**New Neutrino Physics Data**

The latest neutrino physics data favors a normal mass hierarchy over an inverted mass hierarchy for neutrinos at a statistically insignificant 1.2 sigma level (roughly 2-1 odds in favor of normal v. inverted mass hierarchy).

The data favor a CP violation phase of 3/2pi (i.e. 270 degrees) but no CP violation is a possibility that is within the 90% confidence interval of the results. Some earlier estimates of the CP violating parameter are here.

The new estimates of theta23 and of the difference in mass between the second and third neutrino mass states confirms prior estimates.

The new data also continue to constrain the parameter space of a fourth light neutrino species, which looks increasingly unlikely on a variety of fronts.

**The Muon Anomalous Magnetic Moment**

In other physics news, there is lots of work being done to refine the hadronic light by light contribution to the muon anomalous magnetic moment (aka "muon g-2"). While this is only one small part of about eight different sets of calculations that go into the final number, this part is the source of the lion's share of the uncertainty in the current theoretical prediction of this physical constant which is at a three sigma tension with the experimentally measured result. There is a roughly 10% uncertainty in the hadronic light by light contribution to the muon anomalous magnetic moment, while many other contributions to the calculations (which make up most of the result) have uncertainties on the order of parts per million.

Despite this tension, in both absolute and percentage terms, the theoretical results and experimental result are both extremely close to each other. The theoretical result has a current 0.5 parts per million uncertainty. The experimental uncertainty is currently similar, but new measurements in the process of being made will bring the experimental uncertainty to 0.1 parts per million. So, the odds are pretty good that the tension between theory and experiment that we are seeing right now arises because either the current theoretical estimate, or the current experimental measurement, or both, have understated margins of error. It is hard to even devise a beyond the Standard Model theory that produces just the right amount of subtle discrepancy from the Standard Model theoretical prediction although many papers have been written trying to do so (usually in the context of SUSY models).

It could be that fixing the QCD uncertainty in the current theoretical estimate could produce a new theoretical prediction that could be reconciled with the experimental data, eliminating one or the more glaring tensions between theory and experiment in Standard Model physics and closing the door to many new Beyond the Standard Model possibilities.

As background, most of the calculations that go into determining the anomalous magnetic moment of the muon involve straight forward and extremely precisely known electroweak force factors. But, there is some probability that a muon will decay into quarks and back, and determining the precisely impact of that possibility is very hard because the precision of QCD calculations is profoundly smaller than the precision of electric and weak force calculations (largely because quarks are confined making their low energy interactions impossible to measure directly).

Most of the recent work focuses on how to identify ways to find parts of the calculation that are exactly equivalent to specific measurable properties of bound mesons and baryons that can be substituted into the calculation which would otherwise have to be done from first principals, since we can measure the properties of bound hadrons with much greater precision than we can the properties of the quarks and gluons that are their components.

**Meson Physics**

**The same conference proceedings that discuss the hadronic light by light calculations linked above also discusses experimental bounds on dark photons, and on a new fifth force that would act only on quarks.**

The bounds on dark photons that interact with Standard Model particles are quite strict (something that disfavors a certain class of self-interacting dark matter models).

The bounds on a fifth leptophobic force with existing data show that any such force would have to be 100,000 times weaker than the strong force and 1000 times weaker than the electromagnetic force. The relevant discussion also discusses how some targeted searches in new experiments, that would be little extra burden in experiments already planned, could tighten this only modestly model dependent bound considerably.

These bounds on a leptophobic fifth force are unexpectedly strict given the considerable uncertainties that exist in most quantitative applications of QCD - for example, we can only theoretically estimate the proton mass from first principals to an accuracy of about 1%.

## 2 comments:

Andrew,

I read this post and re-read your post from April 2013. Thanks for keeping track of what's going on in the field.

I just wanted to make a slight correction to your phrasing.

You mention 180deg as maximal CP violation, but this is a little misleading because, if the CP violation phase is 180deg (pi radians), then there is no CP violation. (e to the power i*pi is a purely real number, and PMNS matrix is symmetric with respect to a CP exchange.)

Maximal CP violation occurs when the phase is 90deg or 270 deg (and assuming there are no degenerate neutrino masses.) Interestingly from the right most graph of Figure 4 of the paper you reference, the best fit to the data is a normal hiieracrchy with a CP violating phase of 270deg...which implies maximal CP violation.

However, a value of 180deg (hence, no CP violation) is still possible within the 1 sigma uncertainty level (68% certainty.)

We need to wait for a meta-analysis of data from multiple research groups in order to state with 5 sigma certainty that the CP violating phase is not 0deg or 180 deg.

With the experiments currently in the planning and construction stage, it will be about four to ten years at the earliest before we can rule out, or confirm, a zero CP violation phase. There simply isn't enough data from all of the experiments combined right now, even combined, to get a CP results that is significant even at the 2 sigma level, and won't be for several years.

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