Lorentzviolating neutrino oscillation refers to the quantum phenomenon of neutrino oscillations described in a framework that allows the breakdown of Lorentz invariance. Today, neutrino oscillation or change of one type of neutrino into another is an experimentally verified fact; however, the details of the underlying theory responsible for these processes remain an open issue and an active field of study. The conventional model of neutrino oscillations assumes that neutrinos are massive, which provides a successful description of a wide variety of experiments; however, there are a few oscillation signals that cannot be accommodated within this model, which motivates the study of other descriptions. In a theory with Lorentz violation neutrinos can oscillate with and without masses and many other novel effects described below appear. However, if Lorentz violation occurs, oscillations could be due to other mechanisms. The general framework for Lorentz violation is called the (SME). The neutrino sector of the SME provides a description of how Lorentz and CPT violation would affect neutrino propagation, interactions, and oscillations. This neutrino framework first appeared in 1997 as part of the general SME for Lorentz violation in particle physics, which is built from the operators of the Standard Model. An isotropic limit of the SME, including a discussion on Lorentzviolating neutrino oscillations, was presented in a 1999 publication. Full details of the general formalism for Lorentz and CPT symmetry in the neutrino sector appeared in a 2004 publication. This work presented the minimal SME (mSME) for the neutrino sector, which involves only renormalizable terms. The incorporation of operators of arbitrary dimension in the neutrino sector was presented in 2011.
The Lorentzviolating contributions to the Lagrangian are built as observer Lorentz scalars by contracting standard field operators with controlling quantities called coefficients for Lorentz violation. These coefficients, arising from the spontaneous breaking of Lorentz symmetry, lead to nonstandard effects that could be observed in current experiments. Tests of Lorentz symmetry attempt to measure these coefficients. A nonzero result would indicate Lorentz violation.
The construction of the neutrino sector of the SME includes the Lorentzinvariant terms of the standard neutrino massive model, Lorentzviolating terms that are even under CPT, and ones that are odd under CPT. Since in field theory the breaking of CPT symmetry is accompanied by the breaking of Lorentz symmetry, the CPTbreaking terms are necessarily Lorentz breaking. It is reasonable to expect that Lorentz and CPT violation are suppressed at the Planck scale, so the coefficients for Lorentz violation are likely to be small. The interferometric nature of neutrino oscillation experiments, and also of neutralmeson systems, gives them exceptional sensitivity to such tiny effects. These oscillations have a variety of possible implications, including the existence of neutrino masses, and the presence of several types of Lorentz violation. In the following, each category of Lorentz breaking is outlined.In the standard Lorentzinvariant description of massiveneutrinos, the oscillation phase is proportional to the baseline L and inversely proportional to the neutrino energy E. The mSME introduces dimensionthree operators that lead to oscillation phases with no energy dependence. It also introduces dimensionfour operators generating oscillation phases proportional to the energy. Standard oscillation amplitudes are controlled by three mixing angles and one phase, all of which are constant. In the SME framework, Lorentz violation can lead to energydependent mixing parameters. When the whole SME is considered and nonrenormalizable terms in the theory are not neglected, the energy dependence of the effective hamiltonian takes the form of an infinite series in powers of neutrino energy. The fast growth of elements in the hamiltonian could produce oscillation signals in shortbaseline experiment, as in the puma model.
The unconventional energy dependence in the theory leads to other novel effects, including corrections cheap jerseys to the dispersion relations that would make neutrinos move at velocities other than the speed of light. By this mechanism neutrinos could become fasterthanlight particles. The most general form of the neutrino sector of the SME has been constructed by including operators of arbitrary dimension. In this formalism, the speed of propagation of neutrinos is obtained. 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. Moreover, different neutrino flavors could also have different speeds.
L E conflicts
The L E conflicts refer to null or positive oscillation signals for values of L and E that are not consistent with the Lorentzinvariant explanation. For example, KamLAND and SNO observations require a masssquared difference to be consistent with the Lorentzinvariant phase proportional to L/E. Similarly, SuperKamiokande, K2K, and MINOS observations of atmosphericneutrino oscillations require a masssquared difference . Any neutrinooscillation experiment must be consistent with either of these two masssquared differences for Lorentz invariance to hold. To date, this is the only class of signal for which there is positive evidence. The LSND experiment observed oscillations leading to a masssquared difference that is inconsistent with results from solar and atmosphericneutrino observations. The oscillation phase requires . Since the fixed SME background cheap nfl jerseys fields are coupled with the particle fields, periodic variations associated with these motions would be one of the signatures of Lorentz violation.
There are two categories of periodic variations:
Sidereal variations: As the Earth rotates, the source and detector for any neutrino experiment will rotate along with it at a sidereal frequency of . Since the 3momentum of the neutrino beam is coupled to the SME background fields, this can lead to sidereal variations in the observed oscillation probability data. Sidereal variations are among the most commonly sought signals in Lorentz tests in other sectors of the SME.
Annual variations: Variations with a period of one year can arise due to the motion of the Earth around the Sun. The mechanism is the same as for sidereal variations, arising because the particle fields couple to the fixed SME background fields. These effects, however, are challenging to resolve because they require the experiment to provide data for a comparable length of time. There are also boost effects that arise because the earth moves around the Sun at more than 30 kilometers per second. These processes violate leptonnumber conservation, but can readily be accommodated in the Lorentzbreaking SME framework. The breaking of invariance under rotations leads to the nonconservation of angular momentum, which allows a spin flip of the propagating neutrino that can oscillate into an antineutrino. Because of the lost of rotational symmetry coefficients responsible for this type of mixing always introduce direction dependence.
Classic CPT tests wholesale jerseys
Since CPT Cheap Jerseys violation implies Lorentz violation, traditional tests of CPT symmetry can also be used to search for deviations from Lorentz invariance. This test seeks evidence of . Some subtle features arise. For example, although CPT invariance implies , this relation can be satisfied even in the presence of CPT violation.
Global models of neutrino oscillations with Lorentz violation
Global models are descriptions of neutrino oscillations that are consistent with all the established experimental data: solar, reactor, accelerator, and atmospheric neutrinos. The general SME theory of Lorentzviolating neutrinos has shown to be very successful as an alternative description of all observed neutrino data. One of the main characteristics of this model is that neutrinos are assumed to be massless. This simple model is compatible with solar, atmospheric, and longbaseline neutrino oscillation data. A novel feature of the bicycle model occurs at high energies, where the two SME coefficients combine to create a directiondependent pseudomass. In 2007, Barger, Marfatia, and Whisnant constructed a more general version of this model by including more parameters. In this paper, it is shown that a combined analysis of solar, reactor, and longbaseline experiments excluded the bicycle model and its generalization. Despite this, the bicycle served as starting point for more elaborate models.
Keywords: Lorentzviolating neutrino oscillation