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
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
=⇒
−
=
λ
λρ
6/3/
6/1
2/1
3/1
0
000
0013/1
3331
3331
−=⇒
−
−
=
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
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.
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