http://arxiv.org/pdf/1109.4897v1 Measurement of the neutrino velocity with the OPERA detector in the CNGS beam Abstract: The OPERA neutrino experiment at the underground Gran Sasso Laboratory has measured the velocity of neutrinos from the CERN CNGS beam over a baseline of about 730 km with much higher accuracy than previous studies conducted with accelerator neutrinos. […] An early arrival time of CNGS muon neutrinos with respect to the one computed assuming the speed of light in vacuum of (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) ns was measured. This anomaly corresponds to a relative difference of the muon neutrino velocity with respect to the speed of light (v-c)/c = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) x 10 -5
HERE we focus on two theoretical proposals for superluminal behavior 1) Tachyons 2) Coleman-Glashow The Hypothesis of Superluminal Neutrinos: comparing OPERA with other Data A.Drago, I.Masina, G.Pagliara, R.Tripiccione e-Print: arXiv:1109.5917 [hep-ph] While waiting for the experimental community to further check these results, it is worth to ask: Which theoretical consequences would follow from the hypothesis that the muon neutrino is a superluminal particle?
http://web.mit.edu/redingtn/www/netadv/XftlNu.html For an up-to-date web page about experimental & theoretical aspects of superluminal neutrinos:
0) RECALL WHATS SUBLUMINAL A particle with mass m and velocity v < c, has energy and momentum given by They are thus related via the DISPERSION RELATION
These expressions can be extended to the region v > c provided we substitute in the numerator m i m i i SO THAT
Tachyon a particle with mass m and velocity v > c, with energy and momentum given by They are thus related via MODIFIED DISPERSION RELATION
PROBLEMS OF A TACHYONIC INTERPRETATION OF OPERA RESULTS
a) Energy independence of the early arrival times After having traveled a distance L, the neutrino early arrival time is 2.4ms
a) Energy independence of the early arrival times After having traveled a distance L, the neutrino early arrival time is 2.4ms Consider two tachyonic neutrino beams of energy E1 and E2, with E1 E2 for E 2 3E 1, one expects δt 1 9δt 2 OPERA: considers two neutrino beams with mean energy E 1 = 13.9 GeV and E 2 = 42.9 GeV. The experimental values of the associated early arrival times are respectively δt 1 = (53.1 ± 18.8(stat) ± 7.4(sys)) ns and δt 2 = (67.1 ± 18.2(stat)±7.4(sys)) ns consistent with energy dependence of δt
TACHYON MASS RANGE FROM OPERA E=17GeV OPERA mμc2mμc2 110-130 MeV at 1σ
b) Production from pion Simple kinematics (conservation of energy and momentum)
TACHYON MASS RANGE FROM OPERA E=17GeV OPERA mμc2mμc2 110-130 MeV at 1σ EXCLUDED BY π
Better look at the kinematics for π μ ν μ Tachyon vs subluminal (Bradyon) mc 2 < 10 MeV (v-c)/c < 10 -7 too small for OPERA
SUPERNOVA SN1987a It is L = 1.68 × 10 5 ly far from the Earth and exploded releasing a huge neutrino signal, with energies E=1020 MeV; allowed the first direct detection of astrophysical neutrinos. All neutrino flavors were emitted but Kamiokande-II, IMB and Baksan were designed to detect mainly electron anti-neutrinos.
The signal lasted about 10 s and the photons also arrived within a few hours.
The signal lasted about 10 s and the photons also arrived within a few hours. The time spread T = |T 2 T 1 | of two neutrinos with energies E 1 and E 2 (with E 1 E 2 ) is Suppose that SN1987a also emitted a 100 MeV tachyonic muon neutrino: its advance with respect to light would be of about δt 4yr, but with an enormous spread! These neutrinos would have certainly escaped detection.
c) Neutrino oscillations The ratio between the tachyonic mass of the muon neutrino suggested by OPERA and the mass of the electron anti-neutrino suggested by SN1987a would be 10 5 |m 2 | 10 4 MeV 2 It appears impossible to agree with neutrino oscillation experiments, setting stringent bounds on the difference of neutrino masses squared: |m 2 32 | 2.4 × 10 3 eV 2 and m 2 21 7.6 × 10 5 eV 2 In principle, the formalism of neutrino oscillation in the tachyonic case is the same as for an ordinary neutrino.
These simple arguments disfavor the tachyon explanation of the OPERA data
The idea (Coleman and Glashow, 1987) is that the i-th particle has, in addition to its own mass m i, its own maximum attainable velocity c i, and obeys the standard dispersion relation Clearly IF c i > c superluminal In the relativistic regime
Consider now two CG neutrino mass eigenstates with masses m 1 and m 2 O(eV)/c 2, and different limit speeds c 1 and c 2 |c 1 c|/c 10 9 to agree with SN1987a (c 2 c)/c 2 × 10 5 as suggested by OPERA TAKE Suppose that ν 2 has a significant mixing with the muon neutrino, while ν 1 mixes significantly with the electron neutrino
1)Energy independence of the early arrival time of ν μ beam is guaranteed! (c 2 is a constant already chosen to reproduce the results from OPERA)
1)Energy independence of the early arrival time of ν μ beam is guaranteed! (c 2 is a constant already chosen to reproduce the results from OPERA) 2) Production from pion. Kinematics imposes Since in OPERA E π 60GeV E ν 3.5 GeV which is NOT the case!
1)Energy independence of the early arrival time of ν μ beam is guaranteed! (c 2 is a constant already chosen to reproduce the results from OPERA) 2) Production from pion. Kinematics imposes Since in OPERA E π 60GeV 3) SN1987a. A beam of CG ν 2 would have arrived (not spread out) about 4 years before photons and the other ν 1 s. But it would have escaped detection since the detectors had a lower sensitivity to ν μ. E ν 3.5 GeV which is NOT the case!
4) Neutrino oscillations, pose another problem. The two CG neutrino eigenstates travel at different speeds and this affects the neutrino oscillation probability where θ is the mixing angle, R is the distance from source to detector E is the ν energy, typically in the MeV range for reactor and solar experiments Oscillation experiments indicate (m 2 2 m 2 1 ) c 4 10 4 eV 2 sensitivity to δc/c 10 18, much smaller than what would be needed to explain the OPERA data! For numerical estimates, it is safe to replace c ̄ with c.
Also CG superluminal neutrinos do not to provide a satisfactory explanation of the OPERA results
PAIR BREMSSTRAHLUNG Cohen Glashow arXiv:1109.6562 Superluminal neutrinos would lose energy rapidly via the bremsstrahlung of electron-positron pairs For the claimed velocity and at the stated mean neutrino energy, most of the neutrinos would have suffered several pair emissions en route, causing the beam to have E 12.5 GeV at Gran Sasso.
SYSTEMATIC ERROR IN SYNCHRONISATION OF CLOCKS C.Contaldi, arXiv:1109.6160 Since the Earth is rotating, one-way speed measurements require a convention for the synchronisation of clocks in non-inertial frames. We argue that the effect of the synchronisation convention is not properly taken into account in OPERA and may well invalidate their interpretation of superluminal neutrinos. As an example, let us assume that the travelling Time-Transfer Device was stationary at the LNGS site for 4 days while the apparatus for clock comparison was set up. this would result in a total shift of t -30ns.
CONCLUSIONS No obvious theoretical solution to reconcile OPERA with other data Systematic errors have been fully understood by the OPERA Collaboration? Do not miss the talk by A.Paoloni tomorrow at 14.30