Lepton Number - Conservation Laws For Leptonic Numbers

Conservation Laws For Leptonic Numbers

Many physical models, including the Standard Model of particle physics, rely on the conservation of lepton number (identified by György Marx, Hungarian physicist), in which the lepton number stays the same through an interaction. For example, in beta decay:

\begin{matrix} & n & \rightarrow & p & + & e^{-} & + & {\overline{\nu}}_e \\ L: & 0 & = & 0 & + & 1 & - & 1 \end{matrix}

The lepton number before the reaction is 0 (the neutron, n, is a baryon and therefore there were no leptons before), whereas the total lepton number after the reaction is 0, with the proton having 0, the electron (a lepton) +1, and for the antineutrino (an antilepton) −1. Thus the lepton number is 0 after the decay, and so this quantity is conserved.

The lepton family numbers arise from the fact that lepton number is usually conserved in each leptonic family. For example, the muon almost always decays as:

\begin{matrix} & \mu^{-} & \rightarrow & e^{-} & + & {\overline{\nu}}_e & + & \nu_{\mu} \\ L: & 1 & = & 1 & - & 1 & + & 1 \\ L_e: & 0 & = & 1 & - & 1 & + & 0 \\ L_{\mu}: & 1 & = & 0 & + & 0 & + & 1 \end{matrix}

thus preserving the electronic and muonic numbers. This means that a lepton family number conservation law exist for each one of Le, Lμ, and Lτ.

Read more about this topic:  Lepton Number

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