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

Famous quotes containing the words conservation, laws and/or numbers:

    The putting into force of laws which shall secure the conservation of our resources, as far as they may be within the jurisdiction of the Federal Government, including the more important work of saving and restoring our forests and the great improvement of waterways, are all proper government functions which must involve large expenditure if properly performed.
    William Howard Taft (1857–1930)

    Surely it is one of the simplest laws of taste in dress, that it shall not attract undue attention from the wearer to the worn.
    Elizabeth Stuart Phelps (1844–1911)

    Think of the earth as a living organism that is being attacked by billions of bacteria whose numbers double every forty years. Either the host dies, or the virus dies, or both die.
    Gore Vidal (b. 1925)