Lorentz and $CPT$ invariance violation in high-energy neutrinos

High-energy neutrino astronomy will be capable of observing particles at both extremely high energies and over extremely long baselines. These features make such experiments highly sensitive to the effects of $CPT$ and Lorentz violation. In this article, we review the theoretical foundation and motivation for $CPT$ and Lorentz violating effects, and then go on to discuss the related phenomenology within the neutrino sector. We describe several signatures which might be used to identify the presence of $CPT$ or Lorentz violation in next generation neutrino telescopes and cosmic ray experiments. In many cases, high-energy neutrino experiments can test for $CPT$ and Lorentz violation effects with much greater precision than other techniques.

Figure 1

The estimated effects of Lorentz violation on the ratio of neutrino flavors observed after propagation. The top frames correspond to neutrinos produced through pion decay, while the lower frames correspond to (anti)neutrinos produced through the decay of neutrons. The left and right frames display the behavior of models with Lorentz violating parameters proportional to $E^2$ and $E^3$, respectively.

Figure 2

The effect of quantum decoherence on the ratios of neutrino flavors. In the left frame, the initial ratios are set to those values found from pion decay (${\nu }_e:{\nu }_{\mu }:{\nu }_{\tau }=1/3:2/3:0$) while in the right frame the ratios from neutron decay (${\nu }_e:{\nu }_{\mu }:{\nu }_{\tau }=1:0:0$) are shown. In both cases, we have considered a model with $\delta L=(E/10\hspace{0.17em}000\mathrm{GeV}{)}^2$. In the case of neutrinos generated in pion decay, quantum decoherence has little impact on the flavor ratios (left frame). The flavor ratios of (anti)neutrinos generated in neutron decay, on the other hand, can be dramatically affected (right frame).

Figure 3

The effect of quantum decoherence on the events observed in a next generation high-energy neutrino telescope, such as IceCube or KM3. Solid lines are the predicted distribution of events with no effects of quantum decoherence, while the dashed lines represent the cases of $\delta L=(E/10\hspace{0.17em}000\mathrm{GeV}{)}^2$ (left frame) and full decoherence (right frame). The (from top to bottom on the left side of the frames) blue, red and black lines show the distributions of muon events, electromagnetic/hadronic shower events, and all muon events with a vertex contained in the detector volume, respectively. The flavor ratios used are for a source producing (anti)neutrinos via neutron decay. The rates have been normalized to a total neutrino flux of $E_{\nu }^{2}d{N}_{\nu }/d{E}_{\nu }={10}^{-7}\mathrm{GeV}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$.