Archive for September, 2011
If you are reading this blog, then you know I care about the latest results from OPERA. No one knows whether they are right or wrong (most people are highly skeptical, perhaps too much so…) but there is no doubt that this issue has attracted a lot of attention.
SCIENCE magazine does some of the best reporting on science, thanks to the excellent science reporters employed there. So I am happy that SCIENCE will host a live chat about neutrinos traveling above the speed of light. In order to participate, click here:
I hope we all can enjoy it!
I’ve written twice about the contradiction of the OPERA results on high-energy neutrino velocities by the low-energy SN1987a results. I tried to show that this contradiction should not be taken for granted and certainly should not be used to dismiss the OPERA results.
A much better analysis was put forth by Giacomo Cacciapaglia, Aldo Deandrea and Luca Panizzi (arXiv:1109.4980, 23-Sep-2011). The authors made some interesting theoretical remarks regarding possible dispersion relations. I had considered only a quadratic relation (δv/c) = (Eν/M)2 but there are good arguments for other relations, and the authors allowed the exponent to vary (in other words, to be non-integer).
When considering the SN1987a and MINOS data, there are two things to keep in mind:
- the arrival times (or times of flight) of the neutrinos
- the spread of arrival times, or the lack thereof
The authors emphasized the importance of the latter.
For SN1987a, there are a couple dozen events recorded with energies in the 5 – 40 MeV range, and times spreading across 10 or 12 seconds. The range in energies is quite large and should result in a much larger spread of recorded times, if the dispersion relation depends quadratically on the energy. This fact holds quite independently of the near-coincidence of the neutrino signals with the photons coming from SN1987a.
For MINOS, the story is similar. The neutrino energy spectrum peaks around 3 GeV but there is a long tail up to 120 GeV. So if the dispersion is a strong function of the energy, the time structure will be broader than the length of the spill, but this is not observed. If we write δv/c = (1/2)(Eν/M)α, then α should not be large. A fit to the MINOS data favors α < 0.5 which means that the actual observed δv/c from MINOS is in tension with SN1987a. The OPERA results make this tension only worse, even without an analysis of the time structure of the OPERA data. (The authors intend to do such an analysis in the near future.)
So the OPERA, MINOS and SN1987a data don’t really allow an interpretation along the lines of δv/c = (1/2)(Eν/M)α. (My own analysis did not incorporate the constraints from the lack of spread in time of the SN1987a and MINOS data, and hence was much weaker than this analysis.)
This means that the data require a stronger – perhaps bizarre – dispersion relation. An exponential curve does not work, as it turns out, but a smooth step curve, parametrized by a hyperbolic tangent, can be made to work. The position of the threshold would have to be around 1 GeV, and the rise would have to be quite fast, occurring within 0.1 GeV or so. Here is an example of the allowed parameter space, where δ is δv/c, μ controls the rise at the step, which is given by m.
No one claims that a step function parametrized by a hyperbolic tangent is well-motivated or pleasing. The point is that simpler functions don’t work so well. A second point is that the data are still sparse and poorly understood, so ad hoc treatments meant to give relatively soft answers to the question “Does this all make sense?” are justified.
Certainly an actual quantitative analysis like the one by Cacciapaglia, Deandrea and Panizzi is much better than simple dismissive statements one sees in the blogosphere…
Yesterday I tried to point out that the results from OPERA are not necessarily contradicted by the SN1987a results.
Today I have tried to take this simple analysis one step further, by fitting a simple quadratic ansatz for the OPERA results and comparing to the SN1987a and also the MINOS measurement (Phys. Rev. D76 072005 2007).
I assumed that
δv/c = (E/M)2
where E is the energy of the neutrino and M is a phenomenological mass parameter to be determined by measurements. A simple χ2 linear regression analysis indicates that
M = 7.9 ± 1.4 TeV.
I ignored the systematic uncertainties which are fully correlated between the two OPERA measurements. Continuing to take only the statistical uncertainties into account, I find χ2 = 5.9 for one degree of freedom, which is rather poor, but including the systematic uncertainty would improve this value somewhat.
Here is a plot showing the fit:
The fit looks incorrect (it passes close to the second point but is far from the first point) because it is constrained to come from the origin (ie, zero neutrino energy means zero deviation). This is not a parabolic fit — it is a linear fit to 1/M2. The MINOS data were not included in the fit.
Taking the fit as it is, we can compare to SN1987a again:
The SN1987a constraint is indicated by the dashed line – the region above the line is disallowed. Clearly the red line is not excluded by the SN1987a data.
The MINOS data point appears to be inconsistent with the red line, but one has to be quite careful with a double-log plot like this one. The solid error bars are one-sigma limits as reported by MINOS. The lower two-sigma limit, however, encompasses zero and is indicated by the dotted line. As you can see in the linear plot above, the MINOS data is consistent with the red curve at better than the two-sigma level.
This little analysis does not indicate that the OPERA results are correct, of course. The experimental work done is very impressive and I admire the Lyon group for their achievement. But I agree with everyone else, including the OPERA Collaboration, that confirmation by another experiment is needed before the result can be taken to be true. Meanwhile, common statements that SN1987a rules out the OPERA result should be couched in more tentative language, in my opinion.
Everyone is talking about the exciting results from OPERA on the superluminal velocities of neutrinos (arXiv:1109.4897, 23-Sep-2011), which were explained in an excellent CERN EP Seminar given this afternoon. The speaker was Dario Autiero (Institut de Physique Nucleaire de Lyon):
Many people point out that the OPERA result:
δv/c = (2.48 ± 0.28(stat) ± 0.30(syst)) × 10-5,
would seem to be contradicted by constraints coming from Supernove 1987a. viXra quotes this constraint as δv/c < 2 × 10-9 for typical neutrino energies of 10 MeV.
The OPERA analysis was essentially described in a paper by John Ellis, Nicholas Harries, Anselmo Meregaglia, Andre Rubbia, Alexander Sakharov
(arXiv:0805.0253, May 2008) who are motivated by considerations of Quantum Gravity. They consider two scenarios, in which the deviations from c depend linearly or quadratically on the neutrino energy.
Motivated by this idea, and the number quoted on viXra log, I made the following plot. It shows the upper limit on δv/c as a function of the neutrino energy, for the quadratic and the linear assumptions. These limits are drawn as continuous curves (straight lines on a double-log plot). The region above the curve is excluded.
As you can see, the OPERA points are not exluded by the SN1987a limit as cited by viXra log, in the quadratic case. In the linear case, there is apparently a contradiction.
Of course, this does not mean that the OPERA results are right. Only confirmation by an independent experiment, preferably with different metrology techniques, will convince me and everyone else that this astounding result is correct.