<< Chapter < Page Chapter >> Page >

Check Your Understanding What is the baryon number of a hydrogen nucleus?

1

Got questions? Get instant answers now!

Lepton number conservation

Lepton number conservation states that the sum of lepton numbers before and after the interaction must be the same. There are three different lepton number     s : the electron-lepton number L e , the muon-lepton number L μ , and the tau-lepton number L τ . In any interaction, each of these quantities must be conserved separately . For electrons and electron neutrinos, L e = 1 ; for their antiparticles, L e = −1 ; all other particles have L e = 0 . Similarly, L μ = 1 for muons and muon neutrinos, L μ = −1 for their antiparticles, and L μ = 0 for all other particles. Finally, L τ = 1 , −1 , or 0, depending on whether we have a tau or tau neutrino, their antiparticles, or any other particle, respectively. Lepton number conservation guarantees that the number of electrons and positrons in the universe stays relatively constant. ( Note: The total lepton number is, as far as we know, conserved in nature. However, observations have shown variations of family lepton number (for example, L e ) in a phenomenon called neutrino oscillations. )

To illustrate the lepton number conservation law, consider the following known two-step decay process:

π + μ + + ν μ μ + e + + ν c + ν μ .

In the first decay, all of the lepton numbers for π + are 0. For the products of this decay, L μ = −1 for μ + and L μ = 1 for ν μ . Therefore, muon-lepton number is conserved. Neither electrons nor tau are involved in this decay, so L e = 0 and L τ = 0 for the initial particle and all decay products. Thus, electron-lepton and tau-lepton numbers are also conserved. In the second decay, μ + has a muon-lepton number L μ = −1 , whereas the net muon-lepton number of the decay products is 0 + 0 + ( −1 ) = 1 . Thus, the muon-lepton number is conserved. Electron-lepton number is also conserved, as L e = 0 for μ + , whereas the net electron-lepton number of the decay products is ( −1 ) + 1 + 0 = 0 . Finally, since no taus or tau-neutrons are involved in this decay, the tau-lepton number is also conserved.

Lepton number conservation

Based on the law of conservation of lepton number, which of the following decays can occur?

( a ) n p + e + ν e ( b ) π μ + ν μ + ν μ

Strategy

Determine the total lepton number for the reactants and products, and require that this value does not change in the reaction.

Solution

For decay (a), the electron-lepton number of the neutron is 0, and the net electron-lepton number of the decay products is 0 + 1 + ( −1 ) = 0 . Since the net electron-lepton numbers before and after the decay are the same, the decay is possible on the basis of the law of conservation of electron-lepton number. Also, since there are no muons or taus involved in this decay, the muon-lepton and tauon-lepton numbers are conserved.

For decay (b), the muon-lepton number of the π is 0, and the net muon-lepton number of the proposed decay products is 1 + 1 + ( −1 ) = 1 . Thus, on the basis of the law of conservation of muon-lepton number, this decay cannot occur.

Significance

Lepton number is conserved in the first reaction, but not in the second. Lepton number conservation constrains what reactions can and cannot occur in nature.

Got questions? Get instant answers now!
Practice Key Terms 3

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 3' conversation and receive update notifications?

Ask