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We review the status of CPT violation in the neutrino sector. Apart from LSND, current data favors three flavors of light stable neutrinos and antineutrinos, with both halves of the spectrum having one smaller mass splitting and one larger mass splitting. Oscillation data for the smaller splitting is consistent with CPT. For the larger splitting, current data favor an antineutrino mass-squared splitting that is an order of magnitude larger than the corresponding neutrino splitting, with the corresponding mixing angle less-than-maximal. This CPT-violating spectrum is driven by recent results from MINOS, but is consistent with other experiments if we ignore LSND. We describe an analysis technique which, together with MINOS running optimized for muon antineutrinos, should be able to conclusively confirm the CPT-violating spectrum proposed here, with as little as three times the current data set. If confirmed, the CPT-violating neutrino mass-squared difference would be an order of magnitude less than the current most-stringent upper bound on CPT violation for quarks and charged leptons.
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We present an analysis designed to search for Lorentz and CPT violations as predicted by the SME framework using the charged current neutrino events in the MINOS near detector. In particular we develop methods to identify periodic variations in the normalized number of charged current neutrino events as a function of sidereal phase. To test these methods, we simulated a set of 1,000 experiments without Lorentz and CPT violation signals using the standard MINOS Monte Carlo. We performed an FFT on each of the simulated experiments to find the distribution of powers in the sidereal phase diagram without a signal. We then injected a signal of increasing strength into the sidereal neutrino oscillation probability until we found a 5$sigma$ deviation from the mean in the FFT power spectrum. By this method, we can establish upper limits for the Lorentz and CPT violating terms in the SME.
In order to accommodate the neutrino oscillation signals from the solar, atmospheric, and LSND data, a sterile fourth neutrino is generally invoked, though the fits to the data are becoming more and more constrained. However, it has recently been shown that the data can be explained with only three neutrinos, if one invokes CPT violation to allow different masses and mixing angles for neutrinos and antineutrinos. We explore the nature of neutrinos in such CPT-violating scenarios. Majorana neutrino masses are allowed, but in general, there are no longer Majorana neutrinos in the conventional sense. However, CPT-violating models still have interesting consequences for neutrinoless double beta decay. Compared to the usual case, while the larger mass scale (from LSND) may appear, a greater degree of suppression can also occur.
A search for mixing between active neutrinos and light sterile neutrinos has been performed by looking for muon neutrino disappearance in two detectors at baselines of 1.04 km and 735 km, using a combined MINOS and MINOS+ exposure of $16.36times10^{20}$ protons-on-target. A simultaneous fit to the charged-current muon neutrino and neutral-current neutrino energy spectra in the two detectors yields no evidence for sterile neutrino mixing using a 3+1 model. The most stringent limit to date is set on the mixing parameter $sin^2theta_{24}$ for most values of the sterile neutrino mass-splitting $Delta m^2_{41} > 10^{-4}$ eV$^2$.
CPT violation has the potential to explain all three existing neutrino anomalies without enlarging the neutrino sector. CPT violation in the Dirac mass terms of the three neutrino flavors preserves Lorentz invariance, but generates independent masses for neutrinos and antineutrinos. This specific signature is strongly motivated by braneworld scenarios with extra dimensions, where neutrinos are the natural messengers for Standard Model physics of CPT violation in the bulk. A simple model of maximal CPT violation is sufficient to explain the exisiting neutrino data quite neatly, while making dramatic predictions for the upcoming KamLAND and MiniBooNE experiments. Furthermore we obtain a promising new mechanism for baryogenesis.
We perform the covariant canonical quantization of the CPT- and Lorentz-symmetry-violating photon sector of the minimal Standard-Model Extension, which contains a general (timelike, lightlike, or spacelike) fixed background tensor $k_{AF}^mu$. Well-known stability issues, arising from complex-valued energy states, are solved by introducing a small photon mass, orders of magnitude below current experimental bounds. We explicitly construct a covariant basis of polarization vectors, in which the photon field can be expanded. We proceed to derive the Feynman propagator and show that the theory is microcausal. Despite the occurrence of negative energies and vacuum-Cherenkov radiation, we do not find any runaway stability issues, because the energy remains bounded from below. An important observation is that the ordering of the roots of the dispersion relations is the same in any observer frame, which allows for a frame-independent condition that selects the correct branch of the dispersion relation. This turns out to be critical for the consistency of the quantization. To our knowledge, this is the first system for which quantization has consistently been performed, in spite of the fact that the theory contains negative energies in some observer frames.
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