Conservation Laws

Saturday, April 9, 2022

Lepton Number Conservation

Just like how in a chemical reaction electrons are conserved or like how in nuclear reactions nucleons are conserved, the lepton number of a reaction is conserved. Electrons and neutrinos have lepton number $+1$ , positrons and antineutrinos have lepton number $-1$ , and all mesons and baryons have lepton number $0$ .

As an example of lepton number conservation,

$\text{n}\rightarrow\text{p}+\text{e}^-+\overline{\nu_\text{e}}$

has the lepton numbers

$0\rightarrow 0+1+\left(-1\right)$

Lepton number conservation applies to each type of lepton separately. In other words, the electron lepton number must be conserved, the muon lepton number must be conserved, and the tauon lepton number must be conserved. These different lepton numbers are designated $L_\text{e}$ , $L_\mu$ , and $L_\tau$ .

Baryon Number Conservation

Similarly, baryons have baryon number $+1$ , anti-baryons have baryon number $-1$ , and all leptons and mesons have baryon number $0$ . In any process, the total baryon number must remain constant. In particle physics, $B$ is used to represent baryon number, just like how $A$ represented the number of nucleons (which is a subset of baryons).

Strangeness Conservation

Unlike leptons and baryons, mesons are not subjected to a conservation law. For instance, any number of pions can be produced in a reaction. However, there is another quantity conserved with mesons: strangeness, $S$ . In reactions with the K-meson, strangeness is conserved with the electromagnetic and strong interactions (since those both conserve strangeness). However, the weak interaction does not conserve strangeness and so can result in reactions like

$\text{K}^+\rightarrow\mu^++\nu_\mu$

Decays caused by the weak interaction can change the strangeness by one unit. In summary, in processes governed by the strong or electromagnetic interactions, the total strangeness must remain constant. In processes governed by the weak interaction, the strangeness either remains constant or changes by one unit.

The strangeness of an antiparticle has the opposite sign as the particle's strangeness. The strangeness of baryons affects which reactions can occur via the strong versus weak interaction as well.