Testing CPT Symmetry with Supernova Neutrinos

Diagnosing core of supernova requires favor-dependent reconstruction of three species of neutrino spectra, \nu_e, \bar{\nu}_{e} and \nu_x (a collective notation for \nu_{\mu}, \bar{\nu}_{\mu}, \nu_{\tau}, and \bar{\nu}_{\tau}). We point out that, assuming the information 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 informations from terrestrial experiments help identifying CPT violation by narrowing down the possible flux patterns. Although the method may not be good at precision test, it is particularly suited to uncover gross violation of CPT such as different mass patterns of neutrinos and antineutrinos. The power of the method is due to the nature of 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 \bar{\nu} beams. Implications of our discussion to the conventional analyses with CPT conservation are also briefly mentioned.