Testing CPT symmetry with supernova neutrinos

Diagnosing the core of supernova requires favor-dependent reconstruction of three species of neutrino spectra, nu(e), (nu) over bar (e), and nu(x) (a collective notation for nu(mu), (nu) over bar (mu), nu(tau), and (nu) over bar (tau)). We point out that, assuming the information is available, CPT symmetry can be tested with supernova neutrinos. We classify all possible level crossing patterns of neutrinos and antineutrinos into six cases and show that half of them contains only the CPT-violating mass and mixing patterns. We discuss how additional information from terrestrial experiments helps in identifying CPT violation by narrowing down the possible flux patterns. Although the method may not be a good precision test, it is particularly suited for uncovering gross violation of CPT such as different mass patterns of neutrinos and antineutrinos. The power of the method is due to the nature of the level crossing in supernova which results in the sensitivity to neutrino mass hierarchy and to the unique characteristics of in situ preparation of both nu and (nu) over bar beams. Implications of our discussion to the conventional analyses with CPT invariance are also briefly mentioned.