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The most common version of Sakharov's first condition that I see is "Baryon number violation." Of course this makes sense because without baryon number violation, you can't start out with a matter-antimatter symmetric state and end with a net baryon asymmetry.

However, I've also seen the claim (e.g. slide 16 of Koichi Hamaguchi's talk on Leptogenesis) that actually B-L violation is the true necessary condition. This is because sphaleron processes would wipe out any generated asymmetry. For example, if you have a baryon number violating process but B-L is respected, then you could produce, say, 9 baryons and 9 leptons. But sphaleron processes would transmute the leptons into anti-baryons, which would then wash out the net baryon asymmetry.

Is this a general statement? Is it really true that the necessary Sakharov condition would be B-L violation, rather than just B violation?

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