The generalization of the theory by incorporating Lorentz violation has shown to provide alternative scenarios to explain all the established experimental data through the construction of global models.
This neutrino framework first appeared in 1997[1] as part of the general SME for Lorentz violation in particle physics, which is built from the operators of the Standard Model.
[4] Full details of the general formalism for Lorentz and CPT symmetry in the neutrino sector appeared in a 2004 publication.
These coefficients, arising from the spontaneous breaking of Lorentz symmetry, lead to non-standard effects that could be observed in current experiments.
The interferometric nature of neutrino oscillation experiments, and also of neutral-meson systems, gives them exceptional sensitivity to such tiny effects.
This holds promise for oscillation-based experiments to probe new physics and access regions of the SME coefficient space that are still untested.
These oscillations have a variety of possible implications, including the existence of neutrino masses, and the presence of several types of Lorentz violation.
The fast growth of elements in the hamiltonian could produce oscillation signals in short-baseline experiment, as in the puma model.
The unconventional energy dependence in the theory leads to other novel effects, including corrections to the dispersion relations that would make neutrinos move at velocities other than the speed of light.
Some of the interesting new features introduced by the violation of Lorentz invariance include dependence of this velocity on neutrino energy and direction of propagation.
There are two categories of periodic variations: The breaking of rotation invariance can also lead to time-independent signals arising in the form of directional asymmetries at the location of the detector.
The breaking of invariance under rotations leads to the non-conservation of angular momentum, which allows a spin flip of the propagating neutrino that can oscillate into an antineutrino.
These global models are based on the SME and exhibit some of the key signals of Lorentz violation described in the previous section.
A novel feature of the bicycle model occurs at high energies, where the two SME coefficients combine to create a direction-dependent pseudomass.
[15] In this paper, it is shown that a combined analysis of solar, reactor, and long-baseline experiments excluded the bicycle model and its generalization.
[17] It turns out that the tandem model is consistent with atmospheric, solar, reactor, and short-baseline data, including LSND.
When the tandem is applied to short-baseline accelerator experiments, it is consistent with the KARMEN null result, due to the very short baseline.
The MiniBooNE results, released a year after the tandem model was published, did indeed show an unexplained excess at low energies.
A seesaw mechanism is triggered, similar to that in the bicycle model, making one of the eigenvalues proportional to 1/E, which usually come with neutrino masses.
Additionally, since the model includes a term associated to a CPT-odd Lorentz-violating operator, different probabilities appear for neutrinos and antineutrinos.
[21][22] In 2011, Barger, Liao, Marfatia, and Whisnant studied general bicycle-type models (without neutrino masses) that can be constructed using the minimal SME that are isotropic (direction independent).
From a general model-independent point of view, neutrinos oscillate because the effective hamiltonian describing their propagation is not diagonal in flavor space and has a non-degenerate spectrum, in other words, the eigenstates of the hamiltonian are linear superpositions of the flavor eigenstates of the weak interaction and there are at least two different eigenvalues.
The effective Lorentz-violating Hamiltonian is a 6 × 6 matrix that takes the explicit form[6] where flavor indices have been suppressed for simplicity.
The widehat on the elements of the last term indicates that these effective coefficients for Lorentz violation are associated to operators of arbitrary dimension.
The four-momentum shows explicitly that the direction of propagation couples to the mSME coefficients, generating the periodic variations and compass asymmetries described in the previous section.
Finally, note that coefficients with an odd number of spacetime indices are contracted with operators that break CPT.
[25] Data analysis has been performed using the LSND,[26] MINOS,[27][28] MiniBooNE,[29][30] and IceCube[31] experiments to set limits on the coefficients
In these cases, Lorentz violation can be introduced as a perturbative effect in the form where h0 is the standard massive-neutrino Hamiltonian, and δh contains the Lorentz-breaking mSME terms.
In the two-flavor limit, the first-order correction introduced by Lorentz violation to atmospheric neutrinos takes the simple form This expression shows how the baseline of the experiment can enhance the effects of the mSME coefficients in δh.
An analysis has been done in the case of several long-baseline experiments (DUSEL, ICARUS, K2K, MINOS, NOvA, OPERA, T2K, and T2KK),[33] showing high sensitivities to the coefficients for Lorentz violation.