# Puzzled by a new result on neutrino speeds

In a paper appearing today on arXiv, Wie et al. have used the close coincidence of the time of arrival of gamma rays from GRBs and the detection of single 3-30 TeV neutrinos at the IceCube observatory, to say that the velocity difference between neutrinos and photons is no bigger than $$| v-c | < 2.5\times 10^{-18} c.$$

Leaving aside whether these are genuine coincidences, this means the Lorentz factor of these neutrinos is $\gamma >4.4\times 10^{8}$, and for a neutrino energy of 3 Tev, means that the neutrino rest mass energy is $< 6.8$ keV.

The authors do not calculate this mass and do not comment on the neutrino rest mass. My question is surely we already know (from cosmological considerations) that the rest mass of neutrinos is (much) less than 6.8 keV so is this result in any way noteworthy, or am I missing a bigger picture?

• In the first case, this should be closed as homework-like, while the question of whether or not this is a new sharpest bound is easily answered by looking at the Wikipedia page on neutrino's. – Danu Mar 26 '16 at 9:51
• @Danu I've removed the first part, since I'm pretty sure my numbers (extracted from the paper) are correct. I don't usually look for comment on a new research result in wikipedia. – Rob Jeffries Mar 26 '16 at 10:40
• @RobJeffries OK. The bounds provided by other things such as indeed cosmology or KamLAND-Zen (for a Majorana mass) are indeed much more stringent, as can be seen on the Wikipedia page. They're on the order of $0.1$ eV (Planck bounded the sum to be $\sim 0.3$ eV). Given this, can you tell me what exactly you'd like an answer to address? (PS: Your numbers were of course correct ;-) ) – Danu Mar 26 '16 at 11:24
• @Danu Is there something about a constraint on the speed of a neutrino (and I think this is the most stringent constraint) that tells us something different to an upper limit to the neutrino mass? If not, then why is this finding at all important? – Rob Jeffries Mar 26 '16 at 11:48
• What role would neutrino oscillations play in this limit? – Lewis Miller Mar 26 '16 at 13:51

Let's turn it around and ask a different question. Is there another direct measurement of the neutrino speed that sets such a tight limit? (Admittedly, the directness is contingent on the coincidence representing both a common source and negligible delay between the gammas and the nus at the source, but just taking that as a given arguendo.)

It might be significant in that sense even if the mass limit set is rather uninteresting.

And indeed, the authors write in the summary

We showed that significant improvements can be obtained on limits on the neutrino velocity, the violation of Lorentz invariance, and the accuracy of the EEP, by using the observed time delays between the neutrinos and photons.

They also discuss some other limits that are set by the measurement (I think they are taking the conditions above as a given here, though I haven't read in enough detail to be sure).

• arguendo ! Must try to use that in a paper. – Rob Jeffries Mar 27 '16 at 7:33

It looks like the authors emphasize model-independence as an advantage of their approach. This sounds reasonable. I would think the result is useful, even if not very impressive.