CP Violation

So there's some pretty exciting news coming out of Fermilab:
To witness CP violation, physicists study particles to see if there is any difference in the rate of decay between normal particles and their antiparticles. The accepted theory of elementary particles, the standard model, allows for a low level of CP violation—including that revealed in the discoveries of the 1960s and 2000s—but not enough to explain the prevalence of normal matter. So researchers have been trying to find cases in which CP violation is higher. In November, the LHCb team reported that the decay rates differed by 0.8%—some eight times the amount the standard model is generally expected to allow, and perhaps enough to help explain the origin of matter's prevalence over antimatter.
This sort of difference in decay rates is a pretty difficult thing to measure since it's really a very slight difference, and as the article talks about, it's not entirely clear if this actually violates the Standard Model or not. And, even if it did, it's not totally clear where this would take us. Is the difference due to some essential difference between quarks and antiquarks? Are there differences between electrons and positrons as well? Muons and anti-muons? I won't even get into antineutrinos, since they're neutral particle anyway, and the difference that is coming to light from these experiments is likely due to some sort of electrical charge difference.