Testing CPT symmetry with supernova neutrinos

Diagnosing the core of supernova requires favor-dependent reconstruction of three species of neutrino spectra, ${\nu }_e$, ${\overline{\nu }}_e$, and ${\nu }_x$ (a collective notation for ${\nu }_{\mu }$, ${\overline{\nu }}_{\mu }$, ${\nu }_{\tau }$, and ${\overline{\nu }}_{\tau }$). 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 $\overline{\nu }$ beams. Implications of our discussion to the conventional analyses with CPT invariance are also briefly mentioned.

Figure 1

Level crossing diagrams for neutrino flavor conversion in supernova. In the neutrino sector there are 2 diagrams which correspond to the normal [(a) $\Delta m_{31}^2>0$] and the inverted [(b) $\Delta m_{31}^2<0$] hierarchies. In the antineutrino sector there are 4 diagrams which correspond to the normal [(c),(e) $\Delta m_{31}^2>0$] and the inverted [(d),(f) $\Delta m_{31}^2<0$] hierarchies, each doubled by two patterns of small mass splittings, the reactor-normal [(c),(d) $\Delta {\overline{m}}_{21}^2>0$] the reactor-inverted [(e),(f) $\Delta {\overline{m}}_{21}^2<0$] hierarchies. In the CPT invariant case the diagrams (a)– (d) remain.

Figure 2

The primary energy spectra of three effective neutrino species ${\nu }_e$ (red solid curve), ${\overline{\nu }}_e$ (green dashed curve), and ${\nu }_x$ (blue dotted curve) of neutrinos just outside the neutrino sphere are shown. The flux model is based on the Livermore simulation whose parameters are given in Table  in Sec. 7. The absolute normalization is arbitrary.

Figure 3

The energy spectra of the three effective neutrino species ${\nu }_e$ (red solid curves), ${\overline{\nu }}_e$ (green dashed curves), and ${\nu }_x$ (blue dotted curves) at terrestrial detectors corresponding to six different patterns of neutrino flavor conversion $P_{31}$ to $P_{22}$ defined in (18) are presented. The Livermore flux model with the same values of parameters as in Fig. 2 is used. Although an overall absolute normalization is arbitrary, the relative normalization between the six patterns is meaningful.

Figure 4

The energy spectra of the three effective neutrino species ${\nu }_e$ (red solid curves), ${\overline{\nu }}_e$ (green dashed curves), and ${\nu }_x$ (blue dotted curves) at terrestrial detectors corresponding to six different patterns of neutrino flavor conversion $P_{31}$ to $P_{22}$ defined in (18) are presented. The Garching flux model parameters G1 (upper panels) and G2 (lower panels) are used.