Probing Flavor Ratios and Flavor

Transitions Mechanisms of

Astrophysical Neutrinos by Neutrino

TelescopesBy G.-L Lin

National Chiao-Tung U. Taiwan

K.-C. Lai, G.-L. Lin and T. C. Liu,

Phys. Rev. D 80, 103005 (2009); Phys. Rev. D 82, 103003 (2010)

T. C. Liu, M. A. Huang and G.-L. Lin, arXiv:1005.5154

F.-S. Lee, G.-L. Lin, T. C. Liu and Y. Yang, in progress

Pacific 2011, Moorea

Outline

• Review on possible types of astrophysical neutrino sources

• What can we learn by detecting these neutrinos?

(1) the original neutrino flavor ratio at astrophysical source-assuming three flavor oscillations

(2) the neutrino flavor transition mechanism during its propagation from source to Earth—with a clear knowledge on the source flavor ratio

‧Answering the above questions by flavor discriminations in neutrino telescopes

(1,0,0)

(0,1,0) (0,0,1)

( ) ( ) ( )( )( ) ( ) ( ) 1

,,

000

0000

=++

=Φ

τµ

τµ

νφνφνφ

νφνφνφ

e

e

( )1,1,02

1−

( )1,1,26

1−●(1/3,2/3,0)

Common astrophysical neutrino sources

νe

νµ ντ

From πdecays

Pion source (1/3,2/3,0)

ee ννµ

νµπ

µ

µ

++→

+→++

++

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.

++ +→∆→+ πγ np CMB

Muon damped source (0,1,0)

ee ννµ

νµπ

µ

µ

++→

+→++

++

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: 0708.3007

Neutrino flux from muon decays is negligible

See more detailed studies in

T. Kashti and E. Waxman Phy. Rev. Lett. 2005

P. Lipari, M. Lusignoli and D. Meloni, Phys. ReV. D 2007

T. Kashti and E. Waxman Phy. Rev. Lett. 2005

Transition from pion source to muon-damped source

⇒due to particle density and background field strength at the source

S. Hummer, M. Maltoni, W. Winter,and C. Yaguna, Astropart.

Phys. 34, 205 (2010).

Systematically studying sources on Hillas plot

( ) 2−∝ pp EEφ

Sources with significant ντ fractions

Neutrinos from WIMP annihilations

Tau lepton and b can decay into ντ

bb,−+→ ττχχ

Reconstructing the neutrino flavor ratio

at the source

( )( )( )

( )( )( )

( ) iiii

i

e

e

e

eeeee

UUUPP

PPP

PPP

PPP

νννν

νφνφνφ

νφνφνφ

αααβαβαβ

τ

µ

τττµτ

µτµµµ

τµ

τ

µ

*2

3

1

2

0

0

0

where, ==→≡

=

∑=

Measured flux Φ

Flavor EigenstateMass Eigenstate

Uααααi contains 3 mixing angles--θ12, θ23, and θ13one CP phase δ

Source flux Φ0

Standard neutrino

oscillations

Reconstructing the neutrino flavor ratio at the

source--continued

• How well can we distinguish astrophysical sources

with different neutrino flavor ratio, assuming three

flavor neutrino oscillations?

• This depends on our understanding of neutrino

mixing parameters and flavor discrimination

capabilities in neutrino telescopes.1σσσσ

3σσσσ Normal hierarchy

Flavor discrimination capability

At water Cherenkov detectors such as ANTARES, IceCube

and KM3NeT, track to shower event ratio can be used to

extract the flux ratio

In appropriate energy window, one can further identify tau

shower so that one can measure

J. F. Beacom et al. Phys. Rev. D 2003, arXiv: hep-ph/0307027v3

W. Winter, Phys. Rev. D 74, 033015 (2006).

( )( ) ( )τ

µ

νφνφ

νφ

+=

e

R

( )( )τνφνφ eS =

Flavor discrimination--continued

( )( ) ( )τµ νφνφ

νφ+

= eR '

( )( )τ

µ

νφ

νφ='S

In newly proposed Askaryan Radio Array (ARA)

with Eν>1017 eV, νe may be separated from other flavors By LPM effect. One can determine

ARA Collaboration: P. Allison et al.

arXiv: 1105.2854

At this energy, it is difficult

to measure

E. Bugaev et al., Astropart. Phys. 21, 491 (2004).

( )( ) ( )τµ νφνφ

νφ+

= eR '

ARA sensitivity on GZK neutrinos

Water Cherenkov detectors (astrophysical sources)

Only R is measured Both R and S are measured

15% accuracy

(~100 events)

1σ

3σ

Radio wave detectors (GZK neutrinos)

Only R’ is measured Both R’ and S’ are measured

15% accuracy

(~100 events)

Summary for part I

• We have reviewed various sources of

astrophysical neutrinos with different neutrino

flavor ratios.

• The possibility of reconstructing the above

flavor ratios through flavor discrimination in

neutrino telescopes is discussed.

Probing neutrino flavor transition

mechanisms—model independent

parameterizationThe flavor transition mechanisms of

astrophysical neutrinos might be probed.

Earlier discussions on this issue:G. Barenboim and C. Quigg, Phys. Rev. D 2003,

J. Beacom et al. Phys. Rev. Lett. 2003 …

Work out P model by model and calculate the

resultantΦwhich is to be tested by neutrino telescope.

However, we perform a transformation

Classification of flavor transition models can be

done easily on Q. Fit Q to the measurement

0Φ=Φ P source fluxterrestrially measured flux

.1PAAQ −=

K.-C. Lai, G.-L. Lin and T. C. Liu,

Phys. Rev. D 82, 103003 (2010)

(1,0,0)

(0,1,0) (0,0,1)

( )1,1,0 −

( )1,1,2 −−●(1/3,2/3,0)

bab

bba TTT

−≤≤+−

≤≤−−−+−+=Φ

3/11/3

3/11/6 ,)1,1,2()1,1,0()1,1,1(3

10

TTT )1,1,2()1,1,0()1,1,1( −−+−+=Φ λρκ

κ=1/3 corresponds to conservation of neutrino flux

νe

νµ ντ

( ) ( ) ( )( )Te τµ νφνφνφ ,,

( ) ( ) ( )( )( ) ( ) ( ) 1

,,

000

000

=++ τµ

τµ

νφνφνφ

νφνφνφ

e

T

e

0Φ=Φ P a=-1/3,b=0

a=-1/2,b=-1/6

a

b

A simple transformation

.

111

111

201

with

where,

3/1

1

333231

232221

131211

333231

232221

131211

−

−−=

=

=

−

A

A

PPP

PPP

PPP

A

QQQ

QQQ

QQQ

b

a

QQQ

QQQ

QQQ

e

e

eeee

τττµτ

µτµµµ

τµ

λρκ

( ) ( )( ) ( ) ( ) ( )

( ) ( ) ( ) κνφνφνφ

νφνφνφλνφνφρ

τµ

τµµτ

3

23

1 ,

2

1

=++

+−=−=

e

e

Pαβ≡P(νβ�να)

0,11 131211 ===⇒=∑ QQQPα

αβ

This then implies κ=1/3Gives the meaning of

Q matrix

Classify flavor transition models

Flux conservation

=

333231

232221

001

QQQ

QQQQ

Flux conservation+νµ--ντ symmetry

=

3331 0

000

001

QQ

Q

Values for Q31 and Q33determine the model

Fit Q31 and Q33 to the data

limit 0,45 1223°° == θθ

Recent T2K result makes it more complicated.

Q matrix for standard oscillation

=

3/100

000

001

Q

0sin

,3/1sin

,2/1sin

13

2

12

2

23

2

=

=

=

θ

θ

θ

9/cossin29/2cos2 1323 δθθε +≡

i.e., Q31=0, Q33=1/3

Evaluated in tribimaximal

limit:

To the first order in

−=

3/10

300

001

εεQ

0.27/3

3/24.03

−=

−=− ε Normal hierarchyInverted hierarchy

Take T2K best fit: sin22θ13=0.11 (N), 0.14 (I) atδ=0Also assume θ23=π/4

Q matrix for neutrino decays—just for illustration

=

002/1

000

001

Q

Normal hierarchy Inverted hierarchy

3

2

1 3

2

1

−

=

002/1

000

001

Q

i.e., Q31=0.5, Q33=0i.e., Q31=-0.5, Q33=0

Observing pion source and muon damped

source to determine Q31 and Q33

3/

0

3/1

3/1

0

000

0013/1

31

3331

Q

QQ

=⇒

−

=

λ

λρ

6/3/

6/1

2/1

3/1

0

000

0013/1

3331

3331

QQ

QQ

−=⇒

−

−

=

λ

λρ

Pion source

Muon-damped source ( )( ) ( )

+−≡

23

1 τµ νφνφνφλ e

1σσσσ

3σσσσ

NHIH

OSC

Compare oscillation with neutrino decays (H, M�L)

( )( ) ( )τ

µ

νφνφ

νφ

+=

e

R Water Cherenkov detector ~50 events

Change the input model

IH

OSC

NH

Change the input model--continued

OSC

NHIH

GZK neutrino dominates at Eν>1017 eV

We have a pure pion source

( ) ( ) ( ) 3/23

1

so ,

0

3/1

3/1

0

000

0013/1

31

3331

Q

QQ

e =

+−≡

−

=

τµ νφνφνφλ

λρ

Pion source can only probe Q31

Compare oscillation with neutrino decays (H, M�L)

%10/ =∆ RR %10/ =∆ RR

%10/ =∆ RR

%20/ '' =∆ RR%10/ '' =∆ RR

( )( ) ( )τµ νφνφ

νφ+

= eR '

OSC

NHIH

5.0osc' =R

Radio wave detection

~50 events

Change the input model

%10/ =∆ RR %20/ =∆ RR

%10/ =∆ RR

OSC

IH NH

%10/ '' =∆ RR %20/'' =∆ RR

2NH =R

Change the input model

0IH' =R

Assume ∆R’IH=0.1

IH

OSC

NH

Summary (I)

• We have proposed a model-independent parameterization, the Q matrix, for flavor transition mechanisms (standard oscillations and beyond) of astrophysical neutrinos.

• Each row of matrix Q carries a definite physical meaning. Q1i for normalization, Q2i for µ-τ symmetry breaking and Q3i governing the flux difference

• In the µ-τ symmetry limit with flux conservation, only Q31 and Q33 are non-vanishing. They are useful for classifying neutrino flavor transition models.

( ) ( ) ( )2

τµ νφνφνφ+

−e

Summary (II)

• Kilometer size neutrino telescopes such as IceCube

and KM3NeT are suitable for detecting neutrinos

with energies up to few tens of PeV. They are

capable of distinguishing track and shower signals.

The parameters Q31 and Q33 can both be probed by

simultaneously observing pion source and muon-

damped source. However, an astrophysical neutrino

source is generally a mixture of the two, and the

degree of the mixture depends on the neutrino

energy.

Summary (III)

• For Eν>1017 eV, one expects the dominance of GZK

neutrino flux which is a pion source.

• The Askaryan Radio Array (ARA) experiment is optimized for observing GZK neutrino flux. The discrimination of νe from νµ and ντ can help to probe the parameter Q31.

• A 20% accurate measurement on flavor ratio is

generally sufficient to distinguish neutrino decay models (H,M�L) from standard neutrino oscillations at the 3σ level.