Flavor Distribution of UHE -Oscillations at -Telescopes Zhi-zhong Xing (IHEP, Beijing) Toulon, France, April 22-24, 2008

Outline 1. UHE Neutrino Oscillations and the 1:1:1 Rule 2. -Telescopes as a Probe of the Flavor Mixing 3. Flavor Distributions at Astrophysical Sources

Neutrino Astronomy UHE 

High-energy Cosmic Messengers Neutrino (1e:2) Light absorbed Proton scattered by magnetic field (1e:1:1) CMB

Optical Cherenkov -Telescopes NESTOR Pylos, Greece ANTARES La-Seyne-sur-Mer, France NEMO Catania, Italy BAIKAL Russia AMANDA and IceCube South Pole, Antarctica

KM3 ~ WaterCube WaterCube  Green Olympic Concept A WaterCube in the Mediterranean Sea to hunt for UHE ’s?

UHE Neutrino Oscillations The transition probability: For , the oscillation length in vacuum The expected sources (AGNs etc) at typical distances: ~100 Mpc So, after many oscillations, the averaged transition probability of UHE neutrinos is atmosphere

Conditions for the 1:1:1 Rule Given a source with At the -telescope: If there is a - symmetry for V : Then the unitarity of V leads to: or CPC: CPV: In the standard parametrization: 2 cases:

Reversed Points of View First, to discover UHE ’s; second, to measure them precisely. Point A: if the production mechanism of UHE ’s from a distant astrophysical source is really understood (e.g., with the help of –astronomy), then one may use –telescopes to determine or to constrain one or two of three neutrino mixing angles and the Dirac CP phase. Example: Z.Z. Xing, Phys. Rev. D 74, 013009 (2006) Point B: if three neutrino mixing angles and the Dirac CP phase have been measured to a good degree of accuracy in terrestrial neutrino oscillation experiments, one may use –telescopes to determine or to constrain the flavor composition of UHE cosmic neutrino fluxes from a distant astrophysical source. Example: Z.Z. Xing, S. Zhou, Phys. Rev. D 74, 013010 (2006)

Incomplete List of Papers ■ Learned, Pakvasa, APP 3, 267 (1995) ★ Athar et al, PRD 62, 103007 (2000) ★ Bento et al, PLB 476, 205 (2000) ★ Gounaris, Moultaka, hep-ph/0212110 ★ Barenboim, Quigg, PRD 67, 073024 (2003) ★ Beacom et al, PRD 68, 093005 (2003) ★ Keraenen et al, PLB 574, 162 (2003) ★ Beacom et al, PRD 69, 017303 (2004) ★ Hooper et al, PLB 609, 206 (2005) ★ Serpico, Kachelriess, PRL 94, 211102 (2005) ★ Bhattacharjee, Gupta, hep-ph/0501191 ★ Serpico, PRD 73, 047301 (2006) ● Xing, PRD 74, 013009 (2006) ● Xing, Zhou, PRD 74, 013010 (2006) ★ Winter, PRD 74, 033015 (2006) ★ Athar et al, MPLA 21, 1049 (2006) ★ Rodejohann, JCAP 0701, 029 (2007) ★ Majumdar, Ghosal, PRD 75, 113004 (2007) ● Xing, NPB (Proc. Suppl.) 168, 274 (2007) ★ Blum, Nir, Waxman, arXiv:0706.2070 ★ Lipari et al, PRD 75, 123005 (2007) ★ Meloni, Ohlsson, PRD 75, 125017 (2007) ★ Awasthi, Choubey, PRD 76, 113002 (2007) ★ Hwang, Kim, arXiv:0711.3122 ● Xing, NPB (Proc. Suppl.) 175-176, 421 (2008) ★ Pakvasa et al, JHEP 0802, 005 (2008) ★ Choubey, Niro, Rodejohann, arXiv:0803.0423 ★ Farzan, Smirnov, arXiv:0803.0495 ★ Maltoni, Winter, arXiv:0803.2050 ★ ……

Conventional UHE -Sources  High-energy pp collisions:  charged poins  muon and electron neutrinos  High-energy p collisions: There is no production of electron anti-neutrino, since the produced neutrons can escape the source before decaying (Ahlers et al, 2005) In either case, the sum of neutrinos & antineutrinos

Data and Approximations A global analysis of current neutrino oscillation data yields - symmetry (Strumia, Vissani 2006)

Effect of - Symmetry Breaking At the detector of a neutrino telescope: Two small parameters to measure tiny - symmetry breaking:

Correction to the 1:1:1 Rule The bound appears when two small - symmetry breaking parameters turn to take their maximal (upper limit) values The allowed range of  : Xing: hep-ph/0605219

Signals at -Telescopes Can  = 0 non-trivially hold? Yes, if the following relation is by accident satisfied: A signal of   0 is in general expected, however. The working observables: It makes sense to consider the complementarity between -telescopes and terrestrial -oscillation experiments, so as to pin down the parameters of -mixing and CP violation.

Glashow Resonance A novel possibility to detect the UHE electron anti-neutrino flux from distant astrophysical sources (Glashow 1960): A -telescopes may measure (a) the GR-mediated electron anti-neutrino events; (b) the muon neutrino  muon anti-neutrino charged-current-interaction events in the vicinity, to extract Comment 1: it is possible to probe the - symmetry breaking; Comment 2: it is likely to probe the solar neutrino mixing angle..

Unitarity Violation In a seesaw model with heavy Majorana neutrinos, the mixing matrix of three light neutrinos must be non-unitary. The standard parametrization [Xing, PLB 660, 515 (2008)]: 9 new mixing angles can maximally be of O(0.1); while 9 new CP-violating phases are entirely unrestricted (see, Antusch et al 2006; Fernandez-Martinez et al 2007) Question: can unitarity of -mixing be tested at a -telescope?

Signal of UV at -Telescopes For example, we consider a non-unitary correction to the tri-bi-maximal neutrino mixing pattern (Xing 2008): Consider the conventional –sources: (Xing, Zhou, in preparation) UV ≤ O(1%) maximally, too small ? - symmetry breaking

Typical UHE -Sources Conventional (or standard) source: ’s are generated from p+p or p+ collisions. UHE ’s produced from the decays of ’s and the secondary ’s. Postulated neutron source (Crocker et al 2005): UHE neutrinos are produced from the beta decay of neutrons. Muon-damped source (Rachen, Meszaros 1998): The source is optically thick to ’s but not to ’s.

General Parametrization Parametrization [Xing, Zhou, Phys. Rev. D 74, 013010 (2006)]: where  characterizes the small amount of tau ’s at the source [e.g., from Ds- or B-meson decays (Learned, Pakvasa 1995)]. Conventional (or standard) source: Postulated neutron source: Possible muon-damped source:

Working Observables We define the following observables: Only two of them are independent, because with Another observable is the total neutrino flux of all flavors: Question: can all of the three observables be well measured? Point: by using any two observables, we may determine the initial flavor composition of UHE neutrino fluxes (i.e.,  and )

Determination of the source parameters Analytical Result Definition: Parametrization: Determination of the source parameters

Numerical Result the Dirac CP-violating phase  : the source parameter  : the source parameter  :

Three UHE -Sources The source might be contaminated: Conventional source Postulated neutron source Possible muon-damped source In our numerical illustration, we typically input

Contaminated Conventional Source

Contaminated Neutron Source

Contaminated Muon-damped Source

Do Flavor Physics with -Telescopes The astrophysical sources of UHE neutrinos: puzzles Do ultra-long baseline & ultra-high energy neutrino oscillation experiments with ultra-large -telescopes? Neutrino telescopes can do this, at least in principle The initial flavor distribution of UHE neutrino fluxes should be determined experimentally Given a well-understood source, a -telescope can help determine the neutrino mixing parameters There is some important complementarity between terrestrial -experiments and -telescopes

No Exact Flavor Democracy Last but not Least Source Detector Unless two conditions are satisfied in 2 cases No Exact Flavor Democracy