# Is there a lepton anti-lepton asymmetry?

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?

• More on leptogenesis. Dec 9 '19 at 18:08
• here is a review up to 2006 of theories arxiv.org/abs/hep-ph/0703087 Dec 10 '19 at 6:12
• – SRS
Jan 2 '20 at 20:27

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.