A recent paper based on data from the T2K experiment which observed electron neutrinos in a muon neutrino beam touts in its abstract the unremarkable and well proven fact that parameter theta13 in the PMNS matrix is non-zero, which it limits to certain counter-factual or speculative assumptions about the value of other PMNS matrix parameters.

More interestingly, if their data is evaluated in light of the already fairly accurately estimated values of theta13, theta23 and the neutrino mass eigenstate differences, the T2K data show a preferences for a CP violating phase of the PMNS matrix that governs neutrino oscillation of about -pi/2 (or equivalently -90 degrees, 270 degrees, or 3/2pi aka pau). This result is insensitive to the question of whether the neutrino masses have a normal or inverted hierarchy and apparently also to the value of theta12.

This is midway between two prior efforts to make a best fit CP violation phase for the PMNS matrix, one of about 1.08pi and the other of about 1.7pi. The average of the three estimates is about 1.42pi. It is also not far removed from the CP violating phase in the CKM matrix of about 1.23pi.

All of the estimates, of course, have significant margins of uncertainty. But, the gross consistency of the three measurements does suggest that a non-zero CP violation phase for the PMNS matrix is likely, and favors one half of the allowed 0 to 2pi range over the other.

## 4 comments:

Thanks for the update.

I think that you hit the nail on the head with the comment that the CP violating phase in the PMNS and CKM matrices might be the same value (or perhaps somehow related.)

If my educated guess is correct, there is ultimately only 1 source of CP violation, and it shows up in both the PMNS and CKM matrices.

My guess is that there can only be one cause of CP violation (and hence T violation) because there is only one time dimension. If there were ultimately two causes of CP violation, we would be in a weird situation in which there were 2 time dimensions.

In other words, the source of time and the source of CP violation in the two matrices are the same.

Also, the fact that neutrinos are a source of CP violation and the fact that neutrinos are everywhere means that CP violations are occurring all around us, and have been occurring even after the quarks settled down into their "mostly" stable states as neutrons and protons.

Any thoughts on the hypothesis that the 1 CP violating term (which happens to only appear in the weak nuclear force) is the cause of the arrow of time?

CP violation is certainly an arrow of time, although perhaps not the only one.

While a single CP violating phase is an interesting possibility, and I strongly suspect that there are functional relationships between the twelve fermion masses, four CKM matrix parameters, and four (or six if Majorana) PMNS parameters, that reduce the total number of parameters, I am agnostic over the question of whether the CP violation phases for the CKM and PMNS are the same.

I do not believe that this would necessarily imply two time dimensions or some such. It could be, for example, that CP violation has sources in both EM and weak interactions and that neutrino violations reflect only one of those two components.

Thanks for the follow up.

Like you, I assume that we will slowly over time decrease the number of free parameters in the Standard Model. (Roughly 23 right now, correct?)

It seems to me that there can only be one arrow of time, and that all of the apparent arrows of time (CP violation, entropy increase, experience, etc...) are related to the CP violation term in the fundamental forces, which is why I suspect that there can only be one underlying source for CP violation (or else we would be effectively living in a world with multiple time dimensions.) There only appears to be one "relativistically-invariant" time dimension, so its underlying source had better be the same or else time could flow in different directions in two different locations at rest next to each other.

My understanding is that there is no CP violation in the gravitational, E&M or the strong nuclear force. (Though, I wouldn't be shocked if it turned out that there was a CP violating term in the strong nuclear force as long as it was somehow related to the CP violating term in the weak nuclear force.) My understanding is that there can't be a CP violating term in E&M because its underlying symmetry is U(1), which only has one Lie symmetry generator (the photon.) The smallest Lie algebra with no-zero Lie brackets would be su(2), which is the Lie symmetry for the weak nuclear force.

You mention E&M and CP violation. Is there something you know that I'm missing, or is that speculation?

Thanks for your input

CORRECTION TO OP:

The CKM CP violating phase is about 1.23 (70some degrees), not 1.23pi.

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