Lepton numbers...? Particle Physics!?

Question

Ca anyone tell me whether anti-neutrinos all have lepton number of -1?


Furthermore could anyone explain why a pi0 decays into two virtual photons?

Thank you :D

Answer 1

No, I don't think that anti-neutrinos always have lepton numbers of -1. There is a lot of controversy about this. Of course, any assertion of empirical results should be qualified by the phrase "within experimental accuracy". Some people have suggested that there is something "weird" about Eisberg and Resnik's line of reasoning (quoted from the 2nd Edition of "Quantum Physics"),but compare their comments with the following remarks taken from "Subatomic Physics" by Frauenfelder and Henley:

"Is the assignment of a lepton number meaningful and correct?
We first notice that a positive answer defies intuition.
Altogether four neutrinos exist, electron and muon neutrino
and their two anti-particles. Neutrinos have no charge or
mass; they possess only spin and momentum. How can such a simple particle appear in four versions? If, on the other
hand, it turns out that the neutrino and anti-neutrino are
identical, then the assignment of a lepton number is wrong...

To be honest, I'm not sure pi0 decay so I can't comment on that part of your question.

Answer 2

According to the Standard Model there are two different families of fundamental particles: the quarks and the leptons. Three types of neutral leptons, called neutrinos, and three types of charged leptons are known to exist. One type is the old, familiar electron. Another is the muon, an unstable particle with mass 210 times that of the electron. And finally there is the tau-lepton, which is roughly 3600 the mass of the electron and was first discovered in a particle accelerator in 1974. For each of t he charged leptons there is an associated neutrino, and together the charged lepton and its associated neutrino make up its generation or flavor. Of course, each of these particles also has an anti-particle. Leptons have half integer spin and therefore obey fermion conservation laws. One conserved quantity is lepton number. A lepton number L_e, L_\mu, L_\tau of +1 is given to each generation of lepton, and -1 to each flavor of antilepton. However, theory does not necessitate that lepton number always be conserved. Instead, to this point, lepton flavor conservation is an experimental fact. This project is a test of that fact made possbile by the accurate detectors and high luminosity of the Kaons at the Tevatron (KTeV)experiment. For this pro ject Monte Carlo simulations of the particular lepton flavor violating decay \pi^0 \rightarrow \mu e have been made and data analysis performed to enable a search of the data from KTeV, which should enable a tightening of the conservation rule by severa l orders of magnitude if no violation is found.

Pi0 decays ;-
The following general theorem is formulated: The matrix element for the decay of spin-zero mesons with mass m into two leptons with masses μ1 and μ2 respectively contains only terms proportional to μ1/m and μ2/m, if in the open polygonal arc of lepton lines the number of matrices γμ plus the number of internal lines (SF-functions) is odd. There can also be terms proportional to μi/m if virtual leptons with μi≠μ1, μ2 appear in the arc. Application of this theorem to the reaction π0→e++e- leads to a ratio of the one pair to the two pair decay of the order (μe/mπ0)2∼10-5. A priori one would expect this ratio to be of the order one. Furthermore, the theorem provides a more general basis for the discussion of the relative probability of the reactions π→μ+ν and π→e+ν.