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The hypothesis of Lorentz violation in the neutrino sector has intriguedscientists for the last two to three decades. A number of theoretical argumentssupport the emergence of such violations first and foremost for neutrinos,which constitute the "most elusive" and "least interacting" particles known tomankind. It is of obvious interest to place stringent bounds on theLorentz-violating parameters in the neutrino sector. In the past, the moststringent bounds have been placed by calculating the probability of neutrinodecay into a lepton pair, a process made kinematically feasible by Lorentzviolation in the neutrino sector, above a certain threshold. However, even morestringent bounds can be placed on the Lorentz-violating parameters if one takesinto account, additionally, the possibility of neutrino splitting, i.e., ofneutrino decay into a neutrino of lower energy, accompanied by "neutrino-pairCerenkov radiation". This process has negligible threshold and can be used toimprove the bounds on Lorentz-violating parameters in the neutrino sector.Finally, we take the opportunity to discuss the relation of Lorentz and gaugesymmetry breaking, with a special emphasis on the theoretical models employedin our calculations.

Squeezing the Parameter Space for Lorentz Violation in the Neutrino Sector by Additional Decay Channels