Astrophysical consequences of the OPERA superluminal neutrino

-(5.1 ± 2.9) x 10 -5 (MINOS, 2007) -(2.48 ± 0.28) x 10 -5 (OPERA, 2011) These figures are much stronger than the prediction of any standard extrapolation from Lorentz symmetry violation (LSV) generated at the Planck scale [3]. Therefore, a first question requiring a close study is that of the consistency of these data with existing and well-established results from particle physics experiments and astrophysical observations.

In particular, astrophysical bounds on possible critical speed anomalies with respect to the speed of light appear to be much more stringent than suggested by the recent OPERA data. It therefore seems necessary to study more closely the possible consistency of the OPERA result.

In the high-energy approximation, using a kinematics of the Lorentz type, the energy E of a particle X with critical speed in vacuum c X , mass m X and momentum p can be written as :

Taking c to be the speed of light, and assuming that charged leptons have the same critical speed in vacuum c, the emission of a neutrino with critical speed in vacuum c ν = c + δc (ν) and δc (ν) > 0 would cost extra energy as compared to the situation where c ν = c.

In the case of pion decay and with the above hypotheses, this extra energy δE = p ν δc (ν), where p ν is the neutrino momentum, can only be provided by the pion mass term m 2 π c 3 π (2 p π ) -1 (m π = charged pion mass, p π = pion momentum, c π = charged pion critical speed in vacuum).

Therefore, if one assumes c π = c, the emission of such a neutrino will in any case be precluded by kinematics if p ν δc (ν) > m 2 π c 3 (2 p ν ) -1 . This leads to the equation :

Taking the OPERA value δc(ν) c -1 = 2.5 x 10 -5 , one gets :

Taking into account the mass term of the produced muon, the bound actually becomes p ν ≤ 14 GeV /c, so that decays of charged pions with a critical speed c π = c cannot produce muon neutrinos with energies larger than ≃ 14 GeV. Such an effect cannot be compensated by a critical speed lower than c for charged leptons, as in this case a high-energy photon would spontaneously decay into charged lepton pairs. Taking δc(µ) = -δc (ν), where δc(µ) = c µ -c and c µ is the muon critical speed in vacuum, would lead to photon spontaneous decay into a µ + µ -pair at energies above ≃ 40 GeV .

As OPERA reports a similar result for neutrinos with an average energy of 42.9 GeV, the only way out seems to be a positive value for δc (π) = c π -c not much smaller than δc (ν). However, this would allow for spontaneous photon emission by charged pions and imply a propagation of the critical speed anomaly to the hadronic sector, including the proton.

If δc (π) = δc (ν), spontaneous photon emission by a charged pion would be allowed for pion energies above 20 GeV. Taking δc (π) = 10 -5 c would lead to spontaneous photon emission at pion energies above ≃ 32 GeV. Because of its electromagnetic coupling, we expect this channel to be the leading one for pion decay at very high energy astrophysical sources.

In all cases, on the grounds of the recent OPERA results, a strong suppression of very high-energy neutrinos produced through pion decay should be expected.

Another related issue is that of electronpositron pair emission. As the critical speed c e of these particles must remain close to that of light in order to avoid their own spontaneous decays, the OPERA data would imply the possibility of e + e -pair emission by neutrinos at energies p ν c (m e = electron mass):

A decay channel that, in any case, cannot be ignored at astrophysical energies and distances when considering cosmic neutrino fluxes.

A similar calculation for 100 TeV neutrinos with an arbitrary value of δc(ν) leads to an allowed e + e -pair emission for δc(ν) c -1 > ∼ 10 -16 .

Therefore, even if a violation of Lorentz symmetry can explain the lack of a 100 TeV neutrino signal from gamma-ray bursts, the relevant figures have little to do with the strong LSV inferred from the OPERA signal that would, on the contrary, suppress pion-emitted neutrino fluxes at much lower energies.

Similarly, it seems very difficult to reconcile the OPERA result with hadronic cosmic-ray physics.

As a significant critical speed anomaly for pions, δc (π) of the order ≈ 10 -5 c, seems in any case necessary to explain the data, such an anomaly will in principle be transmitted to all hadrons through standard couplings.

We therefore expect the proton critical speed anomaly to be at least of the order ≈ 10 -6 c. But such a result leads to obvious phenomenological problems :

-If δc (p) = c p -c (c p = proton critical speed) is positive and ≈ 10 -6 c, the same kind of calculations as before lead to a proton spontaneous decay by photon emission allowed above an energy E ≃ 700 GeV , eight orders of magnitude below the highest observed