PX156 - F3 - leptons

properties

• leptons don't carry colour charge

• therefore don't feel the strong force

• since the leptons have either $T_W=\frac{1}{2}$ (neutrinos), or $T_W=-\frac{1}{2}$ (charged leptons)

• the weak force (W boson) only sees two variations of leptons

• masses of neutrinos are unknown but $<30meV/c^2$

lepton number

• 'lepton number' is defined for each lepton

• the associated lepton has a lepton number of $+1$, and its anti-particle has a lepton number of $-1$

• $L_e:$ electron lepton number

  • $+1:e^{-},{\nu }_e$
  • $-1:e^{+},{\overline{\nu }}_e$
  • $0:$ otherwise

• $L_{\mu }:$ muon lepton number

  • $+1:{\mu }^{-},{\nu }_{\mu }$
  • $-1:{\mu }^{+},{\overline{\nu }}_{\mu }$
  • $0:$ otherwise

• $L_{\tau }:$ tau lepton number

  • $+1:{\tau }^{-},{\nu }_{\tau }$
  • $-1:{\tau }^{+},{\overline{\nu }}_{\tau }$
  • $0:$ otherwise

• global lepton number: $L=L_e+L_{\mu }+L_{\tau }$

  • it is always always conserved

• eg:

- $Q:-1\to -1+0+0:$ conserved
- $L_e:0\to 0+0+0:$ conserved
- $L_{\mu }:0\to +1+(-1)+0:$ conserved
- $L\tau :+1\to 0+0+1:$ conserved
- $L:+1\to +1+(-1)+1:$ conserved
- $T_w:-\frac{1}{2}\to -\frac{1}{2}+(-\frac{1}{2})+\frac{1}{2}:$ conserved

• good theoretical reasons why $Q,T_w,L$ are conserved

• nothing to motivate the conservation of $L_e,L_{\mu },L_{\tau }$ separately

• experiments test for lepton number conservation by looking for decay

  • ${\mu }^{-}\to e^{-}+\gamma :$ probability$<{10}^{-10}$