutrino (μ; we can treat it as massless here). In this decay of pion (→ μ± + V), typically only the muon is detected, the neutrino being an electrically neutral particle that rarely interact with other matter. Properties of neutrinos in this decay are inferred from measured properties of pion and muon. Explain, as conceptually as possible, why it is not possible for a pion to simply decay into a muon, without an associated neutrino. That is, why is this decay, π‡ → µ‡, impossible? (Note: If you happen to know about lepton numbers and neutrino flavors, please give an explanation that does not make use of concepts we have not yet covered.)