Indirect limits on the CPT violating background in the neutrino sector

CPT violation in the neutrino sector, suggested as a new way to reconcile different neutrino anomalies, induces at the radiative level observable effects among charged leptons, where high-precision tests of the CPT symmetry are available. We show that, in the models with heavy right-handed Majorana neutrinos, constraints imposed by these experiments require CPT violation in neutrino spectrum be suppressed to a level undetectable for any conceivable neutrino experiment. We find that the CPT violation in the neutrino sector may evade indirect constraints only at the expense of light right-handed neutrinos with small Yukawa couplings to the Standard Model sector or by allowing non-locality well below the electroweak scale.