CP violation (as I understand it) allows for non-conservation of baryon number, and thus can contribute (at least a little) to the baryon asymmetry in the universe today (far more matter than antimatter).

But have we ever seen baryon number change in the laboratory? Or had almost-but-not-quite-conclusive evidence of it?

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    $\begingroup$ CP violation is something different than B violation. One may exist without the other and vice versa. We have indirectly observed both by seeing that the Universe has an excess of B, a total positive B, which means that since the time when the Universe had B zero or nearly zero, B had to be violated. No direct lab observation of B violation has been made - which effectively means that the proton decay hasn't been observed. $\endgroup$ – Luboš Motl Sep 24 '13 at 4:48

Short answer: nothing has been seen.

Long answer: Questions like this on the experimental limits in particle physics can usually be answered by looking things up in the Particle Data Group's annual Review of Particle Physics. There is a summary online version and an extensive (but free!) print version. EDIT: Here (pdf) is the full section on conservation laws. (And if you are game for a 44 MB pdf download you can get the full 2012 review here.) See page 23 of the linked pdf for the relevant section, though if you trust the standard model the limits on lepton number violation can also be converted into an indirect limit on baryon number violation because $B-L$ is a conserved quantum number in the standard model. Usually people look for $B$ violation in models beyond the standard model because it is exponentially suppressed in the standard model at temperatures below the electroweak phase transition (above the phase transition, at very early times in the universe, $\Delta B=\Delta L$ processes are in thermal equilibrium; but now there is an insurmountable energy barrier to $B$ violating reactions, which can only happen by quantum tunneling at an extremely small (i.e. unobservable) rate).

The full review lists about a dozen odd searches for baryon violation, all of which are limits, i.e. maximum constraints on the rates. No $B$ violating processes have been observed in nature. (Obviously baryogenesis happened somehow in the early universe, but we have no direct evidence for how. By the way, the CP violation in the standard model is in principle able to create baryogenesis above the electroweak phase transition, but it turns out to be numerically far too small to get the right answer. That is why people look for beyond-SM sources of CP violation.)

The PDG limits on $B$ violating decay rates look like $\Gamma(Z\to p e)/\Gamma_{tot} < 1.8\times10^{-6}$ at 95% confidence. That means that the $Z$ boson undergoes this particular $B$ violating decay less than about one in a million times. The exponents for all the processes listed are in the same range, $-5$ to $-8$, so any $B$ violating processes are quite rare and below current detection thresholds.

The most famous $B$ violating process is proton decay, which is stringently constrained. The lifetime of the proton is $>2.1\times 10^{29}$ years. Constraints on individual decay channels are even tighter, for example $\tau(p\to e^+ \pi)>8200\times 10^{30}$ years. Constraints on bound neutron decays are similar. $n\leftrightarrow\bar{n}$ oscillation is constrained to $\gtrsim 10^8$ seconds, a surprisingly weak bound. But then again, neutrons are funny like that. :)

EDIT: Prompted by Lumo's good comment above to clarify the relationship between $B$ and $CP$ violation. They are logically independent things: one can exist without the other. The reason they are often brought up in the same breath is that they are both part of the Sakharov conditions which are needed to dynamically produce a baryon-antibaryon asymmetry in the early universe:

  1. $B$ violation,
  2. $C$ and $CP$ violation,
  3. departure from thermal equilibrium.

The proof that these are necessary conditions for baryogenesis is pretty trivial (see the wiki page) so I won't go into that. But neither are they sufficient conditions - you have to do detailed calculations to work out the asymmetry in a given particle physics model. It turns out that the standard model falls about eight orders of magnitude short in its predicted asymmetry despite having all the conditions 1-3 fulfilled at the electroweak phase transition. This is why people attack the problem hoping to find beyond standard model physics. (A few still hope that the standard model can work if exotic quark matter states get involved in the QCD phase transition somehow. I don't know enough about the QCD phase transition to tell you how reasonable this is, but quark matter proposals have had a checkered history.)


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