SupernovaNeutrinoOscillations GeorgG.RaffeltMax-Planck-Institutf¨urPhysik(Werner-Heisenberg-Institut)F¨ohringerRing6,80805M¨unchen,Germany

April 2004 Report-No. MPP-2004-45 Contribution to Proc. 12th Workshop on Nuclear Astrophysics, 22–27 March 2004, Ringberg Castle, Tegernsee, Germany, edited by E. M¨ uller and H.-T. Janka

Supernova Neutrino Oscillations

Georg G. Raffelt

Max-Planck-Institut f¨ ur Physik (Werner-Heisenberg-Institut) F¨ohringer Ring 6, 80805 M¨ unchen, Germany

Neutrino oscillations are now firmly established from solar and atmospheric neutrino ob- servations and from purely terrestrial long-baseline experiments [1]. The mass differences between the three neutrino mass eigenstates are established and the 12 and 23 mixing angles are measured to be large while only an upper limit exists for the 13 mixing angle which is thus known to be small. The absolute neutrino mass scale remains unknown; the best upper limit of about ^P m

< 1 . 0 eV comes from cosmological arguments [2, 3, 4]. In future, the tritium beta decay experiment KATRIN will reach a comparable sensitivity [5], while neutri- noless double-beta decay experiments may well reveal the magnitude of the neutrino masses and their Majorana nature [6]. The magnitude of the 13 mixing angle as well as a possible CP-violating phase are to be searched at future long-baseline experiments [7]. As for the mass ordering, from matter effects in solar neutrino oscillations it is known that m

< m

, but it is not known if m

< m

< m

(normal hierarchy) or if m

< m

< m

(inverted hierarchy).

Determining this mass ordering depends on matter effects in 13 oscillations and thus requires a long baseline experiment, probably involving a future neutrino factory.

Alternatively, the mass ordering can be determined from the observation of the neutrino signal of a future galactic supernova because of resonant matter-oscillation effects in the supernova (SN) mantle and envelope [8]. One requirement to observe any oscillation effects in SN neutrinos, of course, is that the fluxes and/or spectra are different for different flavors. Our detailed studies of SN neutrino spectra formation implies that the flavor-dependent spectral differences are much less pronounced than had sometimes been claimed, but on the other hand that such differences do generically exist [9, 10, 11]. However, it will be difficult to establish the occurrence of SN neutrino oscillation simply by comparing a measured signal with theoretical predictions.

A model-independent approach is to take advantage of the Earth matter effect on the SN neutrino signal which leads to partial “regeneration,” i.e. the SN oscillation effect is partly undone if the SN is shadowed by the Earth relative to the neutrino detector. If Earth effects were to be observed in the ¯ ν

channel, the dominant channel in detectors such as Super- Kamiokande or IceCube, and if the 13 mixing angle has been established to be sufficiently large by other experiments (sin

θ

> 10

), then the mass hierarchy would be established to be normal. On the other hand, failing to observe Earth effects in the ¯ ν

channel would be ambiguous as it could be caused by the inverted hierarchy or by a smaller-than-expected flavor dependence of the SN fluxes and spectra.

The Earth effects would manifest themselves in an energy-dependent modulation of the

SN neutrino signal [12, 13] or by a difference between the measured signals in a detector that

2

measures the SN signal directly and one that measures it shadowed by the Earth [14]. In this sense Super-Kamiokande or the future Hyper-Kamiokande and IceCube are geographically complementary. In order to establish if the SN was shadowed by the Earth or not requires knowledge of its position in the sky. If the SN were obscured in all electromagnetic bands, the neutrino signal alone can reveal its position with sufficient accuracy, at least in a detector like Super-Kamiokande [15, 16].

In summary, the high-statistics neutrino observation of a future galactic SN would offer a huge scientific harvest regarding our understanding of SN physics. In addition, such a measurement could well reveal the nature of the neutrino mass hierarchy that is extremely difficult to determine in long-baseline experiments.

Acknowledgements

This work was supported, in part, by the Deutsche Forschungsgemeinschaft under grant No.

SFB-375 and by the European Science Foundation (ESF) under the Network Grant No. 86 Neutrino Astrophysics.

References

[1] M. C. Gonzalez-Garcia and Y. Nir, “Neutrino masses and mixing: Evidence and impli- cations,” Rev. Mod. Phys. 75 (2003) 345 [hep-ph/0202058].

[2] S. Hannestad, “Neutrino masses and the number of neutrino species from WMAP and 2dFGRS,” JCAP 0305 , 004 (2003) [astro-ph/0303076].

[3] Ø. Elgarøy and O. Lahav, “The role of priors in deriving upper limits on neutrino masses from the 2dFGRS and WMAP,” JCAP 0304 (2003) 004 [astro-ph/0303089].

[4] S. Hannestad and G. Raffelt, “Cosmological mass limits on neutrinos, axions, and other light particles,” hep-ph/0312154.

[5] L. Bornschein [KATRIN Collaboration], “KATRIN: Direct measurement of neutrino masses in the sub-eV region,” eConf C030626 (2003) FRAP14 [hep-ex/0309007].

[6] H. V. Klapdor-Kleingrothaus, I. V. Krivosheina, A. Dietz and O. Chkvorets, “Search for neutrinoless double beta decay with enriched Ge-76 in Gran Sasso 1990–2003,” Phys.

Lett. B 586 (2004) 198 [hep-ph/0404088].

[7] P. Huber, M. Lindner, M. Rolinec, T. Schwetz and W. Winter, “Prospects of accelerator and reactor neutrino oscillation experiments for the coming ten years,” hep-ph/0403068.

[8] A. S. Dighe and A. Y. Smirnov, “Identifying the neutrino mass spectrum from the neu- trino burst from a supernova,” Phys. Rev. D 62 (2000) 033007 [hep-ph/9907423].

[9] G. G. Raffelt, “Mu- and tau-neutrino spectra formation in supernovae,” Astrophys. J.

561 (2001) 890 [astro-ph/0105250].

[10] R. Buras, H. T. Janka, M. T. Keil, G. G. Raffelt and M. Rampp, “Electron-neutrino pair annihilation: A new source for muon and tau neutrinos in supernovae,” Astrophys.

J. 587 (2003) 320 [astro-ph/0205006].

3

[11] M. T. Keil, G. G. Raffelt and H. T. Janka, “Monte Carlo study of supernova neutrino spectra formation,” Astrophys. J. 590 (2003) 971 [astro-ph/0208035].

[12] A. S. Dighe, M. T. Keil and G. G. Raffelt, “Identifying earth matter effects on supernova neutrinos at a single detector,” JCAP 0306 (2003) 006 [hep-ph/0304150].

[13] A. S. Dighe, M. Kachelriess, G. G. Raffelt and R. Tom`as, “Signatures of supernova neu- trino oscillations in the earth mantle and core,” JCAP 0401 (2004) 004 [hep-ph/0311172].

[14] A. S. Dighe, M. T. Keil and G. G. Raffelt, “Detecting the neutrino mass hierarchy with a supernova at IceCube,” JCAP 0306 (2003) 005 [hep-ph/0303210].

[15] J. F. Beacom and P. Vogel, “Can a supernova be located by its neutrinos?,” Phys. Rev.

D 60 (1999) 033007 [astro-ph/9811350].

[16] R. Tom`as, D. Semikoz, G. G. Raffelt, M. Kachelriess and A. S. Dighe, “Supernova

pointing with low- and high-energy neutrino detectors,” Phys. Rev. D 68 (2003) 093013

[hep-ph/0307050].