1. Determining the neutrino flavor ratio at the astrophysical source
EPS HEP09, July
Determining the neutrino flavor ratio at the astrophysical source
By G.-L. Lin
National Chiao-Tung U. and Leung Center for Cosmology and Particle Astrophysics, National Taiwan U.
K.-C. Lai, G.-L. Lin and T. C. Liu,
arXiv: [hep-ph]

2.  source (1,0,0) Pion source (1/3,2/3,0) (0,1,0) (0,0,1) Muon damped●
(0,1,0)
(0,0,1)
Muon damped
source

3. The  source (1,0,0)
Motivated by the correlation of the arrival direction of the
cosmic rays to the Galactic Plane (GP) near EeV (1018 eV)
energies
AGASA 1998; Fly’s Eye 1998
Directional signal requires relatively-stable neutral
primaries.
Neutron decay length is about 10 kpc for En=1 EeV.
Smaller energy neutrons can decay
L. A. Anchordoqui, H. Goldberg, F. Halzen
and T. J. Weiler, 2004

4. Pion source (1/3,2/3,0)
Energies of various neutrinos are comparable, i.e.,
muon decays before losing its energy by interactions.
Cosmogenic (GZK) neutrinos produced by
and the subsequent pion decay fit into this category.

5. Muon damped source (0,1,0)
Muon loses significant amount of energy before it decays:
(1) muon interacts with matter
J. P. Rachen and P. Meszaros, 1998
(2) Muon interacts with background photon field
M. Kacherliess, O. Ostapchenko and R. Tomas,
arXiv:
See also
T. Kashti and E. Waxman Phy. Rev. Lett. 2005
Neutrino flux from muon decays is negligible

6. Transition from pion source to muon-damped source
T. Kashti and E. Waxman Phy. Rev. Lett. 2005
Transition from pion source to muon-damped source

7. Source with a significant tau neutrino flux
Optically thick sources: highly relativistic GRB jets
Neutrinos already oscillate inside the object.
O. Mena, I. Mocioiu and S. Razzaque, 2006 e  

8. The previous works   + 0 flavor ratio measured ij,  on Earth
Assumed source
flavor ratio
Probe neutrino mixing parameters

9. List of previous works

10. Our work   P + 0+0 source flavor ratio deduced flavor ratio
with certain accuracy
flavor ratio
measured on Earth
Oscillation matrix
depending on ij, 
See also A. Esmaili and Y. Farzan,
arXiv: [hep-ph]

11. Reconstructing the source flavor ratio
Measured flux P
Flavor Eigenstate
Mass Eigenstate
Ui contains 3 mixing angles--12, 23, and 13
one CP phase 

12. The exact form of oscillation probability matrix

13. 23=45, 13=0
This matrix is singular!

14. Uncertainties: mixing parameter and measurements
(1,0,0)
Becomes a band if
uncertainties on
mixing parameters are taken
into account
(1/3,2/3,0) ●
(0,1,0)
(0,0,1)
Degeneracy direction: 0()+0()=constant

15. Pion Source Results for the Reconstruction of Source Flavor Ratio
M.C. Gonzalez-Garcia and
M. Maltoni, Phys. Rept. 2008

16. Critical measurement accuracy for ruling out
muon damped source

17. Muon Damped Source

18. Critical measurement accuracy for ruling out
pion source

19. Pion Source For a non-vanishing best-fit value of 13 Gray: =0
G.L. Fogli et al.,
Phys. Rev. Lett. 2008
Pion Source
Gray: =0
Red: =
Blue: =/2

20. Muon damped source
Gray: =0
Red: =
Blue: =/2

21. What if one only measures R?
It is more challenging to measure S
Relies on double bang signature of 
Pion source
No constraint obtained!

22. Muon damped source
Very weak constraint!

23. Detectors of astrophysical neutrinos
IceCube—PMT array in South Pole ice
ANTARESKM3Net—PMT array in the Mediterranean
ANITA—radio wave detector above South Pole
Pierre Auger—earth skimming tau neutrinos
IceRay—radio extension of IceCube

24. Event rate
Taking Waxman-Bahcall upper bound E2Φ0=210-8 GeV/cm2 s sr, we estimate that it takes IceCube detector a decade to accumulate O(100)  events.
A rescaling from
J. Ahrens et al. [IceCube Collaboration], Astropart. Phys. 20, 507 (2004).

25. Summary
The structure of the oscillation probability matrix P makes it difficult to constrain
Accuracies in the measurements of R and S should both be better than 10% in order to distinguish the pion source and the muon-damped source at the 3 level—this takes IceCube detector more than a decade to achieve (assuming WB flux).
Future improvement on the accuracy of determining neutrino mixing parameters can help to distinguish astrophysical sources– see P. 16
To use the astrophysical source for probing the neutrino mixing parameter or new physics beyond the standard model, it is not realistic to assume a precise knowledge on the neutrino flavor ratio at the source. One should take a more relaxed assumption on the source.