To Determine the Initial Flavor Composition of UHE Neutrino Fluxes with Neutrino Telescopes

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: Zhi-zhong Xing and Shun Zhou, astro-ph/0603781

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

4. What are neutrino telescopes?

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

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

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

8. Where do ultrahigh-energy neutrinos come from? • Conventional ( or standard ) source: Pions aregenerated inthe ppor p collisions, thenUHEneutrinos 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. 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) • Conventional (or standard) source: • Postulated neutron source: • Possible muon-damped source: How to describe the sources? A useful parametrization: ( Xing & Zhou, astro-ph/0603781 ) where the parameter characterizes the small amount of tau neutrinos at the sources.

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

11. with Working Observables We define the following observables: Only two of them are independent due to 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  . another one is the total neutrino flux of all flavors:

12. Definition Parametrization Analytical results Determination of the source parameters

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

14. Numerical results • 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.

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

16. A modified version of conventional source • Conclusions • The observables are sensitive to the deviations of  from its standard value; • 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  ; • The case (a) is almost indistinguishable from the case (c).

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

18. A modified version of • Conclusions • The behaviors of observables changing with the small departure of  from its given value can be understood as before. • 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 • . possible muon-damped source

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!