# Question on “new CNGS/OPERA measurement of neutrino velocity” (hep-ex/1212.1276)

A "new measurement of the limit on muon neutrino velocity with respect to the speed of light " by the OPERA neutrino experiment in collaboration with CERN has become public recently, as preprint http://arxiv.org/abs/1212.1276

The results concerning neutrinos (i.e., not considering anti-neutrinos) are stated there (in particular in the Conclusions) as

[...]
$\delta t_{[nu]} = (0.6 \pm 0.4 (stat.) \pm 3.0 (syst.))$ ns,
giving the limit
$- 1.8 \times 10^{-6} \lt (v_{nu} - c) / c \lt 2.3 \times 10^{-6}$ at 90 % C.L.

Question (1): Can the relation between these two results be made more explicit? How exactly does the result obtained for the quantity $\delta t_{nu}$ "give" the stated limit on the quantity $(v_{nu} - c) / c$?

(Note on v2.71828: A second, subsequent question has been removed for separate posting.)

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Hi user12262 - could you please edit out the second part of this question and post it as a separate question? – David Z Dec 12 '12 at 21:29
Velocity is time/distance, right? And they tell you the distance (i.e. baseline) and by how much the arrival times differ from the expectation, right? So...are you stuck on how one should combine statistical and systematic errors, on how to propagate errors through a division operation or what? As for question two you can use the measured distance and time to determine a speed or the measured time and an assumed velocity to measure the distance or the measured distance and an assumed velocity to measure the time. – dmckee Dec 12 '12 at 21:32
@David Zaslavsky: Since (or as long as) there seems to be a version history attached to the remaining question (1), yes I could edit out the second part and post it separately (or at least some version, after considering replies to question (1)). Of course, the title of the (then remaining) question might be properly altered to "A question on ...". – user12262 Dec 12 '12 at 21:45
Yeah, that's what I'm suggesting. Edit out the second part, post it as a new question, and change the title of each part to be more specific. And of course, all changes are tracked and publicly available. – David Z Dec 12 '12 at 21:47
@dmckee: "Velocity is time/distance"? No: "Speed is distance/duration", where the duration in question is (somewhat misleadingly) often called "time". Now, unfortunately, they haven't given us the TOF value (of the setup being occupied by some particular neutrino, at least on average) explicitly; but at best the value/range of $\delta t$. Nor have they quite given us the applicable distances, e.g. between CNGS "proton beam target" and OPERA "detector element". And the "baseline" estimate of Tab. 1 apparently involved not only "CNGS target" and "OPERA reference" but satellites, theodolites – user12262 Dec 12 '12 at 22:17