Neutrino Flavor ratio on Earth and at Astrophysical sources

K.-C. Lai, G.-L. Lin, and T. C. Liu,National Chiao Tung university

Taiwan

INTERNATIONAL SCHOOL OF NUCLEAR PHYSICS31st Course

Neutrinos in Cosmology, in Astro-, Particle- and Nuclear PhysicsErice-Sicily: 16 - 24 September 2009

Neutrino flavor ratio at sources

(0, 0, 1)

1

,,

000

0000

e

e

Source (1, 0, 0)

Muon damped source (0, 1, 0)

●

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

●

Basic measured parameter definition– R : The ratio of track to shower events.– S: The ratio of two flavor shower.

• Experimental results are limited by number of detected events, fluctuation R and S

• Assumed

e

e

SR

i

i

i

i

i

i

i

i

R

R

R

R

S

S

S

S

1

1

K. Blum, Y. Nir and E. Waxman, arXiv:0706.2070 [hep-ph].

Basic idea I:What is the real source we observed.

From measured data to original source:

P

True flavor ratio at sourceMeasured flavor ratio at Earth

Ri,th and Si,th

Ri,exp and Si,exp 2

1 region

2 < 2.3

2 < 11.8

3 region.

0

’0

’0

+

Choubey et al., PHYSICAL REVIEW D 77, 113006 (2008)

# 1: Only 10% R

• For E < 0.3PeV, difficult to distinguish e from . Only R

• Even at R/R ~ 10%, could not resolve muon damp source from pion source.

muon damp source

Pionsource

0

C.L.) (90% 019.0sin

,45.0sin

,32.0sin

132

09.006.023

2

02.002.012

2

R only is unable to determine the original source.

Measuring S is necessary.

M. C. Gonzalez-Garcia and M. Maltoni, Phys. Rep. 460, 1(2008); M. Maltoni, T. Schwetz, M. A. Tortola, and J. W. F.Valle, New J. Phys. 6, 122 (2004); S. Choubey, Phys. At.Nucl. 69, 1930 (2006); S. Goswami, Int. J. Mod. Phys. A21, 1901 (2006); A. Bandyopadhyay, S. Choubey, S.Goswami, S. T. Petcov, and D. P. Roy, Phys. Lett. B 608,115 (2005); G. L. Fogli et al., Prog. Part. Nucl. Phys. 57,742 (2006).

# 2-1: sin213 =0 for

• Can rule-out pion source from muon-damped source under R/R ~ 10%, S/S ~ (11~14)%

• Astrophysical hidden source (1/2, a, (2/3 –a)) can be rule-out too.

112/04/18 6

sin223 =0.45 sin223 =0.55

muon damp source

Pionsource

Astrophysical Hidden source

O. Mena, et al., PRD, 2007

# 2-2: sin213 = 0 for

• Can't rule-out muon-damped source from pion source under R/R ~ 10%, S/S ~ (11~12)%,

sin223 =0.45 sin223 =0.55

muon damp source

Pionsource

# 3-1: CP phase ,

Under R/R ~ 10%, S/S ~ 13%112/04/18 8

muon damp source

sin213 = 0 sin213 = 0.016 0.01(non zero)

Gray: =0Blue: =/2Red: =Pion

source

No dependence on CP phase

when (sin2 13) best-fit = 0

# 3-2: CP phase for

muon damp source

sin213 = 0 sin213 = 0.0160.01

Gray: =0Blue: =/2Red: =Pion

source

Under R/R ~ 10%, S/S ~ 13%

# 4-1: Critical uncertainty

R /R = 13%

S /S = 16%

• R /R = 5%

• S /S = 6%

Need several hundreds of neutrino events

to confirm the source.

Basic idea II: From Oscillation mechanism to new physics

flavor ratio measured on Earth

oscillation

Possible source flavor ratio

o

ij,

ij,

Decay

ij,

Other mechanism

Normal hierarchy:sin2θ13 < 0.14 and 0.37 < sin2θ23 <0.65Inverted hierarchy:sin2θ13 < 0.27 and 0.37 < sin2θ23 <0.69

Possible measured region with different strategy

Pion source with normal hierarchy

Muon source with normal hierarchy

Pion source with inverted hierarchy

Muon source with inverted hierarchy

*

* Inverted hierarchy is only possible

#

# Allow both hierarchySuper-Kamiokande Collaboration Phys. Rev. D 74, 032002 (2006)

All possible measured ratio for neutrino oscillation mechanism

1000 e

Neutrino oscillation#

# New physics

Beyond osciallationnormal hierarchy

inverted hierarchy

measured ratio

All possible source

One example: Decay with normal mixing angle

#

#

#: Only decay in this region is available.

Michele Maltoni et al JHEP07(2008)064

Another example: Decay with inverted hierarchy mixing angle

# ##

#: Only decay in this region is available.

Conclusion

• Part I• Measuring the R ratio only is not sufficient to

determine the source type.• The Critical uncertainties required to distinguish

between pion and muon damped source: for pion source: R /R = 5% S /S = 6% for muon source: R /R = 13% S /S = 16%

• Part II• New method to probe new physics.

Reference:

The exact form of oscillation probability matrix

K.-C. Lai, G.-L. Lin, and T. C. Liu, arXiv:0905.4003 [hep-ph]

ω ≡ sin22θ12, Δ ≡ cos2θ23, D ≡ sinθ13,

δ the CP phase.