I dont know is this a stupid question or not but I wanted to ask

We all familiar with the fact that there must be some more baryons w.r.t antibaryons. Since we do not observe any anti-baryons we claim that

$$N_B - \overline{N}_B = \eta N_{\gamma}$$

Is there a similar argument for the leptons and anti-leptons?

In particle interactions, lepton number is conserved so should someone expect a lepton-antilepton symmetry?


The baryon content of the universe is made of protons and neutrons, nearly all of which exist as hydrogen and helium nuclei. In contrast, the lepton content of the universe has significant contributions from

  • electrons in atoms and neutral plasmas
  • neutrinos produced in stellar cores
  • anti-neutrinos produced in decays of neutron- rich nuclei
  • the cosmic neutrino background, which decoupled thermally from matter earlier in the evolution of the universe than the cosmic microwave background. The one-sentence version is that the neutrino background decoupled when the temperature of the universe, in energy units, fell (somewhere) below the masses of the weak bosons.

The baryon asymmetry, normalized to the microwave background, is $10^{-9}$: there are a billion times more microwave photons than baryons. If the neutrino background has a number density remotely like the microwave background, its own matter-antimatter asymmetry probably has much more bearing on the universe's total lepton matter asymmetry than does the existence of a universe full of matter electrons. We have not yet collected any convincing evidence of interactions with the cosmic (sometimes "relic") neutrinos, so we don't know their matter asymmetry.

To clarify with some examples: If $CP$ were an exact symmetry in the neutrino sector, the C$\nu$B would be equal parts matter and antimatter neutrinos. (I think, but don't know, that annihilation wouldn't change this population much after decoupling; neutrino annihilation is a weak process.) But we don't actually even know whether neutrinos and antineutrinos are different particles. Maybe matter and antimatter neutrinos are distinct, but there's some reason why the relic neutrinos are 100% matter. Or maybe they are 60% antimatter. If the universe's population of leptons is 60% antineutrinos, 40% matter neutrinos, and $10^{-9}$ matter electrons, the matter-antimatter asymmetry for leptons comes entirely from the neutrino background. We haven't observed these relic neutrinos, so we don't know their asymmetry.


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