Measurements of the neutrino velocity

Measurements of the neutrino velocity are carried out as tests of the special theory of relativity and to determine the mass of neutrinos . It is investigated whether light and neutrinos, which were emitted at the same time from a distant astronomical radiation source, also arrive on earth at the same time. Terrestrial methods consist in determining the neutrino speed by measuring the time of flight using synchronized clocks, or comparing its speed with that of other particles.

Since the neutrinos are not massless , their speed must depend on their energy and in any case be below the speed of light . With the energies actually occurring, the difference is insignificant. Previous measurements show that such a deviation, if it exists, only has an upper limit of (relatively) 10 ⁻⁹ , i.e. approximately one billionth of the speed of light. This agrees with the prediction within the scope of the measurement accuracy.

overview

Kinetic energy	1 eV	10 eV	100 eV	1 keV	1 MeV	1 GeV	1 TeV	1 PeV
Dimensions	Speed ​​deficit ${\displaystyle 1-{\tfrac {v}{c}}}$
0.2 eV	0.014	1.92 · 10 −4	2 · 10 −6	2 · 10 −8	2 · 10 −14	2 · 10 −20	2 · 10 −26	2 · 10 −32
1 eV	0.134	4.14 · 10 −3	5 · 10 −5	2 · 10 −7	5 · 10 −13	5 · 10 −19	5 · 10 −25	5 · 10 −31
2 eV	0.255	1.40 · 10 −2	2 · 10 −4	2 · 10 −6	2 · 10 −12	2 · 10 −18	2 · 10 −24	2 · 10 −30

For a long time, the Standard Model of particle physics assumed that neutrinos are massless . Then, according to the special theory of relativity, they would have to move at the speed of light. But since the discovery of neutrino oscillations it has been known that they have mass and are therefore slightly slower than light, since only massless particles move at the speed of light. The total energy is given by

${\displaystyle E={\frac {mc^{2}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}$,

with the neutrino speed v and the speed of light c . The neutrino mass m is below 2  eV / c ², and is probably less than 0.2 eV / c ². Only at low neutrino energies would there be a clearly measurable deviation in speed (figure and table on the right, calculated for 0.2, 1 and 2 eV).

Previous experiments have used neutrino energies in excess of 10 MeV. The speed differences predicted for these energy ranges by the special theory of relativity cannot therefore be determined with the current accuracy of the time measurement. The fact that experiments are nevertheless carried out is related to the theoretical possibility of violations of the Lorentz invariance , a fundamental property of the special theory of relativity. These are motivated by speculative variants of quantum gravity , according to which significantly larger deviations from the speed of light could be possible (see modern tests of Lorentz invariance ). In addition to time-of-flight measurements, this also enables the indirect determination of the neutrino speed by analyzing possible Lorentz-damaging effects.

Fermilab (1970s)

In the 1970s, Fermilab carried out terrestrial measurements in which the speed of muons was compared with that of neutrinos and antineutrinos (with energies between 30 and 200 GeV). The Fermilab narrow-band neutrino beam was used for the measurement. 400 GeV protons hit a target , whereupon secondary beams of pions and kaons arise. These then decay into neutrinos and muons in a 345 meter long, evacuated decay tube. The remaining hadrons are stopped by a secondary absorber so that only the neutrinos and a few high-energy muons penetrate the 500-meter-long earth and steel shield to get to the particle detector .

Since the protons were transmitted in bundles of one nanosecond duration and at a distance of 18.73 ns, the speed of the muons and neutrinos could be determined, because a speed difference would firstly lead to a stretching of the neutrino bundles and secondly to a shift in the entire neutrino time spectrum. First, the velocities of muons and neutrinos were compared. Later antineutrinos were also considered. Within the scope of the measurement accuracy, there was no deviation from the speed of light, which was relative uncertainty

${\displaystyle {\frac {|v-c|}{c}}<4\cdot 10^{-5}}$(95% confidence interval ).

An energy dependency of the neutrino speed could not be determined with this measurement accuracy either.

Supernova 1987A

The closest correspondence to the speed of light to date was established in 1987 by observations of antineutrinos with an energy of 7.5 to 35 MeV, which were formed during the 1987A supernova at a distance of about 160,000 light years . The few hours that the neutrinos arrived before the light correspond to a relative deviation of

${\displaystyle {\frac {|v-c|}{c}}<2\cdot 10^{-9}}$,

but are attributed to the fact that the low-interaction neutrinos were able to cross the area of ​​the supernova unhindered, while the light took longer to do so.

MINOS (2007)

The first measurement of the absolute transit time of 3-GeV neutrinos was carried out by the MINOS group (2007) from Fermilab over a distance of 734 km. To generate the neutrinos (NuMI beam), MINOS used the Fermilab Main Injector, with which 120 GeV protons were shot at a graphite target in five to six bundles per extraction phase. The resulting mesons decayed into muon neutrinos (93%) and muon antineutrinos (6%) in a 675 meter long decay tunnel. The arrival time was determined by comparing the arrival times with the near and far detectors from MINOS. The clocks of both stations were synchronized with each other by GPS .

There was an early neutrino arrival of approximately 126 ns. In the uncertainty of systematic errors, the two fiber optic connections for the transmission of the time signals between the GPS receivers on the earth's surface and the underground laboratories dominate. In relation to the distance between the two detectors, there is an apparent faster than light speed with a relative deviation of (68% confidence interval), which at 1.8σ was not significant . 5σ would be required for recognition as a scientific discovery. ${\displaystyle (5{,}1\pm 2{,}9)\cdot 10^{-5}}$

On the other hand, on the confidence interval of 99%, this experiment shows a relative speed deviation of

${\displaystyle -2{,}4\cdot 10^{-5}<{\frac {v-c}{c}}<12{,}6\cdot 10^{-5}}$,

so that the result can also be reconciled with the speed of less than light.

OPERA (2011, 2012)

OPERA neutrino anomaly (2011)

The OPERA group carried out time-of-flight measurements with 17 GeV muon neutrinos (CNGS) from 2009 to 2011. The measurement took place over a distance of about 730 km between a target at the Super Proton Synchrotron at CERN , where pions and kaons are formed, some of which decay into muons and muon neutrinos, and the OPERA neutrino detector in the LNGS . GPS was used to synchronize the clocks and determine the exact distance, with fiber cables approximately 8 km in length being used to transmit signals to the OPERA detector. The temporal distribution of the 10.5 µs long proton pulses was compared statistically with approximately 16,000 detected neutrino events. It was found that neutrinos arrived at the detector around 61  ns earlier than would have been expected at the speed of light. The anomaly appeared significant at 6σ, but the failure analysis was designated as preliminary.

In order to rule out some statistical errors, OPERA carried out a measurement under changed conditions in October and November 2011. The proton pulses were divided into short bundles of 3 ns with an interval of 524 ns, so that each neutrino event could be assigned to a bundle. The measurement of 20 neutrino events showed an early arrival of approximately 62 ns, in line with the previous results. In addition, OPERA updated the neutrino early arrival to approximately 57 ns based on the September main statistical analysis. The authors stated that the deviation was 6.2 σ, which would be significant. However, they added that they did not want to draw any further conclusions from the results and that it was necessary to continue searching for unknown systematic errors.

A number of statements and criticisms have been published on this topic in arXiv preliminary publications (which, however, are not subject to precise assessment ). Some of these have since been published in peer-reviewed journals. A significant objection to the OPERA result was published by Andrew G. Cohen and Sheldon Lee Glashow . The authors apply the vacuum Cherenkov effect , which would have to occur in Lorentz-violating theories that allow faster than light speed, to neutrinos. They predict the production of electron-positron pairs , which would cause the neutrinos to lose a lot of energy in a short time. However, this was not observed by the neighboring ICARUS group.

In February and March 2012, however, it was found that further tests revealed two sources of error: on the one hand, a faulty fiber optic cable connection between a GPS receiver and a computer card, and on the other hand, an oscillator that was used to timestamp the neutrino events during GPS synchronization to provide. The errors work in the opposite direction. In further investigations, a comparison of the arrival of cosmic muons at the OPERA detector and the neighboring LVD detector revealed that a time discrepancy occurred for the period 2008 to 2011, compared to 2007 to 2008 and 2011 to 2012. It was caused by the cable fault, so that about 73 ns have to be added to the premature neutrino arrival of −60 ns. The opposite oscillator error was determined to be approximately −15 ns. This confirmed these two problems as the cause of the OPERA anomaly of approximately −60 ns.

Bottom line

In July 2012, the OPERA group published a new analysis of its data from 2009 to 2011, in which the sources of error found were taken into account. There were new upper limits for flight time differences of

${\displaystyle \delta t=6{,}5\pm 7{,}4\ (\mathrm {stat.} ){\textstyle {+8{,}3 \atop -8{,}0}}\ (\mathrm {sys.} )\,\mathrm {ns} }$

and upper limits for speed differences from

${\displaystyle {\frac {v-c}{c}}=(2{,}7\pm 3{,}1\ (\mathrm {stat.} ){\textstyle {+3{,}4 \atop -3{,}3}}\ (\mathrm {sys.} ))\cdot 10^{-6}}$.

The new analysis of the bundled pulses from October and November 2011 also showed

${\displaystyle \delta t=-1{,}9\pm 3{,}7\ (\mathrm {stat.} )\,\mathrm {ns} }$.

All of these results are consistent with the speed of light, with the 10 ⁻⁶ limit being an order of magnitude more accurate than previous terrestrial time-of-flight measurements.

ICARUS (2012)

Even before the OPERA group had corrected its original measurements, the ICARUS group published its own measurement of the neutrino velocity in March 2012. Like OPERA, the ICARUS detector is also located in the LNGS. In some cases, the same equipment was used for external time measurement, whereas the internal time measurement was independent. ICARUS examined the neutrinos of the same proton pulses that were also used by OPERA between October and November 2011, i.e. 3 ns proton pulses with an interval of 524 ns. Seven neutrino events were observed that could be directly linked to the respective proton pulse. The upper limit for the difference between the measured arrival time and that which can be expected at the speed of light is

${\displaystyle \delta t=0{,}3\pm 4{,}0_{stat}\pm 9{,}0_{syst}\,\mathrm {ns} }$.

Within the scope of the measurement accuracy, there is agreement with the speed of light.

LNGS (2012)

In May 2012, CERN again sent CNGS neutrinos to Gran Sasso . The LNGS experiments Borexino , OPERA, ICARUS, and LVD began with the data analysis of the neutrino events, which resulted in agreement with the speed of light. The 17 GeV muon neutrinos consisted of four pulses per beam extraction that were separated by ≈ 300 ns. The pulses were again subdivided into 16 bundles with a distance of ≈ 100 ns, the bundle width being ≈ 2 ns.

Borexino

The Borexino group analyzed the data from the measurements of the bundled CNGS rays from October to November 2011 and from May 2012. From the data from 2011 they were able to evaluate 36 neutrino events and were given an upper limit for the time-of-flight differences between light and neutrinos

${\displaystyle \delta t=-6{,}5\pm 7\ (\mathrm {stat.} )\pm 6\ (\mathrm {sys.} )\,\mathrm {ns} }$.

To evaluate the 2012 data, they improved their measuring devices by installing a new trigger system and a rubidium clock coupled to a geodetic GPS receiver. Together with LVD and ICARUS, they carried out an independent, precise geodesy measurement. For the final analysis 62 neutrino events could be used, whereby the upper limit for flight time differences resulted

${\displaystyle \delta t=0{,}8\pm 0{,}7\ (\mathrm {stat.} )\pm 2{,}9\ (\mathrm {sys.} )\,\mathrm {ns} }$,

corresponding to the upper limit for speed differences of

${\displaystyle {\frac {|v-c|}{c}}<2{,}1\cdot 10^{-6}}$ (90% confidence interval).

LVD

The LVD group first analyzed the bundled CNGS rays from October to November 2011. They evaluated 32 neutrino events and received an upper limit for the time-of-flight differences between light and neutrinos

${\displaystyle \delta t=3{,}1\pm 5{,}3\ (\mathrm {stat.} )\pm 8\ (\mathrm {sys.} )\,\mathrm {ns} }$.

During the May 2012 measurements, they used the external equipment developed by the Borexino group and the geodesy data collected by LVD, Borexino and ICARUS. They also improved their scintillation counter and trigger . 48 neutrino events (with energies greater than 50 MeV, whereby the average neutrino energy was 17 GeV) could be used for the analysis, with an upper limit for time-of-flight differences:

${\displaystyle \delta t=0{,}9\pm 0{,}6\ (\mathrm {stat.} )\pm 3{,}2\ (\mathrm {sys.} )\,\mathrm {ns} }$

and for speed differences

${\displaystyle -3{,}8\cdot 10^{-6}<{\frac {v-c}{c}}<3{,}1\cdot 10^{-6}}$ (99% confidence interval).

ICARUS

After analyzing the bundled CNGS rays from October to November 2011 (see #ICARUS (2012) above), the ICARUS group also published the analysis of the measurements from May. They improved their internal timekeeping as well as that between CERN and LNGS, used the geodetic measurements together with Borexino and LVD, and used Borexino's LNGS time system. 25 neutrino events could be evaluated, with an upper limit for time-of-flight differences between neutrinos and light of

${\displaystyle \delta t=0{,}18\pm 0{,}69\ (\mathrm {stat.} )\pm 2{,}17\ (\mathrm {sys.} )\,\mathrm {ns} }$,

according to speed differences of

${\displaystyle {\frac {v-c}{c}}=(0{,}7\pm 2{,}8\ (\mathrm {stat.} )\pm 8{,}9\ (\mathrm {sys.} ))\cdot 10^{-7}}$.

Neutrino speeds that exceed the speed of light by more than (95% confidence interval) are therefore excluded. ${\displaystyle 1{,}6\cdot 10^{-6}c}$

OPERA

After correcting the original results, OPERA also published the measurements from May 2012. Four different analysis methods and a further, independent timing system were used to evaluate the neutrino events. They resulted in an upper limit for the time-of-flight differences between light and muon neutrinos (48 to 59 neutrino events depending on the analysis method) of

${\displaystyle \delta t=0{,}6\pm 0{,}4\ (\mathrm {stat.} )\pm 3{,}0\ (\mathrm {sys.} )\,\mathrm {ns} }$

and between light and antimuon neutrinos (3 neutrino events) of

${\displaystyle \delta t=1{,}7\pm 1{,}4\ (\mathrm {stat.} )\pm 3{,}2\ (\mathrm {sys.} )\,\mathrm {ns} }$,

consistent with the speed of light in the range of

${\displaystyle -1{,}8\cdot 10^{-6}<{\frac {v-c}{c}}<2{,}3\cdot 10^{-6}}$ (90% confidence interval).

MINOS (2012)

Old timing system

Parallel to the LNGS measurements, MINOS also continued the preliminary measurements from 2007. Neutrino events from over seven years were evaluated. In addition, the GPS timing system has been improved, the delays in the electronic components have been better taken into account and the timing equipment has been improved. The 10 μs neutrino pulses, each containing 5–6 bundles, were analyzed in two ways: First (as in the measurement from 2007), the data of the more distant detector was generally determined statistically from those of the first detector. The following limit for time differences between light and neutrinos was determined:

${\displaystyle \delta t=-18\pm 11\ (\mathrm {stat.} )\pm 29\ (\mathrm {sys.} )\,\mathrm {ns} }$.

The second method used the data from the individual neutrino bundles themselves. It turned out:

${\displaystyle \delta t=-11\pm 11\ (\mathrm {stat.} )\pm 29\ (\mathrm {sys.} )\,\mathrm {ns} }$,

The neutrino speed and the speed of light therefore agree within the scope of the measurement accuracy.

New timing system

In order to further increase the precision, a new timing system was developed. Have been installed

• a "Resistive Wall Current Monitor" (RWCM) to measure the time distribution of the protons,
• Cs atomic clocks,
• Dual frequency GPS receiver
• and auxiliary detectors for measuring the latency times (delays caused by signal processing in the detector).

For the analysis, each neutrino event could be assigned to one of the 10 μs pulses and a likelihood analysis performed . Then the probability values ​​of various events were combined. It turned out:

${\displaystyle \delta t=-2{,}4\pm 0{,}1\ (\mathrm {stat.} )\pm 2{,}6\ (\mathrm {sys.} )\,\mathrm {ns} }$,

and consequently

${\displaystyle {\frac {v-c}{c}}=(1{,}0\pm 1{,}1)\times 10^{-6}}$.

Further precision measurements are to be carried out in 2013/14 with the improved "MINOS +" detector.

Indirect determinations of the neutrino velocity

Lorentz-violating models such as the standard model extension also allow the indirect determination of deviations between the speed of light and the speed of neutrino by examining their energy and the decay rates of other particles. For example, faster than light neutrinos should emit so-called vacuum Cherenkov radiation . This means that much more precise measurement limits can be achieved, for example by Borriello et al. (2013):

${\displaystyle {\frac {|v-c|}{c}}<10^{-18}}$.

For more such tests, see Modern Tests of Lorentz Invariance # Velocity .

Individual evidence

1. ↑ J. Beringer et al. ( Particle Data Group ): Neutrino Properties - Review of Particle Physics . In: Physical Review D . 86, No. 1, 2012, p. 010001. bibcode : 2012PhRvD..86a0001B . doi : 10.1103 / PhysRevD.86.010001 .
2. ↑ ^{a b} Díaz, Jorge S .; Kostelecký, V. Alan: Lorentz- and CPT-violating models for neutrino oscillations . In: Physical Review D . 85, No. 1, 2012, p. 016013. arxiv : 1108.1799 . bibcode : 2012PhRvD..85a6013D . doi : 10.1103 / PhysRevD.85.016013 .
3. ↑ P. Alspector et al .: Experimental Comparison of Neutrino and Muon Velocities . In: Physical Review Letters . 36, No. 15, 1976, pp. 837-840. doi : 10.1103 / PhysRevLett.36.837 .
4. ↑ Kalbfleisch et al .: Experimental Comparison of Neutrino, Antineutrino, and Muon Velocities . In: Physical Review Letters . 43, No. 19, 1979, pp. 1361-1364. doi : 10.1103 / PhysRevLett.43.1361 .
5. ↑ Hirata et al .: Observation of a neutrino burst from the supernova SN1987A . In: Physical Review Letters . 58, 1987, pp. 1490-1493. doi : 10.1103 / PhysRevLett.58.1490 .
6. ↑ Bionta et al .: Observation of a neutrino burst in coincidence with supernova 1987A in the Large Magellanic Cloud . In: Physical Review Letters . 58, 1987, pp. 1494-1496. doi : 10.1103 / PhysRevLett.58.1494 .
7. ^ Longo, Michael J .: Tests of relativity from SN1987A . In: Physical Review D . 236, No. 10, 1987, pp. 3276-3277. doi : 10.1103 / PhysRevD.36.3276 .
8. ^ Stodolsky, Leo: The speed of light and the speed of neutrinos . In: Physics Letters B . 201, No. 3, 1988, pp. 353-354. doi : 10.1016 / 0370-2693 (88) 91154-9 .
9. ↑ ^{a b} MINOS Collaboration: Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam . In: Physical Review D . 76, No. 7, 2007. arxiv : 0706.0437 . bibcode : 2007PhRvD..76g2005A . doi : 10.1103 / PhysRevD.76.072005 .
10. ^ Soap, C .: CERN's gamble shows perils, rewards of playing the odds . In: Science . 289, No. 5488, 2000, pp. 2260-2262. doi : 10.1126 / science.289.5488.2260 .
11. ↑ ^{a b} OPERA collaboration: Measurement of the neutrino velocity with the OPERA detector in the CNGS beam . 2011, arxiv : 1109.4897 .
12. ↑ Giulia Brunetti: Neutrino velocity measurement with the OPERA experiment in the CNGS beam (PDF; 33MB) Università di Bologna and Université Claude Bernard Lyon 1. 2011. Accessed February 1, 2018.
13. ↑ List of relevant arXiv preprints and publications ( memento of September 2, 2012 in the Internet Archive ) and search results at ArXiv
14. ↑ Cohen, Andrew G .; Glashow, Sheldon L .: Pair Creation Constrains Superluminal Neutrino Propagation . In: Physical Review Letters . 107, No. 18, 2011, p. 181803. arxiv : 1109.6562 . doi : 10.1103 / PhysRevLett.107.181803 .
15. ↑ ICARUS Collaboration: A search for the analogue to Cherenkov radiation by high energy neutrinos at superluminal speeds in ICARUS . In: Physics Letters B . 711, No. 3-4, 2012, pp. 270-275. arxiv : 1110.3763 . doi : 10.1016 / j.physletb.2012.04.014 .
16. ^ LVD and OPERA collaboration: Determination of a time-shift in the OPERA set-up using high energy horizontal muons in the LVD and OPERA detectors . In: The European Physical Journal Plus . 127, No. 6, 2012, p. 71. arxiv : 1206.2488 . doi : 10.1140 / epjp / i2012-12071-5 .
17. ↑ LNGS seminar (March 28, 2012): LNGS results on the neutrino velocity topic
18. ↑ Robert Gast: A cable for eternity . The standard. December 23, 2012. Retrieved February 2, 2013.
19. ↑ OPERA collaboration: Measurement of the neutrino velocity with the OPERA detector in the CNGS beam . In: Journal of High Energy Physics . No. 10, 2012, p. 93. arxiv : 1109.4897v4 . doi : 10.1007 / JHEP10 (2012) 093 .
20. ^ ICARUS Collaboration: Measurement of the neutrino velocity with the ICARUS detector at the CNGS beam . In: Physics Letters B . 713, No. 1, 2012, pp. 17-22. arxiv : 1203.3433 . doi : 10.1016 / j.physletb.2012.05.033 .
21. ↑ Geoff Brumfiel: Neutrinos not faster than light . NatureNews. March 16, 2012. doi : 10.1038 / nature.2012.10249 . Retrieved March 16, 2012.
22. ↑ Neutrinos sent from CERN to Gran Sasso respect the cosmic speed limit . CERN press release. June 8, 2012. Archived from the original on September 5, 2012. Retrieved on June 8, 2012.
23. ↑ ^{a b} Borexino collaboration: Measurement of CNGS muon neutrino speed with Borexino . In: Physics Letters B . 716, No. 3–5, 2012, pp. 401-405. arxiv : 1207.6860 . bibcode : 2012arXiv1207.6860B . doi : 10.1016 / j.physletb.2012.08.052 .
24. ↑ Caccianiga et al .: GPS-based CERN-LNGS time link for Borexino . In: Journal of Instrumentation . 7, 2012, p. P08028. arxiv : 1207.0591 . bibcode : 2012arXiv1207.0591C . doi : 10.1088 / 1748-0221 / 7/08 / P08028 .
25. ^ ^{A b} LVD collaboration: Measurement of the velocity of neutrinos from the CNGS beam with the Large Volume Detector . In: Physical Review Letters . 109, No. 7, 2012, p. 070801. arxiv : 1208.1392 . doi : 10.1103 / PhysRevLett.109.070801 .
26. ↑ ICARUS collaboration: Precision measurement of the neutrino velocity with the ICARUS detector in the CNGS beam . In: Journal of High Energy Physics . No. 11, 2012, p. 49. arxiv : 1208.2629 . bibcode : 2012arXiv1208.2629A . doi : 10.1007 / JHEP11 (2012) 049 .
27. ↑ OPERA collaboration: Measurement of the neutrino velocity with the OPERA detector in the CNGS beam using the 2012 dedicated data . In: Journal of High Energy Physics . No. 1, 2013, p. 153. arxiv : 1212.1276 . doi : 10.1007 / JHEP01 (2013) 153 .
28. ^ Adamson, P .: Neutrino Velocity: Results and prospects of experiments at beamlines other than CNGS . In: Nuclear Physics B Proceedings Supplements . 235, 2013, pp. 296-300. bibcode : 2013NuPhS.235..296A . doi : 10.1016 / j.nuclphysbps.2013.04.025 .
29. ↑ MINOS reports new measurement of neutrino velocity . Fermilab today. June 8, 2012. Retrieved June 8, 2012.
30. ^ P. Adamson et al .: Measurement of the Velocity of the Neutrino with MINOS . In: Proceedings of the 44th Annual Precise Time and Time Interval Systems and Applications Meeting . 2012, pp. 119-132.
31. ↑ Exceeding the speed limit? Measuring neutrinos to the nanosecond . Fermilab today. April 13, 2013. Retrieved April 13, 2013.
32. ↑ Borriello et al. : Stringent constraint on neutrino Lorentz invariance violation from the two IceCube PeV neutrinos . In: Physical Review D . 87, No. 11, 2013, p. 116009. arxiv : 1303.5843 . doi : 10.1103 / PhysRevD.87.116009 .