Lepton conservation and neutrinos

In reactions involving neutrinos and other particles, it can be useful to use the conservation of lepton number as a means to figure out whether neutrinos or anti-neutrinos are involved. I'll provide a very, very, very brief guide here.

First, what's a lepton? A lepton is a subatomic particle which has half-integer spin and does not participate in strong interactions. In more simple terms, for our purposes, it's not a baryon (proton or neutron), nor a photon. That leaves

charged leptons: electron/positron, muon/anti-muon, tau/anti-tau
uncharged leptons: neutrinos (all versions)

The table below shows the lepton number associated with each lepton.


   Particle      Lepton Number         Particle        Lepton Number
---------------------------------------------------------------------
   electron           1          |   electron neutrino         1
   positron          -1          |   electron anti-neutrino   -1
                                 |
   muon               1          |   muon neutrino             1
   anti-muon         -1          |   muon anti-neutrino       -1
                                 |
   tau                1          |   tau neutrino              1
   anti-tau          -1          |   tau anti-neutrino        -1
---------------------------------------------------------------------

And here's how to use this information: in any reaction, the lepton number must be the same on both sides; in other words, the lepton number is conserved.

Consider beta decay, in which an isolated neutron turns into a proton and an electron. What sort of neutrino must be produced in this reaction?



                       Before                  After
-----------------------------------------------------------------

  Particle             neutron     |   proton, electron, ???
                                   |
                                   |
  Lepton Number           0        |     0   +   1   +   ????
                                   |
                                   |
-----------------------------------------------------------------
  Total Lepton Number     0        =           0
-----------------------------------------------------------------

The "After" side of the equation must include a particle with a lepton number of -1, in order to yield a total lepton number of zero. That means that this reaction must produce an electron anti-neutrino.