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

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/0603781astro-ph/0603781

Ultrahigh-energy (UHE) cosmic rays

All particle energy spectrum

UHE neutrinos

What are What are neutrino neutrino

telescopes?telescopes?

How to identify How to identify neutrino neutrino flavors?flavors?

17m

eV10GeV10PeV1 156

Learned & Pakvasa, 95

Halzen, astro-ph/0602132

Taking

data

under constructi

on In plannin

g

First First generatiogeneratio

nnAMANDAAMANDA BaikalBaikal

Second Second generatiogeneratio

nn

IceCubIceCubee

ANTARESANTARES

NESTORNESTOR NEMONEMO

in Lake Baikalat the South

Pole

in the Mediterranean Sea

KM3NeKM3NeTT

km-scale

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 );

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.

0:2:1:: τμe

Postulated neutron source ( Crocker et al., 2005 ):UHE neutrinos are present through beta decay of neutrons. 0:0:1:: τμe

Possible muon-damped source ( Rachen & Meszaros, 1998):The sources are optically thick to muons but not to pions.

0:1:0:: τμe

where the parameter characterizes the small amount

of tau neutrinos at the sources.

,sin,coscos,cossin,, 022222

τμe

A useful parametrization: ( Xing & Zhou, astro-ph/0603781 )

How to describe How to describe the sources? the sources?

)0,3.35(),( 0:2:1:: τμe

Conventional (or standard) source:

)0,90(),( 0:0:1:: τμe

Postulated neutron source:

)0,0(),( 0:1:0:: τμe

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)

sD BB

Neutrino Oscillations

.

132313231223121323122312

132313231223121323122312

1313121312

ccescsscesccss

csesssccessccs

escscc

Vii

ii

i

)(D Pβ

)D()D()D(

.||||)(22

3

1i

ii VVPP

The transition probability

252 eV10|| mFor

, the oscillation length in vacuum

where the standard parametrization of neutrino mixing matrix is

.eV1

Mpc105.2||

4 242osc

E

m

EL ( Barenboim & Quigg,

2003 )

,Re2||||)( 2

2

22 E

Lmi

lkklk

lkk

k

kl

eVVVVVVP

,,, e

3,2,1, lk

So the averaged transition probability is

Working Observables

.,,,,DD

D

DD

D

DD

D

ee

ee RRR

We define the following observables:

Only two of them are independent due to

another one is the total neutrino flux of all flavors:

.DDD0 ee

1ˆˆˆ RRRe ;1

ˆ

R

RR

wit

h

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 .

)tancossin(sec

tancossin2222

222

PPP

PPPR

e

e

))(ˆ())(ˆ(

)()(ˆ)(ˆtan

))(ˆ())(ˆ(

)()(ˆ)(ˆsin

2

2

PPPRPPPR

PPPPPPRPPR

PPPRPPPR

PPPPPPRPPR

ee

eeee

ee

)(D Pβ

.,,,,DD

D

DD

D

DD

D

ee

ee RRRDefinitio

n

,sin,coscos,cossin,, 022222

τμe Parametrization

Analytical results

Determination of the source parameters

Numerical Analysis (1)

A global analysis of current neutrino oscillation data yields

.

132313231223121323122312

132313231223121323122312

1313121312

ccescsscesccss

csesssccessccs

escscc

Vii

ii

i

,100

,5436

,3830

13

23

12

at 99% C.L.

]180,0[ the Dirac CP-violating phase :

the source parameter :

]18,0[

]90,0[ the source parameter : 1.0sin2

to the order of

13sin

(Strumia & Vissani, 05)

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

Numerical Analysis (2)

4030

180

100

180

9080

180

)0,3.35(),( Conventional source

)0,90(),( Postulated neutron source

)0,0(),( 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:

),0(),( 13 a. )0,5(),( 13

b.

d.

)180,5(),( 13

)90,5(),( 13c

. 45,34 2312 with

A modified version of )0,3.35(),( 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).

A modified version of

)0,90(),( 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 ;

eR

132sin

)0,0(),( 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

.

4523 013 PP

Summary

We have proposed a useful parametrization to describe the initial flavor composition of UHE neutrino fluxes: ,sin,coscos,cossin,, 0

22222τμe

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.

))(ˆ())(ˆ(

)()(ˆ)(ˆtan

))(ˆ())(ˆ(

)()(ˆ)(ˆsin

2

2

PPPRPPPR

PPPPPPRPPR

PPPRPPPR

PPPPPPRPPR

ee

eeee

ee

Thank Thank you!you!