**The Data**

The sum of the three neutrino masses is less than or equal to 110 meV at a 95% confidence level, according to the latest effort to integrate multiple sources of astronomy data including the Planck satellite cosmic microwave radiation background data, the WiggleZ Dark Energy Survey, the Sloan Digital Sky Survey -Data Release 7 (SDSS-DR7) sample of Luminous Red Galaxies (LRG), and Baryon Acoustic Oscillation (BAO) data.

This is confirmed by an independent analysis of the Lyman-α power spectrum from BOSS cited in the paper, which limits the sum of the three neutrino masses to less than or equal to 120 meV at the 95% confidence level.

**Background**

In an inverted hierarchy of neutrino masses, the minimum sum of the three neutrino masses given current neutrino oscillation data is around 98 +/- 1 meV.

As previously noted at this blog, the state of the art measurements of the difference between the first and second neutrino mass eigenstate is roughly 8.66 +/- 0.12 meV, and the difference between the second and third neutrino mass eigenstate is roughly 49.5 +/- 0.5 meV, which implies that the sum of the three neutrino mass eigenstates cannot be less than about 65.34 meV with 95% confidence.

The hypothesis that there are more than three neutrinos that oscillate with each other has also been largely ruled out by experimental data.

**Hypothesis Testing**

Taken together, this data favors the normal neutrino mass hierarchy over the inverted neutrino mass hierarchy, even though the inverted neutrino mass hierarchy is not yet ruled out at a 95% confidence interval.

The body text of the paper does not expressly compare the relative likelihoods of the minimal mass normal hierarchy hypothesis to the minimal mass inverted hierarchy hypothesis, but, eyeballing the graphs with the pertinent data, it appears that the normal hierarchy is many times more likely than the inverted hierarchy.

**Future Experiments**

We need only about a 10% improvement in measurement precision to rule out the inverted neutrino mass hierarchy at the 95% confidence level. We shouldn't be surprised that the neutrinos appear to have a normal mass hierarchy, as this is what we observe in the up-type quarks, the down-type quarks, and the charged leptons as well.

Knowing whether the neutrino mass eigenstates have a normal or inverted hierarchy also increases the certainty with which we can interpret neutrino oscillation data, for example, in an effort to determine the CP violating phase (if any) of neutrino oscillations.

The tight bound on the absolute neutrino masses discussed below also sets firm expectations regarding the expected amount of neutrinoless double beta decay in any particular model that has Majorana mass neutrinos. Current experimental precision needs to improve by more than a factor of ten before it can meaningfully distinguish between Dirac and Majorana mass scenarios.

**Bounds On Absolute Neutrino Masses Given What We Know**

If the neutrinos do have a normal hierarchy, then the experimental bounds on the three neutrino mass eigenstates at the two sigma level based upon the latest data is:

v1: 0 meV to 12 meV absolute precision +/- 6 meV

v2: 8.42 meV to 21.9 meV absolute precision +/- 6.74 meV

v3: 56.92 meV to 72.4 meV absolute precision +/- 7.74 meV

Any higher masses would violate the 110 meV upper bound on the sum of the three neutrino mass eigenstates. So, while absolute neutrino mass has been called an "unsolved problem" we are tantalizingly close to determining it with a precision that is stunning in absolute terms and compares favorably with the precision with which we know the light quark masses in relative terms.

The bound between the minimum and maximum neutrino mass ranges in an inverted mass hierarchy is currently about 4.7 meV (i.e. +/- 2.35 meV for the lightest of the three). If the neutrinos do indeed have an inverted mass hierarchy, the bounds upon the absolute masses are tight indeed.

**An Unambitious Neutrino Mass Prediction**

Given all of the data and the patterns that we see, I personally would be surprised to see anything other than a normal neutrino mass hierarchy with a lightest neutrino mass eigenstate of 2 eV or less, with a mass of 1 meV or less most favored. If that hypothesis is correct, then the neutrino masses would be:

v1: 0 meV to 2 meV

v2: 8.42 meV to 11.9 meV

v3: 56.92 meV to 62.4 meV

and the sum of the three neutrino masses would be not more than 76.3 meV (and not less than 65.34 meV).

**Footnote On Inflation Constraints**

**In other news, the constraints on evidence of certain kinds of gravitational waves in the early universe which are predicted by inflation theories is also tightening considerably. Generally speaking, this data tends to rule out many of the more elaborate inflation scenarios.**

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