Last update (paper review): 20/03/2012

MS version of the document

Full-format list of papers citing the OPERA generated by SPIRES (PDF, LaTeX): 187 in total.

Disclaimer: this digest is based mostly on reviews of first versions of the papers. I have no possibilities (both technical and physical ones) to track the further updates of all articles cited the OPERA result; changes are made only by direct requests. So, please, dont hesitate to contact me in order to correct and update the obsolete information.

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Explanation&comments on OPERA neutrino tachyon results published on arXiv.org

Experimental result in question

Measurement of the neutrino velocity with the OPERA detector in the CNGS beam

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. The measurement is based on high-statistics data taken by OPERA in the years 2009, 2010 and 2011. Dedicated upgrades of the CNGS timing system and of the OPERA detector, as well as a high precision geodesy campaign for the measurement of the neutrino baseline, allowed reaching comparable systematic and statistical accuracies. An early arrival time of CNGS muon neutrinos with respect to the one computed assuming the speed of light in vacuum of (60.7 \pm 6.9 (stat.) \pm 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 \pm 0.28 (stat.) \pm 0.30 (sys.)) \times 10-5.

News: Updated version (also here) has been published at 17/11/2011, which includes new result (section 9) of test conducted with a short-bunch 3ns (FWHM) wide-spacing 524 ns proton beam. 20 events have been collected in 22/10/11-06/12/11 run with dt distribution shown below (Fig.18, made in classic old-style fashion by PAW):

This result definitely excludes many systematic effects related to the proton PDF profile issues (see p.6 in exp. Section below) and others. In the INFN Press Release it was emphasized that its not yet the final confirmation. Next steps are:

         statistic collection during next year (short-pulse beam made at the price of low intensity);

         clock synchronization issue (one possible solution is fiber connection between sites);

         and new muon detector at CERN placed behind the hadron absorber to perform additional independent studies.

23/02/2012: Hardware fault is the reason of superluminal neutrino?!

15/03/2012 breaking news: ICARUS dont see superluminal nus in the same beam used by OPERA in the second measurement

Measurement of the neutrino velocity with the ICARUS detector at the CNGS beam

The CERN-SPS accelerator has been briefly operated in a new, lower intensity neutrino mode with ~10^12 p.o.t. /pulse and with a beam structure made of four LHC-like extractions, each with a narrow width of ~3 ns, separated by 524 ns. This very tightly bunched beam structure represents a substantial progress with respect to the ordinary operation of the CNGS beam, since it allows a very accurate time-of-flight measurement of neutrinos from CERN to LNGS on an event-to-event basis. The ICARUS T600 detector has collected 7 beam-associated events, consistent with the CNGS delivered neutrino flux of 2.2 10^16 p.o.t. and in agreement with the well known characteristics of neutrino events in the LAr-TPC. The time of flight difference between the speed of light and the arriving neutrino LAr-TPC events has been analysed. The result is compatible with the simultaneous arrival of all events with equal speed, the one of light. This is in a striking difference with the reported result of OPERA [1] that claimed that high energy neutrinos from CERN should arrive at LNGS about 60 ns earlier than expected from luminal speed.

 

Reviews

1)      CosPA2011review talk by Jarah Evslin. Summary of observations and constrains, review of selective tachyon models http://arxiv.org/abs/1111.0733.

2)      The phantom of the OPERA (long waited association with Gaston Leroux novel - Andrew Lloyd Webber's musical) review of experimental results and challenges of theoretical interpretation. http://arxiv.org/abs/1111.7050.

3)      Review of neutrino propagation and mixing in the presence of Lorentz and CPT violation operators of arbitrary dimension using any known experimental data http://arxiv.org/abs/1112.6395.

Experiment comments&critics&suggestions

1)      Clock systematic. Problem with clock synchronization, which could be failed while clock has been transported between CERN and LGSN. http://arxiv.org/abs/1109.6160 3 errors have been found and effect annulated in http://arxiv.org/abs/1110.2909; Clock correction due to slowing down of photon in non-inertial frame. http://arxiv.org/abs/1110.3287; Incorrect calculation of GPS timing, right Lorentz transformations give 64 ns correction. http://arxiv.org/abs/1110.2685; other calculations followed the same idea give 56 ns effect due to wrong clock synchronization http://arxiv.org/abs/1111.1922; GPS clock signal should be correct due to interaction of photon with media, which is flow of alpha particles from rocks. Also taking into account second term orders (v^2/c^2) in the theory might help to match OPERA result with conventional theory http://arxiv.org/abs/1110.4095; also second order calculation with conclusion that GPS could be part of the problem, but numeric evaluations are not given http://arxiv.org/abs/1112.2202. Clock effects related to non-inertial frame have been simulated for OPERA experiment with software Tempo2 used to correct non-inertial effects in astrophysical measurements in most accurate inertial frame Barycentric Celestial Reference System (BCRS), which is non-rotating and located at the Solar System Barycenter (SSB). Conclusion is the effect for OPERA = -80 ns. Effect varies with shift of measurement period inside the year. E.g. it should be + 50 ns if exposition would be in January-March http://arxiv.org/abs/1201.4147.

2)      Statistical analysis. Extraction of 60 ns shift from 10 0000 ns pulse and treatment it as superluminal nu is incorrect. http://arxiv.org/abs/1110.3642; Statistical effect due to small number of protons converted to neutrinos. 1D damped Gaussian model shows effect observed http://arxiv.org/abs/1109.5727 alternative derivation of the same effect, but it is concluded that its unlike explains the OPERA result http://arxiv.org/abs/1112.1324; systematics due to incorrect transition function and statistic analysis method used in calculations. http://arxiv.org/abs/1110.0644 : problem with statistical analysis. Main problem is again no proofs that proton-neutrino PDF transition is known + low neutrino CR. Only edges can be used for fit instead of entire PDF as a consequence. Analysis of PDF edges by 2 methods shows that noise at leading edge, or deformation of neutrino PDF relatively to proton PDF at trailing edge, or mixture of both scenarios cant be excluded as explanations. It means that statistical constrains dont allow to conclude unambiguously the nu superluminosity. Crucial role of quality of statistical analysis is pointed and full complex analysis strategy (averaging of individual probability functions) which includes: summing of proton waveform, using individual waveform, construction, performance of estimator http://arxiv.org/abs/1111.0282.

3)      Phase/group/mean speed business. No assumption about travelling medium: OPERA measured phase speed as the neutrino is wave pocket. http://arxiv.org/abs/1110.0302 . The phase measurement is also claimed in http://arxiv.org/abs/1110.0762 . Phase/group speed effect is also claimed in http://arxiv.org/abs/1110.4805 OPERA nu extra speed ~ 7.5 km/s is due to addition of neutrino beam broadening speed 8.16 km/s. This assumption is based on pure classic Galileo transformations (?). Relativistic calculations are not given, only concept is discussed with the same idea: OPERA measures neutrino group velocity + beam broadening speed, which should be treated as quantum effect (?). http://arxiv.org/abs/1111.0805: close idea mean speed could > c due to quantum effect. But calculation gives value of effect 10^{-16}. Travelling in specific medium: (which one? no SR breaking, but some new physics must be behind this medium, see theor. section below). Travelling of nu in medium with special property, where group velocity is bigger then c. Analogous with photons in medium http://arxiv.org/abs/1109.6121 ; http://arxiv.org/abs/1109.5357 ; http://arxiv.org/abs/1110.1253 extended at http://arxiv.org/abs/1110.5453 derived group velocity as function of nu mixing pars. It is finally claimed that effect of final width of nu wave packet is too small then OPERA effect; possibility of group velocity essentially more than c is also rejected in http://arxiv.org/abs/1110.2463 ; http://arxiv.org/abs/1110.2832 : effect of final wave function width addressed as weak measurement estimated at level 10^-24 far out form OPERAs 10^-5; http://arxiv.org/abs/1202.0953: OPERA results was refused from studies of group nu velocities in vacuum and matter in the frame of Lorentz invariance. Coordinate-dependent oscillation is dominant effect for distortion of nu wave packet, increase of distance as small as 1 cm in comparison with OPERA result required 20m.

4)      Other quantum effects under the SM. Effect of stimulated neutrino efficient in pion decay, some sort of coherence (laser) effect. Muons arriving in later spikes of single bunch are interacting with neutrinos (due to large wave functions) produced in previous spikes and has bigger probability to be created at longer distances (life-times of pion) and have shorter baseline (50 ns -> 30 m) (? Strange stimulation which gives bigger life-time of initial particle). http://arxiv.org/abs/1110.0243; revised article, for first experiment with 10.5 mks nu pulse effect is that neutrino is producing in the decay channel early then it is assuming now due to stimulated absorption-emission processes. In the second test with sig=3 ns pulses the effect is different due to relativistic time shift that produce a deformation of the wave distribution function that shift the maximum and Dt = -gamma_pi * sig^2/tau_o = -65.8 ns, where gamma_pi pion Lorentz factor, sig = pulse sigma, and tau_o=26 ns mean life time pion in the pion in the muon reference frame. If its true the time shift for short pulses will be linear in the Lorentz factor (dt(gamma_pi) dependence could be checked at higher statistics by OPERA next year) and quadratic in the mean Gaussian width (e.g. increasing sig by srqt(2) dt=120 ns should be observed). Also its interesting to emphasize that if author is right then the same results in first and second OPERA measurement are driven by different effects and close just occasionally! http://arxiv.org/abs/1112.0815. The coherence is also claimed in http://arxiv.org/abs/1110.0762;

Neutrino cant be treated as point-like objects, but wave pockets as large as a few km in transverse side (this is extracted applying ambiguity principle to the kinematics of neutrino production reactions). In this case OPERA detects nus under small angle to the detector, which is detected earlier http://arxiv.org/abs/1110.0989 answers to some critical comments could be also found here (in Russian); effect is refused due to spherical shape of neutrino wave front http://arxiv.org/abs/1110.2321.

Extremely low mass of lightest neutrino 1.1 10-8/4.9 10-2/ 8.7 10-3 eV which make able quantum excursion outside light cone at level of 18 m (60 ns of OPERA data) http://arxiv.org/abs/1110.1162 . Whats about hierarchy? Similar idea in http://arxiv.org/abs/1110.3266;

Distortion of wave package for ultrarelativistic light mass particles http://arxiv.org/abs/1110.3071; the distortion of wave packet is able to explain the OPERA result assuming neutrino is massless particle http://arxiv.org/abs/1201.1341.

Virtual neutrino is observed, not a real nu motion, instead of successive pi^+ -> mu^+ + nu_mu emission @ CERN and nu_mu + N -> N + mu^- detectrion @ GS we have pi^+ + N -> N + mu^+ + mu^- with virtual neutrino exchange. Virtual nu travels ~ 6 km (LI space-like displacement) with LI space-like energy moment transfer ~ 100 MeV/c http://arxiv.org/abs/1111.7181.

Tunneling effect of neutrinos though the rock between detector and source. Fraction of nu-s from beam stopped in rock is ~ 2 10^-5, and this process violates the travel time and actually rock dwell time is measured by OPERA at level 1 + 10^-5 http://arxiv.org/abs/1201.6496.

5)      Earth movement. Coriolis effect due to Earth motion can add 2.2 ns effect. http://arxiv.org/abs/1110.0392; Earth movement can contribute. Orbital shift is 71 m (OPERA effect ~ 18 m) and impacts if day/night asymmetry in data taking takes place (this can be easily checked in OPERA data). Further seasonal Earth axial tilt is -12 m in average and is not compensated for zero day/night event CR asymmetry http://arxiv.org/abs/1110.3581; Effect due to movement in gravitational Earth field estimated as sqrt(1-2*M(Earth)/R(Earth)). The numerical calculations is not given though http://arxiv.org/abs/1110.5866.

6)      Proton profile (PDF) systematic (see also p. 2 above) (oscillations, broadening, sharpening) could be responsible for the effect http://arxiv.org/abs/1110.0595 ; effect may be explained by beam composition variations at 10% level (the size of effect 50 ns extracted at 500 ns range), which lead to the TOF shift of the same order http://arxiv.org/abs/1110.0239 ; potential systematic shift could be if incorrect method was used to construct global proton PDF (order of normalization and summation is not clarified and can be wrong) http://arxiv.org/abs/1110.3783; discrepant neutrino light curve has been filtered with method used for long-duration gamma-ray bursts in astoparticle physics. Significance of OPERA result has been reduced to 3.75 sigma. http://arxiv.org/abs/1110.4781. Used fit variable dt is not true parameter of PDF distribution as: i) dt variation doesnt change PDF shape, ii) fit results strongly depend on boundaries chosen. So, it must be treated as systematic shift in x-axis (time-scale). Proposed approach: to compare parameters of proton and neutrino PDF as two samples of the same parent distribution. E.g. compare their averages (first momenta) using Student-distribution http://arxiv.org/abs/1110.6291, http://arxiv.org/abs/1111.3116; 7% decrease of neutrino production rate in target during 10.5 mks proton pulse is able to explain time shift in OPERA result. Analysis of target behavior shows that its possible scenario and experiments with short pulses are required (hopefully MINOS will do it late spring 2012). http://arxiv.org/abs/1110.6408 . Smearing of proton PDF do not change the result http://arxiv.org/abs/1110.0424; 3 sources of beam systematic are estimated: a group delay due to low pass filters acting on the particular shape of the proton time distribution (~ 10 ns effect), broadening (~40 ns effect) and movement of the proton beam at the target during the leading and trailing slopes of the spill http://arxiv.org/abs/1111.3284.

Neutrino departure times using PDF have been simulated with MC bootstrap (repetition) techniques. It was found that MLM accuracy to find time shift is +/-6.8 ns, while fluctuation of average time is +/-23 ns. Author is discussing and citing the first version of paper http://arxiv.org/abs/1201.5142.

7)      Non-observed processes. Tachyon nu-s would lose energy rapidly via the Cerenkov-like emission (bremsstrahlung) of e+e--pairs, and nu beam arrived to detector would be depleted to 12.5 GeV and distorted. Cohen-Glashow (CG) model - http://arxiv.org/abs/1109.6562 ; the same addressed in http://arxiv.org/abs/1109.6630 ; detailed analysis of CG-effect has been done, which is parametrically similar to CG results http://arxiv.org/abs/1112.1299. http://arxiv.org/abs/1109.6667 confirmation of CG model in direct calculation and virtual Z-bozon approaches http://arxiv.org/abs/1112.0264. If its right, then the signal should be visible at LHC http://arxiv.org/abs/1110.0821 it is claimed that at some LIV model parameters nu still can be still free from e+e- production http://arxiv.org/abs/1111.1574; precise calculations give decay length of superluminal nu_mu -> nu_mu + e- + e+ = 32 671 km and negligible vs. 730 km OPERA baseline, so OPERA result is consistent with no observation of bremsstrahlung. Later (version4) it was claimed that effect is only %2 for 20 GeV pions, and could be big for higher energies (73% for 100 GeV) http://arxiv.org/abs/1111.2725; deformed special relativity frame also can suppress the bremsstrahlung http://arxiv.org/abs/1111.3716; http://arxiv.org/abs/1110.3763; http://arxiv.org/abs/1111.4994; different nu models has been checked against CG-constrain. It was shown that light-like superluminal nu can evade CG-bremsstralung http://arxiv.org/abs/1112.1090.

. ICARUS rejects OPERA result claiming no Enu spectra distortion and absence of specific reactions expected from superluminal nu-s by Cohen-Glashow model above. The limit d= <4 10-8 was derived compatible with SK and close to SN1987A; the same result from revisiting of NOMAD data http://arxiv.org/abs/1111.0785. BUT Cohen-Glashow model is this only ONE model whats about tens of others? In addition it was shown that bremsstrahlung could be avoided in some models

New bounds on nu_mu -> nu_mu + e- + e+ from CERN PS191 and CHARM experiments (search for sterile nu decay) (v-c)/c < 3.4 10^-7 for 0.2-8 GeV nu energy range, and (v-c)/c < 9.3 10^-10 for 10-280 GeV nu energy range http://arxiv.org/abs/1201.5363;

Decay rates, beam energy depletion. http://arxiv.org/abs/1109.5917 OPERA result is inconsistent with simple standard tachyon model and Coleman-Glashow model. In first case tachyon nu mass should be compatible mu ~100 MeV, which is not observed in other reactions. In second case nu oscillation cant be explained. The OPERA tachyon mass is inconsistent with measurement of pion decay http://arxiv.org/abs/1109.5599 ; the same in http://arxiv.org/abs/1109.6630 , Enu in beam cant be > 14 GeV; and > 5 GeV in http://arxiv.org/abs/1109.6667 ; http://arxiv.org/abs/1110.0241 ; it is claimed that at some LIV model parameters nu still can be produced with required energy http://arxiv.org/abs/1111.1574; precise pion decay rate calculations gives 2% effect, hard to measure.

Significant enhancement of decay channel pi+ -> e+ nu_e (may even dominate over pi+ -> m+ nu_m) as well as large deviations in spectra are predicted for superluminal neutrinos for most of E_nu dispersions proposed for OPERA experiment. Minimal modification of SM is assumed http://arxiv.org/abs/1112.0169.

Result must allow protonÛphoton decays in contradiction with current observations http://arxiv.org/abs/1109.6630.

Total inconsistence with SN1987A. http://arxiv.org/abs/1109.5368, but could be avoided in a most of models (in fact, fit OPERA and SN1987A is treated as primary validation of almost any theoretical model).

Neutrino decay should exist http://arxiv.org/abs/1110.0430.

Tachyon nu-s should give brighter astrophysical neutrino background in ultra high energy cosmic ray (UHECRs) range, which is not detected. Non-detection of UHECR neutrino is inconsistent with OPERA result assuming quadratic extrapolation of OPERA energy scale to UHECR range http://arxiv.org/abs/1111.3045.

8)      Look at v(E) as test of tachyon models. Recent result is not promised indicating no energy dependence. http://arxiv.org/abs/1109.5172; combined study of OPERA, MINOS, FERMILAB79 confirmed absence of energy dependence for tachyons. But in order to fit with SN1987A result power-law scenario with the power close to 0 should be used http://arxiv.org/abs/1110.6577.

Bunch of theories explained Lorentz invariance violation (LIV)

Gravity models

1)      Add 5 force (5 element J ) of gravitational origin http://arxiv.org/abs/1109.6249 ; new gravity like environmental field http://arxiv.org/abs/1109.5685

2)      Rainbow gravity http://arxiv.org/abs/1109.6563

3)      Finsler spacetime bulk gravity http://arxiv.org/abs/1109.6055; Finsler brane http://arxiv.org/abs/1110.0675; Finsler with new dispersion relation http://arxiv.org/abs/1110.6673; Finsler extension of Einstein gravity http://arxiv.org/abs/1112.5641; Finslerian special relativity satisfies all http://arxiv.org/abs/1201.1368.

4)      Models beyond linear and quadratic violations in quantum gravitational models (QGM). http://arxiv.org/abs/1109.4980

5)      High energy cutoff in quantum gravity model in discrete space-time. http://arxiv.org/abs/1110.1317

6)      Dark gravity. http://arxiv.org/abs/1110.2060; SBLI for Hamiltonian gravity. http://arxiv.org/abs/1111.7195.

7)      Dynamic LIV on the base of power-counting renormalizable gravity http://arxiv.org/abs/1110.0889; extended in http://arxiv.org/abs/1201.0095.

Spontaneous breaking of LI (SBLI)

8)      Fermi point splitting model (FPS) http://arxiv.org/abs/1109.5671; FPS is particular case of the SBLI (possibly by the formation of a neutrino fermionic condensate), that is, the spontaneous appearance of a preferred frame in the vacuum, which can be derived from Lorentz-invariant physical laws http://arxiv.org/abs/1109.6624.

9)      SBLI for Hamiltonian gravity. http://arxiv.org/abs/1111.7195.

Extra dimensions including sterile nu

10)  Extra dimensions: its problematic to construct extra dimension model, which fit tachyons and keeps reasonable properties in the observed space. http://arxiv.org/abs/1109.5687 ; Lorentz violating dimension-5 model http://arxiv.org/abs/1111.0093.

11)  String theory explanation (D3 and D7-branes), string scale should be 105. http://arxiv.org/abs/1110.0451

12)  Oscillation to sterile, which goes with superluminal velocity in the bulk with bigger phase space. http://arxiv.org/abs/1109.6282, active-sterile neutrino oscillations in which sterile neutrinos are superluminal and active neutrinos appear superluminal by virtue of neutrino mixing http://arxiv.org/abs/1112.0527. Sterile models + consistency with SN1987A http://arxiv.org/abs/1109.5682 . Sterile superluminal-like neutrino coupling with fermions (dm^2=0.45 eV^2, sin^2(2theta) ~ 0.05), perfect agreement with MINOS, LSND, MiniBooNE data http://arxiv.org/abs/1109.4871; mixing to sterile -> radius of extra dimension 2.7 mm and brane curvature 10-2 http://arxiv.org/abs/1109.6354

13)  Two-phase structured hidden sector comes in a matter/vacuum phases associated/no associated with superluminality http://arxiv.org/abs/1111.6579.

Environmental superluminocity

14)  Scalar field sourced on the Earth. http://arxiv.org/abs/1109.6312; flavor-independent coupling of the neutrino and Higgs fields to scalar field w and w/o Galileon http://arxiv.org/abs/1109.6641 ; scalar domain wall http://arxiv.org/abs/1109.6930; new gauge field sourced on Earth. http://arxiv.org/abs/1110.0931 ; pseudoscalar potential in media http://arxiv.org/abs/1110.2236 ; Horava-Liftshitz Earth gravitational field http://arxiv.org/abs/1110.0697; Earth field for background LIV http://arxiv.org/abs/1110.3451; chameleon mechanism http://arxiv.org/abs/1110.6697; DM in form of cloud of unobserved quarks localized around the Earth (to fit with 1987A result). Speed of light in this DM is c0 < c, which is "speed of light in true vacuum, and nu-s are moving with v, which is c0 < v < c, relativity is not broken http://arxiv.org/abs/1111.1760, close phenomenology with DM refraction index n_g>1 and c = c_true/n_g, where c/c_true are observed/real true speed of light. The origin of DM is not discussed http://arxiv.org/abs/1201.4374. Tachyonic Majorana mass with imaginary mass term interacted with Earth crust http://arxiv.org/abs/1109.5445; simulation of this model has confirmed the experimental result (see Fig. below). lacking of detection and energy loss from Cohen-Glashow effect can be the indirect evidence of a Majorana tachyonic neutrino state violating CPT invariance or a spin-to-orbital angular momentum conversion of the neutrino beam, that acts as a negative-squared mass term http://arxiv.org/abs/1111.4441.

.

15)  Nu dispersion in non-standard vacuum. http://arxiv.org/abs/1109.5411; neutrino moved in imaginary optical potential http://arxiv.org/abs/1110.0234; neutrino refraction in matter. http://arxiv.org/abs/1110.2170 correction of speed of light in vacuum due to photon-DM and/or DE interaction given reflection index <1. No model proposed, but some properties are restricted (energy independent, isotropic, universal to all neutrinos). Can be checked in cosmological red shift time variance studies. http://arxiv.org/abs/1109.6520

Mixing at Universe scale

16)  Neutrino is interacting with Hooft-Polyakov monopole, which is left behind after the spontaneous symmetry breaking (SSB) phase transition of some scalar fields (coupled to nu not photon) in the universe. http://arxiv.org/abs/1110.0449

17)  Mixing with superbradyon as Universe DM-candidate http://arxiv.org/abs/1109.6308,

18)  Superluminal, massless gauge boson is mixing only with nu http://arxiv.org/abs/1111.7268.

19)  Time-like Lorentz-violating background permeating the space is responsible for both superluminal neutrinos and dark energy http://arxiv.org/abs/1112.0300.

Modified relativity models

20)  Deformed Lorentz symmetry (DLS) (also used term deformed special relativity DSR) allows to avoid pion decay problems (p.8) as well as decay (p.16). http://arxiv.org/abs/1110.0521 extended in http://arxiv.org/abs/1110.5643; http://arxiv.org/abs/1110.2146; http://arxiv.org/abs/1111.4994; its claimed also that DLS leads to less stringent restrictions of superluminarity of electron (10^{-4}) that it treated in SM (10^{-14}) http://arxiv.org/abs/1111.0993.

21)  Extended relativity theories (RT). http://arxiv.org/abs/1110.0882 . http://arxiv.org/abs/1110.4754 extra time dimension extension of RT, which also predicts dark matter.

22)  Bimetric relativity (normal +superluminal particles involved). http://arxiv.org/abs/1110.1330 analogous idea of nu bi-velocity, theory built through DM scalar field at Earth (like p. 27) evaluated length L ~ 10^-17 cm and M ~ 1 TeV (expected scale of new phys) http://arxiv.org/abs/1110.6571; phenomenological approach with assumption that portion of nu-s is superluminal (mechanism is not discussed). The minimal fraction of superluminal nu-s is found to be 18% at 3sigma. Challenges the hypothesis with sterile-nu involved. The speed of nu eigenstates (3-component model) is discussing, at least n2 and n3 should are superluminal http://arxiv.org/abs/1110.0424; 3 model based on tachyonic nu eigenstates in the frame of non-linear realizations of the Lorentz group are discussed in http://arxiv.org/abs/1109.6055.

23)  Revised Robertson Test Theory of Special Relativity: in the frame of para-Lorentzian with certain pars transformation gravitational effect of GPS clock synchronization can give the 60 ns http://arxiv.org/abs/1111.2271.

24)  Modified theory of relativity http://arxiv.org/abs/1109.5651 .

25)  Superluminal velocity may be due to noncommutative acoustic black hole metrics http://arxiv.org/abs/1109.6298.

26)  Weyl spinor field represented by Dirac-Hestenes spinor fields (DHSF) http://arxiv.org/abs/1110.2219.

27)  The generalized uncertainty principle (GUP) and doubly special relativity (DSR) http://arxiv.org/abs/1112.3753.

28)  Fourth type of particle elvisebrions (in addition to bradyons, luxons, and tachyons) in emergent special relativity (SR) model. The characteristic feature of elvisebrions, distinguishing them from tachyons,is that they are outside the realm of SR and their energy remains finite (or may even turn to zero) when the elvisebrion velocity approaches the light velocity. Elvisebrion in Georgian means swift as a lightning flash. Admirers of the Elvis Presley music will also appreciate the name, authors hope http://arxiv.org/abs/1112.4714.

Quantum phenomenology

29)  Quantum equivalence principle (QEP): quantum version of Hamilton-Jacobi (HJ) equation model http://arxiv.org/abs/1109.6631; It was claimed later that HJ is in general not the case http://arxiv.org/abs/1110.1857; In further development of HJ model temperature effect as well as neutrino mass has been derived. e^{(m_nuc^2)/(kT)} ~ 2.5 10^-5 gives m_nu ~ 0.3 eV for T=330K, also v=c solution has been found for massless particles http://arxiv.org/abs/1111.0270; concept of quantum trajectories as extension http://arxiv.org/abs/1112.4779.

30)  Lorent-noninvariant interaction terms for mu http://arxiv.org/abs/1109.5749

31)  Modification of Dirac fermions equations. The parity-odd nonbirefringent sector of modified Maxwell theory. It is coupled to a standard Dirac theory of massive spin-1/2 fermions resulting in a CPT-even Lorentz-violating modification of QED http://arxiv.org/abs/1111.4182. Dirac equation for tachyon neutrinos. http://arxiv.org/abs/1110.1943; and further with a claim that neutrinoless double beta decay is not allowed for tachyonic Dirac equation http://arxiv.org/abs/1201.0359; Gross-Neveu model for Dirac fermions http://arxiv.org/abs/1109.6170

32)  Noncommutative U_{*}(1) gauge-theory based on Seiberg-Witten maps (the one-loop quantum correction to the neutral fermion propagator) http://arxiv.org/abs/1111.4951.

SM-close extensions, quantum corrections

33)  Standard Model Extension (SME) game with Langrangian adding LIV terms to fit pars to exp. data http://arxiv.org/abs/1110.4443.

34)  Lorentz invariance violation (LIV) in frame of Standard Model Supplement (SMS) http://arxiv.org/abs/1109.6097

35)  LIV without breaking of causality principle (toy). http://arxiv.org/abs/1110.1875

36)  Neutrino limited velocity model used quantum corrections in self-energy diagrams http://arxiv.org/abs/1110.0132

37)  http://arxiv.org/abs/1110.0132 full Lorentz invariance (LI) gives cº1, if LI is not full, then different limited speeds ci are exists. E.g. quantum corrections can contribute to the differences with time-like and space-like component renormalized in different ways; The same idea in http://arxiv.org/abs/1110.3540.

38)  Helix motion of massive subatomic particle at ultimate limits. http://arxiv.org/abs/1110.0245.

Explicit LIV

39)  Lifshitz-type fermion model with Vtach(E2) and LIV-modification of Abelian gauge theory with axial-vector coupling to fermion. Conventional tachyon model is ruled out by SN1987A result http://arxiv.org/abs/1109.6296.

No LIV

40)  LIV effect small to break CPT http://arxiv.org/abs/1109.5721; no break of local Lorentz invariance http://arxiv.org/abs/1109.5289; No any dispersion in effective field theory can reproduce the result. http://arxiv.org/abs/1110.0783; no any dispersion E(P,\rho) can fit SN1987A, e+e- an nu\bar{nu} emissions simultaneously, where \rho density of the Earth crust http://arxiv.org/abs/1112.3551.

41)  Weak velocity was measured according to weak value principle, no causality violation http://arxiv.org/abs/1110.1790.

42)  Cosmological data rule out explanation of subluminal nu by model of tachyon, whish is a particle with imaginary mass and v > c. At OPERA energy scale (28 GeV) nucleonsynthesis constrain v-c < 8.6 10^-11 and Cosmic Microwave Background (CMB) observations imply v(28 GeV)-c < 7.1 10^-23 v(10 MeV)-c < 5.4 10^-16, which is stronger than SN1987A http://arxiv.org/abs/1201.3284.

Miscellaneous

43)  Consequences of LIV are discussed in term of different thresholds (boundaries) for different processes (e.g. decay, scattering) and allowed regions of observables http://arxiv.org/abs/1111.6340; further development in http://arxiv.org/abs/1112.1466.

Consequences

1)      Thats why we dont see nu-s coincidences with GRB. http://arxiv.org/abs/1109.5378.

2)      Neutrinoless double beta decay is not allowed for tachyonic Dirac equation http://arxiv.org/abs/1201.0359.

Proposed tests:

1)      Compare arrival time of atmospheric muons and neutrino by astrophysical setups. http://arxiv.org/abs/1109.6238

2)      Switch to antineutrino to check imaginary optical model (p.14 in previous paragraph).

3)      Pion decay rate should be violated (LIV in neutrino sector -> LIV in meson sector) and precise measurement will give a check. http://arxiv.org/abs/1110.2123; precise calculations gives 2% effect here, hard to measure and so OPERA result is consistent with no observation of this violation http://arxiv.org/abs/1111.2725.

4)      http://arxiv.org/abs/1110.0736: 8 inconsistencies summarized. Possibility to check 1) study low energy ~1 GeV nu_mu (1.4 c expected); 2) try to search correlation between solar flares and neutrino hits in underground detectors. 3000 flares were during last 15 years, correlation signal could be high.

5)      http://arxiv.org/abs/1110.3642: 730 km tunnel between CERN and GS to send light and nu simultaneously, but who will give the money?

6)      In the second test with sig=3 ns pulses the effect is different due to relativistic time shift that produce a deformation of the wave distribution function that shift the maximum and Dt = -gamma_pi * sig^2/tau_o = -65.8 ns, where gamma_pi pion Lorentz factor, sig = pulse sigma, and tau_o=26 ns mean life time pion in the pion in the muon reference frame. If its true then it could be tested: the time shift for short pulses will be linear in the Lorentz factor and quadratic in the mean Gaussian width, that could easily be tested at OPERA with the actual infrastructure http://arxiv.org/abs/1112.0815

7)      Testing E(P,\rho) dispersion relations of nu-s and other particles (where \rho is the density of the Earth crust). Search for modification of dispersion for muons and pions (by decay rates in rocks) in underground detectors. Send nu-s from the same source (injection) by two paths through the Earth crust and a tunnel simultaneously comparing the velocities http://arxiv.org/abs/1112.3551.

8)      Make a measurement during the period other then spring-autumn. If effect is due to desynchronizing clocks, then effect should depend on measurement period inside the year. E.g. it should be + 50 ns if exposition would be in January-March http://arxiv.org/abs/1201.4147.

Remarks

1)      http://arxiv.org/abs/1109.6562 : SN1987A 10 MEV neutrino d=(v-c)/c<4 10-9 ; KAMLAND for terrestrial neutrinos GeV-TeV d= <1.4 10-8 ; IceCube 10-100 TeV observation at 500 km baseline d= ≤ 10-(10-11) Û OPERA 17GeV d=2.5 10-5. So, tachyon property is energy dependent reducing completely from GeV to MeV scale. LIV differences between flavors have been ruled out at 10-20 Þ all flavors must be involved; For SN1987A 5 neutrinos in LSD arrived 5 h before the others in K-II, IMB, and Baksan giving d=3.3=10-9. Difference with OPERA is because of nu mass difference (nu_e vs nu_mu).

Forum discussions

1)      www.physicsforums.com

2)      Astrosurf (French)

3)      forums.futura-sciences.com (French)

4)      www.astronomy.ru (Russian)

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