A revised analysis of the Planck satellite data which was released in preprint form late last year reveals a 95% confidence limit on the sum of the three neutrino mass eigenstates of 0.26 eV or less. This compares to 0.84 eV or less based upon early results (the old WMAP limit was 0.66 eV or less). The best fit from CMB and lensing data is about 0.06 eV, which is approximately the minimum value for this quantity based upon the differences in masses between the first and second, and between the second and third mass eigenstates for neutrinos derived from neutrino oscillation data.
Adding BAO data brings the best fit point to one consistent with zero. Effectively, this constrains the high end of the 95% confidence interval and squeezes it more tightly towards the minimum value of 0.06 eV from other data (the floor is somewhat greater in an "inverted neutrino mass hierarchy", although this scenario is not ruled out by the Planck data since it would still have a sum of neutrino mass states of less than 0.26 eV).
The revision is due to reconsideration of how to treat physically impossible outcomes (e.g. a sum of neutrino mass state masses that is less than zero) in the statistical analysis.
This shows excellent agreement between the cosmology data regarding the sum of the neutrino mass states and the neutrino oscillation data regarding the neutrino mass states.
The current cosmology data strongly disfavors the existence of a hypothetical fourth neutrino mass state with a mass of about 1 eV which has been proposed as a solution to the "reactor anomaly", as this would cause the sum of the neutrino mass states to be far higher than the 95% confidence interval for that value, even though the direct CMB measurement of the number of neutrino mass states (Neff) isn't that definitive. (Any such fourth neutrino mass state would also have to be "sterile" because precision electroweak measurements rule out more than three neutrinos with masses of 45 GeV or less that interact via the weak nuclear force.)
A 0.26 eV value would imply a first neutrino mass state of about 65 meV, a second one of about 72 meV and a third of about 114 meV, given the known differences in magnitude between the mass states. A 0.06 eV value which is much more likely would imply absolute masses of about 1 meV, 8 meV and 50 meV.
Thus, realistically, the limits on the absolute value of the first neutrino mass state are about 0 meV to 65 meV, the limits on the absolute value of the second neutrino mass state are about 7 meV to 72 meV, and the limits on the absolute value of the third neutrino mass state are about 49 meV to 114 meV. The low end of these ranges are strongly favored and they are perfectly correlated with each other via the variation in the mass of the first neutrino mass state.
Put another way, the cosmology data allows the lightest neutrino mass state to be as heavy as 65 meV at a 95% confidence interval, but strongly favors a lower value with the best fit value approaching zero.
My best read of the data is that a value of zero for the lightest neutrino mass state is favored by something in excess of 50% of the probability distribution if a physical minimum of 0.06 eV from neutrino oscillation data, rather than 0 eV, from logic and cosmology data alone, is imposed.
Note also that for Planck's purposes, a particle that would ordinarily be called a sterile neutrino with a mass >> 1 eV, is not considered a neutrino, regardless of its other properties. So, while Planck constrains reactor anomaly sterile neutrinos, it does not constrain much heavier warm dark matter keV mass scale sterile neutrinos which it would categorize as "dark matter" rather than as a neutrino.
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Other potentially observable tests of reactor anomaly sterile neutrinos based upon supernova behavior are proposed here.
Fits to the reactor anomaly data are discussed here. One model fits the data by assuming that neutrino mixing values are not fixed by random variables with a particular distribution. This paper confirms that the Planck data disfavor a reactor anomaly sterile neutrino but believe that it could be consistent with a hot dark matter component. This paper describes boundaries on the magnitude of fourth generation sterile neutrino mixing with electron neutrinos. This paper suggests that the reactor anomaly is really a flaw in the standard version of the equation used to describe the quantum mechanical laws governing the movement of neutrinos. This paper argues that the reactor anomaly is the result of underestimates of the experimental uncertainty in the experiments where it is claimed to appear. The KamLAND experiment is working on higher precision tests of the reactor anomaly.
Personally, I suspect that better theory and better experiments will make the reactor anomaly go away with no new physics.
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