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

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, don’t hesitate to contact me in order to correct and
update the obsolete information.**

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

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 it’s 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 don’t see superluminal
nus in the same beam used by OPERA in the second measurement**

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.

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 it’s 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 can’t
be excluded as explanations. It means that statistical constrains don’t 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 OPERA’s 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 **D****t = -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 it’s 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 it’s 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 can’t 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 .
What’s 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
doesn’t 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 it’s 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 it’s 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… what’s 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 can’t 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 can’t 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 *proton**Û**photon 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.

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.

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.

10) Extra
dimensions: it’s 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 10^{5}. 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.

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

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.

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; it’s
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.

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.

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.

39) Lifshitz-type
fermion model with Vtach(E^{2}) 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.

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.

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.

1) That’s
why we don’t 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.

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 **D****t = -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 it’s 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.