1. To Determine the Initial Flavor Composition of UHE Neutrino Fluxes with Neutrino Telescopes Shun Zhou ( IHEP, Beijing ) April 23-26, 2006 International UHE Tau Neutrino Workshop

2. To Determine the Initial Flavor Composition of UHE Neutrino Fluxes with Neutrino Telescopes Shun Zhou ( IHEP, Beijing ) This talk is entirely based on the work: astro-ph/0603781 Zhi-zhong Xing and Shun Zhou, astro-ph/0603781

3. Ultrahigh-energy (UHE) cosmic rays All particle energy spectrum UHE neutrinos

4. What are neutrino telescopes?

5. How to identify neutrino flavors? 17m Learned & Pakvasa, 95 Halzen, astro-ph/0602132

6. Taking data under construction In planning First generation AMANDABaikal Second generation IceCube ANTARES NESTORNEMO in Lake Baikal at the South Pole in the Mediterranean Sea KM3NeT km-scale

7. Why neutrino telescopes? Halzen, astro-ph/0602132 The search for neutrinos from the annihilation of dark matter particles; The search for the signatures of the possible unification of particle interactions at the TeV scale; The search for deviations from the established neutrino oscillatory behavior that result from non-standard neutrino interactions; The search for particles from cosmic strings or any other topological defects or heavy cosmic remnants created in the early Universe; The search for the origin of UHE neutrinos by determining the initial flavor composition ( with well established neutrino oscillations );

8. Where do ultrahigh-energy neutrinos come from? Conventional ( or standard ) source: Pions are generated in the pp or p  collisions, then UHE neutrinos result from the decay of pions and the secondary muons. Postulated neutron source ( Crocker et al., 2005 ): UHE neutrinos are present through beta decay of neutrons. Possible muon-damped source ( Rachen & Meszaros, 1998): The sources are optically thick to muons but not to pions.

9.  where the parameter  characterizes the small amount of tau neutrinos at the sources. A useful parametrization: ( Xing & Zhou, astro-ph/0603781 ) How to describe the sources?  Conventional (or standard) source:  Postulated neutron source:  Possible muon-damped source: Remarks  All these kinds of sources can be described in a unified way;  One kind of source may be contaminated by other astrophysical processes, which can be measured by the  source parameter  ;  A small amount of tau neutrinos can be present via the decay of or mesons. ( Learned & Pakvasa, 95)

10. Neutrino Oscillations The transition probability For, the oscillation length in vacuum where the standard parametrization of neutrino mixing matrix is ( Barenboim & Quigg, 2003 ) So the averaged transition probability is

11. Working Observables We define the following observables: Only two of them are independent due to another one is the total neutrino flux of all flavors : with Remarks  In these flux ratios, systematic uncertainties in measuring the total neutrino flux can be largely cancelled out;  We assume that these observables can be well measured;    By use of any two observables, we can determine the initial flavor composition of UHE neutrino fluxes, which are characterized by the source parameters  and .

12. Definition Parametrization Analytical results Determination of the source parameters

13. Numerical Analysis (1) A global analysis of current neutrino oscillation data yields at 99% C.L.   the Dirac CP-violating phase  :   the source parameter  :   the source parameter  : to the order of (Strumia & Vissani, 05)

14.   The source parameter  is restricted to a narrow range;  The numerical uncertainties of neutrino mixing angles and the Dirac CP-violating phase are too large;   The other source parameter  is not specified. Numerical results

15. Numerical Analysis (2) Conventional source Postulated neutron source Possible muon-damped source The source may be contaminated: To examine the sensitivities of the observables to the source parameters and unconstrained neutrino mixing parameters: a. b. d. c. with

16. A modified version of conventional source Conclusions  1.The observables are sensitive to the deviations of  from its standard value;  2.Since the amount of tau neutrinos from neutrino oscillations is much larger than that from the sources, the observables are insensitive to the source parameter  ; 3.The case (a) is almost indistinguishable from the case (c).

17. A modified version of postulated neutron source Conclusions   1.The neutrino flux ratio is sensitive to the small departures of  and  from their given values; 2.The cases (a) and (c) are distinguishable from each other, which is due to the small correction from terms of order ;

18. possible muon-damped source A modified version of Conclusions  1.The behaviors of observables changing with the small departure of  from its given value can be understood as before.  2.The main feature of this scenario is the insensitivity of the observables to the source parameter , which can be seen from the following example: for and, holds and.

19. Summary  We have proposed a useful parametrization to describe the initial flavor composition of UHE neutrino fluxes:  It is really possible to determine the source parameters by observing two independent neutrino flux ratios, provided that three neutrino mixing angles and the Dirac CP-violating phase are well measured in neutrino oscillation experiments;  The analytical results are illustrated with numerical calculations: the full parameter space and some specific cases.

20. Thank you!