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

2. 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

3. Neutrino Astronomy
UHE 

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

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

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

7. 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

8. 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:

9. 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, (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, (2006)

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

11. 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

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

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

14. 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/

15. 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.

16. 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..

17. 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?

18. 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

19. 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.

20. General Parametrization
Parametrization [Xing, Zhou, Phys. Rev. D 74, (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:

21. 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 )

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

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

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

25. Contaminated Conventional Source

26. Contaminated Neutron Source

27. Contaminated Muon-damped Source

28. 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

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