View source for Measurements of neutrino speed

{{Use dmy dates|date=March 2023}}
'''Measurements of neutrino speed''' have been conducted as [[tests of special relativity]] and for the determination of the [[mass]] of [[neutrino]]s. Astronomical searches investigate whether light and neutrinos emitted simultaneously from a distant source are arriving simultaneously on Earth. Terrestrial searches include [[time of flight]] measurements using synchronized clocks, and direct comparison of neutrino speed with the speed of other particles.

Since it is established that neutrinos possess mass, the speed of neutrinos of [[kinetic energy|kinetic energies]] ranging from [[electronvolt|MeV]] to GeV should be slightly lower than the [[speed of light]] in accordance with [[special relativity]]. Existing measurements provided upper limits for deviations from light speed of approximately 10<sup>−9</sup>, or a [[Parts-per notation|few parts per billion]]. Within the [[margin of error]] this is consistent with no deviation at all.

== Overview ==
[[File:RelNeutrinoSpeed.svg|thumb|350px|Neutrino speed as a function of relativistic [[kinetic energy]], with neutrino mass < 0.2 eV/c².
{| class=wikitable style="text-align:center"
|style="border-right:2px solid black"| '''Energy'''||10 eV||1 KeV||1 MeV||1 GeV||1 TeV
|-
|style="border-right:2px solid black; padding-right:10px;"| <math>|v-c|/c</math>||<math>\scriptstyle \lesssim10^{-4}</math>||<math>\scriptstyle\lesssim10^{-8}</math>||<math>\scriptstyle\lesssim10^{-14}</math>||<math>\scriptstyle\lesssim10^{-20}</math>||<math>\scriptstyle\lesssim10^{-26}</math>
|}]]

It was assumed for a long time in the framework of the [[standard model]] of [[particle physics]] that [[neutrino]]s are massless. Thus, they should travel at exactly the speed of light, according to [[special relativity]]. However, since the discovery of [[neutrino oscillation]]s, it is assumed that they possess some small amount of mass.<ref>{{cite journal |author=J. Beringer ([[Particle Data Group]]) |year=2012 |title=Neutrino Properties – Review of Particle Physics |journal=Physical Review D |volume=86 |issue=1 |page=010001 |doi=10.1103/PhysRevD.86.010001|url=http://pdg.lbl.gov/2013/listings/contents_listings.html|bibcode = 2012PhRvD..86a0001B |display-authors=etal|doi-access=free |hdl=10481/34377 |hdl-access=free }}</ref> Thus, they should travel slightly slower than light, otherwise their [[Tests of relativistic energy and momentum|relativistic energy]] would become infinitely large. This energy is given by the formula:

:<math>E=\frac{mc^{2}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}</math>,

with ''v'' being the neutrino speed and ''c'' the speed of light. The neutrino mass ''m'' is currently estimated as being 2 [[electronvolt|eV]]/c², and is possibly even lower than 0.2 eV/c². According to the latter mass value and the formula for relativistic energy, relative speed differences between light and neutrinos are smaller at high energies, and should arise as indicated in the figure on the right.

Time-of-flight measurements conducted so far investigated neutrinos of energy above 10 MeV. However, velocity differences predicted by relativity at such high energies cannot be determined with the current precision of time measurement. The reason why such measurements are still conducted is connected with the theoretical possibility that significantly larger deviations from light speed might arise under certain circumstances. For instance, it was postulated that neutrinos might be some sort of [[faster-than-light|superluminal]] particles called [[tachyon]]s,<ref>{{cite journal |author1=Chodos, Alan |author2=Hauser, Avi I. |author3=Alan Kostelecký, V. |year=1985 |title=The Neutrino as a Tachyon |journal=Physics Letters B |volume=150 |issue=6 |page=431 |doi= 10.1016/0370-2693(85)90460-5|bibcode = 1985PhLB..150..431C |hdl=2022/20737 |hdl-access=free }}</ref> even though others criticized this proposal.<ref>{{cite journal |author1=Hughes, Richard J. |author2=Stephenson, G. J. |year=1990 |title=Against tachyonic neutrinos |journal=Physics Letters B |volume=244 |issue=1 |pages=95–100 |doi=10.1016/0370-2693(90)90275-B|bibcode = 1990PhLB..244...95H |url=https://zenodo.org/record/1258487 }}</ref> While hypothetical tachyons are thought to be compatible with [[Lorentz invariance]], superluminal neutrinos have also been studied in Lorentz invariance violating frameworks as motivated by speculative variants of [[quantum gravity]], such as the [[Standard-Model Extension]] according to which [[Lorentz-violating neutrino oscillations]] can arise.<ref name=diaz>{{cite journal |author1=Díaz, Jorge S. |author2=Kostelecký, V. Alan |title=Lorentz- and CPT-violating models for neutrino oscillations|journal=Physical Review D|volume=85|issue=1 |year=2012|doi=10.1103/PhysRevD.85.016013|pages=016013|arxiv=1108.1799|bibcode = 2012PhRvD..85a6013D |s2cid=55890338 }}</ref> Besides time-of-flight measurements, those models also allow for [[#Indirect determinations of neutrino speed|indirect determinations of neutrino speed]] and other [[modern searches for Lorentz violation]]. All of those experiments confirmed Lorentz invariance and special relativity.

== Fermilab (1970s) ==

[[Fermi National Accelerator Laboratory|Fermilab]] conducted in the 1970s a series of terrestrial measurements, in which the speed of [[muon]]s was compared with that of neutrinos and antineutrinos of energies between 30 and 200 GeV. The Fermilab narrow band [[Accelerator neutrino|neutrino beam]] was generated as follows: 400-GeV [[proton]]s are hitting the target and causing the production of secondary beams consisting of [[pion]]s and [[kaon]]s. Then they are decaying in an evacuated decay tube of 235 meter length. The remaining [[hadron]]s were stopped by a secondary dump, so that only neutrinos and some energetic muons can penetrate the earth- and steel shield of 500 meter length, in order to reach the [[particle detector]].

Since the protons are transferred in bunches of one [[nanosecond]] duration at an interval of 18.73&nbsp;ns, the speed of muons and neutrinos could be determined. A speed difference would lead to an elongation of the neutrino bunches and to a displacement of the whole neutrino time spectrum. At first, the speeds of muons and neutrinos were compared.<ref>{{cite journal |author=P. Alspector|title=Experimental Comparison of Neutrino and Muon Velocities |volume=36 |issue=15| year=1976  |journal=Physical Review Letters|doi=10.1103/PhysRevLett.36.837|pages=837–840|bibcode = 1976PhRvL..36..837A|display-authors=etal|url=https://authors.library.caltech.edu/6406/1/ALSprl76.pdf }}</ref>
Later, also antineutrinos were observed.<ref>{{cite journal |author=Kalbfleisch|title=Experimental Comparison of Neutrino, Antineutrino, and Muon Velocities |volume=43 |issue=19| year=1979  |journal=Physical Review Letters|doi=10.1103/PhysRevLett.43.1361|pages=1361–1364|bibcode = 1979PhRvL..43.1361K |last2=Baggett |first2=Neil |last3=Fowler |first3=Earle |last4=Alspector |first4=Joshua |display-authors=etal}}</ref>
The upper limit for deviations from light speed was:

:<math>\frac{|v-c|}{c}<4\times10^{-5}</math>.

This was in agreement with the speed of light within the measurement accuracy (95% [[confidence level]]), and also no energy dependence of neutrino speeds could be found at this accuracy.

== Supernova 1987A ==

The most precise agreement with the speed of light ({{As of|2012|lc=on}}) was determined in 1987 by the observation of electron antineutrinos of energies between 7.5 and 35 MeV originated at the [[Supernova 1987A]] at a distance of 157000 ± 16000 [[light year]]s. The upper limit for deviations from light speed was:

:<math>\frac{|v-c|}{c}<2\times10^{-9}</math>,

thus more than 0.999999998 times the speed of light. This value was obtained by comparing the arrival times of light and neutrinos. The difference of approximately three hours was explained by the circumstance, that the almost noninteracting [[Supernova neutrinos|neutrinos]] could pass the supernova unhindered while light required a longer time.<ref>{{cite journal |author=Hirata|year=1987 |volume=58 |title=Observation of a neutrino burst from the supernova SN1987A|journal=Physical Review Letters|doi=10.1103/PhysRevLett.58.1490|pages=1490–1493|bibcode = 1987PhRvL..58.1490H |issue=14 |pmid=10034450 |display-authors=etal|doi-access=free}}</ref><ref>{{cite journal |author=Bionta|year=1987 |volume=58 |title=Observation of a neutrino burst in coincidence with supernova 1987A in the Large Magellanic Cloud|journal=Physical Review Letters|doi=10.1103/PhysRevLett.58.1494|pages=1494–1496|bibcode = 1987PhRvL..58.1494B |issue=14 |pmid=10034451 |display-authors=etal|doi-access=free}}</ref><ref>{{cite journal |author=Longo, Michael J.|title=Tests of relativity from SN1987A|journal=Physical Review D|volume=236|issue=10|year=1987 |pages=3276–3277|doi=10.1103/PhysRevD.36.3276|pmid=9958094|bibcode = 1987PhRvD..36.3276L }}</ref><ref>{{cite journal |author=Stodolsky, Leo|title=The speed of light and the speed of neutrinos|journal=Physics Letters B|volume=201|issue=3|year=1988 |pages=353–354|doi=10.1016/0370-2693(88)91154-9|bibcode = 1988PhLB..201..353S }}</ref>

== MINOS (2007) ==
The first terrestrial measurement of the absolute transit time was conducted by [[MINOS]] (2007) at Fermilab. In order to generate neutrinos (the so-called [[NuMI]] [[Accelerator neutrino|beam]]) they used the Fermilab Main Injector, by which 120-GeV-protons were directed to a [[graphite]] target in 5 to 6 batches per spill. The emerging [[meson]]s decayed in a 675 meter long decay tunnel into muon neutrinos (93%) and muon antineutrinos (6%). The travel time was determined by comparing the arrival times at the MINOS near- and far detector, apart from each other by 734&nbsp;km. The clocks of both stations were synchronized by [[GPS]], and long [[optical fiber]]s were used for signal transmission.<ref name=minos>{{cite journal |author=MINOS collaboration |year=2007 |issue=7 |pages=072005 |title=Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam |volume=76 |journal=[[Physical Review D]] |arxiv=0706.0437 |bibcode=2007PhRvD..76g2005A|doi=10.1103/PhysRevD.76.072005|s2cid=14358300 }}</ref>

They measured an early neutrino arrival of approximately 126&nbsp;ns.  Thus the relative speed difference was <math>\scriptstyle (5.1\pm2.9)\times10^{-5}</math> (68% confidence limit). This corresponds to 1.000051±29 times the speed of light, thus apparently faster than light. The major source of error were uncertainties in the fiber optic delays. The statistical significance of this result was less than 1.8[[standard deviations|σ]], thus it was not significant since 5σ is required to be accepted as a scientific discovery.

At 99% confidence level it was given<ref name=minos />

:<math>-2.4\times10^{-5}<\frac{v-c}{c}<12.6\times10^{-5}</math>,

a neutrino speed larger than 0.999976c and lower than 1.000126c. Thus the result is also compatible with subluminal speeds.

== OPERA (2011, 2012) ==

=== Anomaly ===
{{Main|Faster-than-light neutrino anomaly}}

In the [[OPERA experiment]], 17-GeV [[Accelerator neutrino|neutrinos]] have been used, split in proton extractions of 10.5&nbsp;μs length generated at [[CERN]], which hit a target at a distance of 743&nbsp;km. Then pions and kaons are produced which partially decayed into muons and muon neutrinos ([[CERN Neutrinos to Gran Sasso]], CNGS). The neutrinos traveled further to the [[Laboratori Nazionali del Gran Sasso]] (LNGS) 730&nbsp;km&nbsp;away, where the OPERA detector is located. GPS was used to synchronize the clocks and to determine the exact distance. In addition, optical fibers were used for signal transmission at LNGS. The temporal distribution of the proton extractions was statistically compared with approximately 16000 neutrino events. OPERA measured an early neutrinos arrival of approximately 60 nanoseconds, as compared to the expected arrival at the speed of light, thus indicating a neutrino speed faster than that of light. Contrary to the MINOS result, the deviation was 6σ and thus apparently significant.<ref>{{cite arXiv|author=OPERA collaboration|title=Measurement of the neutrino velocity with the OPERA detector in the CNGS beam|eprint=1109.4897v1|date=22 September 2011|class=hep-ex}}</ref><ref>{{cite web|author=Giulia Brunetti|title=Neutrino velocity measurement with the OPERA experiment in the CNGS beam|url=http://operaweb.lngs.infn.it:2080/Opera/ptb/theses/theses/Brunetti-Giulia_phdthesis.pdf|publisher=Dissertation|year=2011|accessdate=24 November 2011}}{{Dead link|date=October 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref name=PrRel>{{cite web|title=OPERA experiment reports anomaly in flight time of neutrinos from CERN to Gran Sasso |publisher=CERN press release |url=http://press.web.cern.ch/Press/PressReleases/Releases2011/PR19.11E.html |date=23 February 2012 |accessdate=23 February 2012 |url-status=dead |archiveurl=https://web.archive.org/web/20120317155256/http://press.web.cern.ch/press/PressReleases/Releases2011/PR19.11E.html |archivedate=17 March 2012 }}</ref>

To exclude possible statistical errors, CERN produced bunched proton beams between October and November 2011. The proton extractions were split into short bunches of 3&nbsp;ns at intervals of 524&nbsp;ns, so that every neutrino event could be directly connected to a proton bunch. The measurement of twenty neutrino events again gave an early arrival of about 62 ns, in agreement with the previous result. They updated their analysis and increased the significance up to 6,2σ.<ref>{{cite arXiv|author=OPERA collaboration|title=Measurement of the neutrino velocity with the OPERA detector in the CNGS beam|eprint=1109.4897v2|date=18 November 2011|class=hep-ex}}</ref><ref>{{cite web|title=New Tests Confirm The Results of OPERA on the Neutrino Velocity, But It Is Not Yet The Final Confirmation|publisher=INFN press release|url=http://www.interactions.org/cms/?pid=1031226|date=18 November 2011|accessdate=18 November 2011}}</ref>

In February and March 2012, it was shown that there were two mistakes in the experimental equipment: An erroneous cable connection at a computer card, making the neutrinos appearing faster than expected. The other one was an oscillator out of its specification, making the neutrinos appearing slower than expected. Then the time of arrival of cosmic high-energy muons at OPERA and the co-located LVD detector between 2007 and 2008, 2008–2011, and 2011–2012 were compared. It was found out that between 2008 and 2011, the cable connector error caused a deviation of approximately 73&nbsp;ns, and the oscillator error caused ca. 15&nbsp;ns in the opposite direction.<ref name=seminar>LNGS seminar (28 March 2012): [http://agenda.infn.it/materialDisplay.py?materialId=slides&confId=4896 LNGS results on the neutrino velocity topic]</ref><ref>{{cite journal |author=LVD and OPERA collaboration|title=Determination of a time-shift in the OPERA set-up using high energy horizontal muons in the LVD and OPERA detectors|journal=The European Physical Journal Plus|volume=127|issue=6|year=2012|pages=71|doi=10.1140/epjp/i2012-12071-5|arxiv=1206.2488|bibcode = 2012EPJP..127...71A |s2cid=118387598}}.</ref>
This and the measurement of neutrino velocities consistent with the speed of light by the ICARUS collaboration (see [[#ICARUS (2012)|ICARUS (2012)]]), indicated that the neutrinos were probably not faster than light.<ref name=cernfinal>{{cite web|title=Neutrinos sent from CERN to Gran Sasso respect the cosmic speed limit |publisher=CERN press release |url=http://press.web.cern.ch/Press/PressReleases/Releases2011/PR19.11E.html |date=8 June 2012 |accessdate=8 June 2012 |url-status=dead |archiveurl=https://web.archive.org/web/20120317155256/http://press.web.cern.ch/press/PressReleases/Releases2011/PR19.11E.html |archivedate=17 March 2012 }}</ref>

=== End result ===
Finally, in July 2012 the OPERA collaboration published a new analysis of their data from 2009 to 2011, which included the instrumental effects stated above, and obtained bounds for arrival time differences (compared to the speed of light):

:<math>\delta t=6.5\pm7.4\ (\mathrm{stat.}){\scriptstyle {+8.3\atop -8.0}}\ (\mathrm{sys.})</math> nanoseconds,

and bounds for speed differences:

:<math>\frac{v-c}{c}=(2.7\pm3.1\ (\mathrm{stat.}){\scriptstyle {+3.4\atop -3.3}}\ (\mathrm{sys.}))\times10^{-6}</math>.

Also the corresponding new analysis for the bunched beam of October and November 2011 agreed with this result:

:<math>\delta t=-1.9\pm3.7\ (\mathrm{stat.})</math> nanoseconds

Although at the extremes of error these results still allow for superluminal neutrino velocities, they are predominantly consistent with the speed of light, and the <math>10^{-6}</math> bound for the speed difference is more precise by one order of magnitude than previous terrestrial time-of-flight measurements.<ref>{{cite journal|author=OPERA collaboration|title=Measurement of the neutrino velocity with the OPERA detector in the CNGS beam|journal=Journal of High Energy Physics|issue=10|pages=93|year=2012|arxiv=1109.4897|doi=10.1007/JHEP10(2012)093|volume=2012|bibcode = 2012JHEP...10..093A |s2cid=17652398}}</ref>

== LNGS (2012) ==
Continuing the OPERA and ICARUS measurements, the [[Laboratori Nazionali del Gran Sasso|LNGS]] experiments [[Borexino]], [[Large Volume Detector|LVD]], OPERA and ICARUS conducted new tests between 10 and 24 May 2012, after CERN provided another bunched beam rerun. All measurements were consistent with the speed of light.<ref name=cernfinal /> The 17-GeV muon neutrino beam consisted of 4 batches per extraction separated by ~300ns, and the batches consisted of 16 bunches separated by ~100ns, with a bunch width of ~2ns.<ref name=borexino />

=== Borexino ===

The Borexino collaboration analyzed both the bunched beam rerun of Oct.–Nov. 2011 and the second rerun of May 2012.<ref name=borexino>{{Cite journal|author=Borexino collaboration|title=Measurement of CNGS muon neutrino speed with Borexino|journal=Physics Letters B|volume=716|issue=3–5|pages=401–405|year=2012|doi=10.1016/j.physletb.2012.08.052|arxiv=1207.6860|bibcode = 2012PhLB..716..401A }}</ref>
For the 2011 data, they evaluated 36 neutrino events and obtained an upper limit for time of flight differences:

:<math>\delta t=-6.5\pm7\ (\mathrm{stat.}) \pm6\ (\mathrm{sys.})</math> nanoseconds.

For the May 2012 measurements, they improved their equipment by installing a new analogue small–jitter triggering system and a geodetic GPS receiver coupled to a [[Rubidium|Rb]] clock.<ref name=Caccianiga>{{Cite journal|author=Caccianiga|title= GPS-based CERN-LNGS time link for Borexino|journal=Journal of Instrumentation|volume=7|pages=P08028|year=2012|doi=10.1088/1748-0221/7/08/P08028|arxiv=1207.0591|bibcode = 2012arXiv1207.0591C|issue=8 |s2cid= 52217499|display-authors=etal}}</ref> They also conducted an independent high precision geodesy measurement together with LVD and ICARUS. 62 neutrino events could be used for the final analysis, giving a more precise upper limit for time of flight differences<ref name=borexino />

:<math>\delta t=0.8\pm0.7\ (\mathrm{stat.}) \pm2.9\ (\mathrm{sys.})</math> nanoseconds,

corresponding to

:<math>\frac{|v-c|}{c}<2.1\times10^{-6}</math> (90% C.L.).

=== LVD ===

The [[Large Volume Detector|LVD]] collaboration first analyzed the beam rerun of Oct.–Nov. 2011. They evaluated 32 neutrino events and obtained an upper limit for time of flight differences:<ref name=lvd12>{{Cite journal|author=LVD collaboration|title=Measurement of the velocity of neutrinos from the CNGS beam with the Large Volume Detector |journal=Physical Review Letters|volume=109|issue=7|pages= 070801|year=2012|doi=10.1103/PhysRevLett.109.070801|arxiv=1208.1392|bibcode = 2012PhRvL.109g0801A|pmid=23006352 |s2cid=2563908 }}</ref>

:<math>\delta t=3.1\pm5.3\ (\mathrm{stat.}) \pm8\ (\mathrm{sys.})</math> nanoseconds.

In the May 2012 measurements, they used the new LNGS timing facility by the Borexino collaboration, and the geodetic data obtained by LVD, Borexino, and ICARUS (see above). They also updated their [[Scintillation counter]]s and the [[Trigger (particle physics)|trigger]]. 48 neutrino events (at energies above 50 MeV, average neutrino energy was 17 GeV) have been used for the May analysis, improving the upper limit for time of flight differences<ref name=lvd12 />

:<math>\delta t=0.9\pm0.6\ (\mathrm{stat.}) \pm3.2\ (\mathrm{sys.})</math> nanoseconds,

corresponding to

:<math>-3.8\times10^{-6}<\frac{v-c}{c}<3.1\times10^{-6}</math> (99% C.L.).

=== ICARUS ===
After publishing the analysis of the beam rerun of Oct.–Nov. 2011 (see [[#ICARUS (2012)|above]]), the ICARUS collaboration also provided an analysis of the May rerun. They substantially improved their own internal timing system and between CERN-LNGS, used the geodetic LNGS measurement together with Borexino and LVD, and employed Borexino's timing facility. 25 neutrino events have been evaluated for the final analysis, yielding an upper limit for time of flight differences:<ref>{{Cite journal|author=ICARUS collaboration|title=Precision measurement of the neutrino velocity with the ICARUS detector in the CNGS beam |journal=Journal of High Energy Physics|issue=11|pages=49|year=2012|doi=10.1007/JHEP11(2012)049|arxiv=1208.2629|bibcode = 2012JHEP...11..049A|volume=2012 |s2cid=51160473 }}</ref>

:<math>\delta t=0.18\pm0.69\ (\mathrm{stat.}) \pm2.17\ (\mathrm{sys.})</math> nanoseconds,

corresponding to

:<math>\frac{v-c}{c}=(0.7\pm2.8\ (\mathrm{stat.})\pm8.9\ (\mathrm{sys.}))\times10^{-7}</math>.

Neutrino velocities exceeding the speed of light by more than <math>1.6\times10^{-6}c</math> (95% C.L.) are excluded.

=== OPERA ===
After the correction of the initial results, OPERA published their May 2012 measurements as well.<ref>{{Cite journal | author=OPERA collaboration|title=Measurement of the neutrino velocity with the OPERA detector in the CNGS beam using the 2012 dedicated data | journal=Journal of High Energy Physics|volume=2013 | issue=1 | pages=153 | year=2013 | doi=10.1007/JHEP01(2013)153|arxiv=1212.1276|bibcode = 2013JHEP...01..153A |s2cid=119258343 }}</ref>
An additional, independent timing system and four different methods of analysis were used for the evaluation of the neutrino events. They provided an upper limit for time of flight differences between light and muon neutrinos (48 to 59 neutrino events depending on the method of analysis):

:<math>\delta t=0.6\pm0.4\ (\mathrm{stat.}) \pm3.0\ (\mathrm{sys.})</math> nanoseconds,

and between light and anti-muon neutrinos (3 neutrino events):

:<math>\delta t=1.7\pm1.4\ (\mathrm{stat.}) \pm3.2\ (\mathrm{sys.})</math> nanoseconds,

consistent with the speed of light in the range of

:<math>-1.8\times10^{-6}<\frac{v-c}{c}<2.3\times10^{-6}</math> (90% C. L.).

== MINOS (2012) ==

=== Old timing system ===
The MINOS collaboration further elaborated on their speed measurements of 2007. They examined the data collected over seven years, improved the GPS timing system and the understanding of the delays of electronic components, and also used upgraded timing equipment. The neutrinos span a 10 [[Microsecond|μs]] spill containing 5-6 batches. The analyses have been conducted in two ways. First, as in the 2007 measurement, the data at the far detector was statistically determined by the data of the near detector ("Full Spill Approach"):<ref>{{Cite journal|author=Adamson, P.|title=Neutrino Velocity: Results and prospects of experiments at beamlines other than CNGS|journal=Nuclear Physics B: Proceedings Supplements|volume=235|pages= 296–300|year=2013|doi=10.1016/j.nuclphysbps.2013.04.025|url=http://inspirehep.net/record/1233787|bibcode = 2013NuPhS.235..296A |osti=1128005}}</ref><ref>{{cite web|title=MINOS reports new measurement of neutrino velocity |publisher=Fermilab today|url=http://www.fnal.gov/pub/today/archive_2012/today12-06-08.html|date=8 June 2012|accessdate=8 June 2012}}</ref>

:<math>\delta t=-18\pm11\ (\mathrm{stat.}) \pm29\ (\mathrm{sys.})</math> nanoseconds,

Second, the data connected with the batches themselves have been used ("Wrapped Spill Approach"):

:<math>\delta t=-11\pm11\ (\mathrm{stat.}) \pm29\ (\mathrm{sys.})</math> nanoseconds,

This is consistent with neutrinos traveling at the speed of light, and substantially improves their preliminary 2007 results.

=== New timing system ===
In order to further improve the precision, a new timing system was developed. In particular, a "Resistive Wall Current Monitor" (RWCM) measuring the time distribution of the proton beam, CS atomic clocks, dual frequency GPS receivers, and auxiliary detectors to measure detector latencies have been installed. For the analysis, the neutrino events could be connected with a specific 10&nbsp;μs proton spill, from which a likelihood analysis was generated, and then the likelihoods of different events have been combined. The result:<ref>{{Cite journal|author=P. Adamson|title=Measurement of the Velocity of the Neutrino with MINOS|journal=Proceedings of the 44th Annual Precise Time and Time Interval Systems and Applications Meeting|pages=119–132|year=2012|url=http://inspirehep.net/record/1223915|display-authors=etal|bibcode=2014arXiv1408.6267A|arxiv=1408.6267}}</ref><ref>{{cite web|title=Exceeding the speed limit? Measuring neutrinos to the nanosecond |publisher=Fermilab today|url=http://www.fnal.gov/pub/today/archive/archive_2013/today13-04-12.html|date=13 April 2013|accessdate=13 April 2013}}</ref>

:<math>\delta t=-2.4\pm0.1\ (\mathrm{stat.}) \pm2.6\ (\mathrm{sys.})</math> nanoseconds,

and

:<math>\frac{v-c}{c}=(1.0\pm1.1)\times10^{-6}</math>.

This was confirmed in the final publication in 2015.<ref>{{Cite journal|author=Adamson, P.|display-authors=etal|title=Precision measurement of the speed of propagation of neutrinos using the MINOS detectors|journal=Physical Review D|volume=92|issue=5|pages=052005|year=2015|doi=10.1103/PhysRevD.92.052005|arxiv=1507.04328|bibcode=2015PhRvD..92e2005A|s2cid=34131180}}</ref>

== Indirect determinations  ==
Lorentz-violating frameworks such as the [[Standard-Model Extension]] including [[Lorentz-violating neutrino oscillations]] also allow for indirect determinations of deviations between light speed and neutrino speed by measuring their energy and the decay rates of other particles over large distances.<ref name=diaz /> By this method, much more stringent bounds can be obtained, such as by Stecker ''et al.'':<ref>{{cite journal |author=Stecker, Floyd W.|title=Constraining Superluminal Electron and Neutrino Velocities using the 2010 Crab Nebula Flare and the IceCube PeV Neutrino Events|journal=Astroparticle Physics|volume=56|year=2014|pages=16–18|arxiv=1306.6095|doi=10.1016/j.astropartphys.2014.02.007|bibcode = 2014APh....56...16S |s2cid=35659438}}</ref>

:<math>\frac{|v-c|}{c}<5.6\times10^{-19}</math>.

For more such indirect bounds on superluminal neutrinos, see {{section link|Modern searches for Lorentz violation|Neutrino speed}}.

== References ==
{{reflist}}

== Related belletristic ==
* "60.7 nanoseconds", by Gianfranco D'Anna ({{ISBN|978-3-9524665-0-6}}): a novel inspired by the superluminal neutrino claim, recounting an incredible story of ambition and bad luck in detail.

== External links ==
* [[INFN]] resource list with many papers on experiments and history: [https://web.archive.org/web/20120902041440/http://www.nu.to.infn.it/SuperLuminal_Neutrino/ SuperLuminal Neutrino]

{{Tests of special relativity}}

[[Category:Physics experiments]]
[[Category:Special relativity]]