PDF Non oscillation flavor physics at future neutrino oscillation facilities

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Tokyo Metropolitan University

Non oscillation flavor physics at future neutrino oscillation facilities

2 July 2008 @nufact08

Osamu Yasuda

(SM+m_ν) + (correction due to New physics) which can be probed through oscillations

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1. Motivation for research on New Physics 2. A word on origin of New Physics

3. New Physics in oscillation experiments 4. New Physics at source and detector

5. New Physics in propagation (matter effect) 6. Violation of unitarity

7. Summary

Notations throughout this talk:

Δ E

_jk

= Δ m

²_jk

/2E

A= 2

^1/2

G

_F

N

_e

(matter effect)

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ν α ν β f f’

ν α l β

f f’

Just like at B factories, high precision measurements of

ν

oscillation in future experiments can be used also to probe physics beyond SM by looking at deviation from SM+massive

ν

charged current neutral current

1. Motivation for research on New Physics

In this talk I will discuss phenomenologically new physics which is described by 4-fermi exotic interactions:

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These operators are supposed to be SU(2) invariant

before symmetry breaking of SM. The lower dimensional operators relevant to neutrino oscillation experiments

are of dim 6 and dim 8.

Jdim 6 operators such as turn out to be strongly constrained by charged lepton processes.

Jdim 8 operators such as do not have strong constraints.

) (

)

(H⁺L_α γ ^μiD_μ HL_β

2. A word on the origin of New Physics

If we have New Physics at higher energy scale, there can be higher dimensional operators:

To justify the discussions below, dim 8 operators will be assumed.

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dim-6 operators

dim-8 operators

Constraints on dimension-6, 8 operators

l

β

ν

α

W

-

f

f ′ ^SM ^NP

strong constraints from charged lepton processes, e.g., μ⁺

J

ê⁺ê⁺ê^-

little constraints from charged lepton

) (

)

(H⁺L_α γ ^μiD_μ HL_β

ν

β

ν

_α

f f ′

NP

f

_μ

′

μ β

α

γ l γ

l

f

_μ

′

μ β

α

γ γ

ν l

(6)

Theoretically the coefficients

ε

_αβ of the exotic

interactions are expected to be suppressed by ratio (M_W/Λ_NP)ⁿ << 1 (n=2 for dim 6, n=4 for dim 8).

In phenomenological analysis, however, we take into account only the constraints from the experiments, and we do not worry about the magnitude of the coefficients

ε

_αβ which may be unnaturally large from a theoretical view point.

The coefficient of the operator is usually normalized in terms of G_F:

where etc

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Effective eigenstate

z

NP at source

Grossman, Phys. Lett. B359, 141 (1995)

3. New Physics in oscillation experiments

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Effective eigenstate

z

NP at detector

(9)

z

NP in propagation (NP matter effect)

SM NP

SM potential due to W exchange is modified by NP

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SM+m ν

NP

z

Oscillation probability w/o and w/ NP

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NB ^o NP effects at production and at detection becomes important when L is smaller

o NP effects in propagation becomes important when L is larger

( )

^U^s ^-¹ ²

Ud P

βα β

α ν

ν ⎥⎥

⎦

⎤

⎢⎢

⎣

→ ⎡

⎟⎠

⎜ ⎞

⎝⎛ → i.e., no BG from ν osc. in the limit of L J 0

because AL ε_αβ ~ ε_αβ (L/2000km)

Experiments with a shorter baseline are advantageous

Experiments with a longer baseline are advantageous Sato: ISS 2^nd plenary @ KEK

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o History of analysis of sensitivity

1. Statistics only 2. Statistics +

systematic errors 3. Statistics +

systematic errors + correlations of errors

4. Statistics +

systematic errors + correlations of errors +

degeneracies

ε

αβ

θ or 2

sin²

t

Unless new ideas appears, sensitivity to unknown parameters is monotonically decreasing as a function of time.

(Just for illustration)

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4. New Physics at source and detector

10 2

6

, _e^d < × ⁻

esμ

ε

μ

ε

10 2

1

, ^d < × ⁻

s μτ

μτ

ε ε

Optimistic bounds on

ε

_αβ are obtained by

and typically are of order 10^-2

1 . 0 , _e^d <

esτ

ε

τ

ε

bound upper

) (

, max

)

(ν_α ν_β

ε

_αβ

ε

_αβ^* ²

ε

_αβ ²

ε

_αβ ² _⎟ ^< ν_α ^→ν_β

⎠

⎜ ⎞

⎝

− ⎛

≅

− P

P ^s ^d ~ ^s ^d

INOMAD

I^MiniBooNE

I^NOMAD

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Gonzalez-Garcia, Grossman, Gusso, Nir, Phys. Rev. D64, 096006 (2001) μ μ

μ μ

e e e e

CP P P

P A P

+

≡ − Sensitivity to

ε

_eμ at

ν

factory

Statistics only;

naïve arguments 10⁻4

×

< a few

esμ

ε

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Ota-Sato-Yamashita, PRD65:093015,’02 10 3

3× ⁻

=

esμ

ε

ν ν

_τ ε_μτ^s^,^m ₌ ₃_×₁₀⁻³

μ →

ν

μ

ν

_e ^→ ^s ₌ ₃_×₁₀⁻³

eτ

ε

Statistics + some correlations of errors

Required data size in unit of 10²¹ μ U100kt

Sensitivity to

ε

_eμ,

ε

_eτ,

ε

_μτ at

ν

factory

Sato: ISS 2^nd plenary @ KEK

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Sensitivity by Noνa + DC-200kt Kopp, Lindner, Ota, Sato, PRD77:013007,2008

d* s e

e μ

μ ε

ε = ε_e^s_τ =ε_τ^d_e^*

μτs

ε

s*

d μτ

τμ ε ε ⁼

μμs

ε

d* s e

eμ εμ

ε = ε_μμ^d =ε_μμ^s^*

se

εμ

d* s ee ee ε ε =

10 2

3× ⁻

s <

μe

ε

Statistical +

systematic errors + correlations of errors +

degeneracies T2K + DCHOOZ

10 2

5 .

1 × ⁻

s <

μe

ε

Noνa + DC-200kt

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5.1 Constraints from various

ν

experiments

(CHARM, LEP, LSND, NuTeV)

Davidson, Pena-Garay, Rius, Santamaria, JHEP 0303:011,2003

ε_ee , ε_eτ , ε_ττ ~O(1) are consistent with accelerator experiments data

5. New Physics in propagation (matter effect)

See also Berezhiani and A. Rossi, PLB535 (‘02) 207; Barranco et al., PRD73 (‘06) 113001; Barranco et al., arXiv:0711.0698.

Because of the relation , the dominant contribution comes from the quantities with largest errors.

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update of JHEP 0303:011,2003 on July 1, 2008 courtesy by Sacha Davidson

Only the bound on | ε_eμ | is modified:

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ε

_ee ^,

ε

_eτ ^,

ε

_ττ ^~O(1) are consistent with atmospheric neutrino data, provided that

5.2 Phenomenology with

ε

_ee ^,

ε

_eτ ^,

ε

_ττ ^~O(1)

95%CL 99%CL 3σCL

Friedland-Lunardini-Maltoni, PRD70:111301,’04; Friedland- Lunardini, PRD72:053009,’05

z Constraints from

ν

_atm

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z Exact analytical formula for the oscillation

probability with

ε

_ee ^,

ε

_eτ ^,

ε

_ττ in the limit

Δ

m²₂₁

J

⁰

OY arXiv:0704.1531 [hep-ph]

Eigenvalues can be exactly obtained in the limit

Δ

^m²²¹

J

^{0 :}

This includes corrections to all orders in

θ

¹³^,

ε

_ee ^,

ε

_e_τ ^,

ε

_ττ ^.

The assumptions are

Δ

^m²²¹^{=0 and}

ε

_ττ

=

^|

ε

_e_τ ^|²

/(1+ ε

_ee

)

Corrections in

Δ

^m²²¹ ^{and other}

ε

^αβ can be also obtained to first order.

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Once the eigenvalues are known, we can easily get the analytical formula for the oscillation probability by KTY’s method Kimura, Takamura, Yokomakura (PLB537:86,2002)

The problem of obtaining the exact analytical oscillation probability is reduced to obtaining only the eigenvalues!

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• ν

_e appearance probability

•

ν

_μ disappearance probability

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• At high energy limit, matter effect becomes

dominant, but because the two eigenvalues of matter potential matrix turn out to be zero, the scenario is

reduced to vacuum oscillation which is consistent with the high energy atmospheric neutrino data.

A>> |

Δ

^E_jk^|

In the limit θ₁₃J0

Friedland-Lunardini, PRD72:053009,’05

At first sight NP with

ε

_ee ^,

ε

_eτ ^,

ε

_ττ ^~O(1) seems to be inconsistent with

ν

_atm, but it is not the case:

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• At low energy or at shorter baseline (such as K2K &

MINOS), matter effect is negligible compared to ΔE_jk, so the sub-GeV atmospheric and K2K + MINOS data are supposed to give us the true value for Δm²₂₃ and sin²2θ₂₃Jc²_β>0.45.

• The multi-GeV atmospheric data should in principle give us a signature for NP, but statistics is so low that we can’t say anything conclusive.

J Will HK improve the situation?

Friedland-Lunardini, PRD72:053009,’05

Thus NP with

ε

_ee ^,

ε

_eτ ^,

ε

_ττ ^~O(1) is consistent with

ν

_atm for the moment.

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So, as approximation, we can eliminate

ε

_ττ by

ε

_ττ ^{= |}

ε

_eτ ^|² ^/(1+

ε

_ee) and we can reduce the problem in (

ε

_ee ^{, |}

ε

_eτ ^|,

ε

_ττ) to the allowed region in (

ε

_ee ^{, |}

ε

_eτ ^{| ).}

|

ε

_eτ ^|=tan

β

⁽¹⁺

ε

_ee^{) (}

β

stands for the gradient of the line), c²_β>0.45 J tan²

β

^<1.2

degeneracy:

(1+ε_ee) Q -(1+ε_ee)

Δ

m²₃₁Q -

Δ

m²₃₁

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Blennow-Ohlsson-Skrotzki, PLB660:522,’08

z

ν

_e ^appearance

Sugiyama, 0711.4303 [hep-ph];

OY, Acta Phys.Polon.B38:3381,’07

If |ε_eτ| is very large then we may be able to prove the existence of NP from ν_e appearance at MINOS

Region testable by ν_e appearance at MINOS

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T2KK

T2K

ν

_e appearance at T2K(K) T2K(T2KK) is insensitive (sensitive) to |ε_eτ |, so if |ε_eτ | is very large then we may be able to prove the

existence of NP from ν_e appearance by T2K-T2KK complex.

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z ν_μ disappearance

Friedland, Lunardini, PRD74:033012,‘06

The allowed region before (left) and after (right) the first MINOS results

Because of the two constraints due to

ν

_atm , sin²2

θ

₂₃ and

Δ

m²₂₃ are correlated:

Region testable by ν_μ disappearance at MINOS

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Speculation on ν_μ disappearance at T2K

In the case where the central values are the same as in νatm

The constraint may not improve very much.

Determination of

ε

_ee ^,

ε

_eτ ^,

ε

_ττ from future long baseline experiments with P_μμ :

z 0.94< sin²2θ_atm <=1 (Raaf@ν2008)

z Δm²_atm=(2.2+0.45-0.55)U10^-3eV² (Raaf@ν2008)

Even if |Δm²₃₁| is determined by T2K precisely in the future, if the central values are the same as in ν_atm, then the errors in sin²2θ_atm

(+-6%) and Δ^m²_atm ⁽+

-

20%) will remain and will be dominant.

from sin²2θ23

tan²β<0.79 from Δm²₂₃ tan²β<0.77

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Friedland, Lunardini, Pena-Garay Phys.Lett.B594:347,2004

z Analysis of solar neutrinos with NP

degeneracy:

(1+ε_ee) Q -(1+ε_ee) θ₁₂ Q π/2-θ₁₂

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The survival probability for solar neutrino can be obtained by KTY formalism

SM+m ν

NP

For simplicity the non- adiabatic corrections are neglected

This agrees with the analytical formula in Friedland, Lunardini, Pena-Garay

Phys.Lett.B594:347,’04

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However, off these lines fit may not be good. J Scanning the whole region may give a new constraint.

Solar ν may give a strong constraint on the allowed region in (ε_ee , |ε_eτ |)

n : 4 points studied in detail by Friedland, Lunardini, Pena-Garay

: =1 : =1

If and , then by adjusting the free parameter arg (ε_eτ) in such a way that θ^’₁₂⁼θ₁₂, we have Thus on the region in the red circles fit is expected to be good.

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z Summary of possibility with

ε

_ee ^,

ε

_eτ ^,

ε

_ττ ^~O(1)

¾

ν

_e appearance at present/near future LBL:

With longer baseline length (L> ~ 1000km), it

may be possible to see the effect of NP if |

ε

_eτ^{| is}

very large.

¾

ν

_μ disappearance at present/near future LBL : Because of dominant errors of atmospheric

neutrino data, even if T2K measures sin²2θ₂₃ and |Δ^m²₃₂| precisely, it is difficult to give a strong constraint on

ε

_ee ^,

ε

_eτ ^,

ε

_ττ ^.

ν

factory will be necessary to pin down |

ε

_eτ| to <<1.

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Gago-Guzzo-Nunokawa-Teves-Zukanovich Funchal, Phys.Rev.D64:073003,2001 Sensitivity at ν factory

ε

ττ

ε

eτ

ε

ττ

μτ

ε

Statistics only

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +

=

ττ τ

τ

ε ε

0 0 0 0

0 1

*

e

A ee

A

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

ττ μτ

μτ

μμ ε

ε ε ε

0 *

0

0 0 A 1

A

5.3 Sensitivity to

ε

_αβ (<<1) in future experiments

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Degeneracy between

θ

₁₃ and

ε

_eτ may be removed by

combining two baselines

@3000km

@7000km

ε

eτ

2

13

sin

²

θ

Huber, Schwetz, Valle, Phys. Rev. Lett. 88, 101804 (2002)

Degeneracy between

θ

₁₃ ^and

ε

_eτ ν factory

ν

μ

ν

_e

→

(36)

Campanelli-Romanino, PRD66:113001,’02

Sensitivity at

ν

^factory

ε

eτ Statistics only

ν

τ

ν

_e ^→

high energy behavior

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Davidson, Pena-Garay, Rius, Santamaria, JHEP 0303:011,2003

) 10 ( ⁻³

< O

eef

ε

• Sensitivity at near detectors of

ν

^factory

) 10 ( ⁻³

< O

μμf

ε

) 10 ( ⁻²

< O

μτf

ε ε

_e^f_τ ^< ^O⁽¹⁰⁻²⁾

• Sensitivity of KamLAND and SNO/SK

3 .

< 0

ττf

ε

d u e f = , ,

leptonic s²_W at

ν

factory s²_W in DIS at

ν

factory

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10⁻3

×

< a few

ε

_eτ

Ribeiro-Minakata-Nunokawa- Uchinami-Zukanovich-

Funchal, JHEP 0712:002,2007.

Statistics + some

correlations of errors Sensitivity at

ν

factory

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +

=

ττ τ

τ

ε ε

0 0 0 0

0 1

*

e

A ee

A

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Sensitivity by superbeam + reactor Kopp, Lindner, Ota, Sato, PRD77:013007,2008

Statistics + systematic errors +

correlations of errors + degeneracies

emμ

ε ε

_e^m_τ

ε

_μτ^m T2K + DCHOOZ

Noνa + DC-200kt emμ

ε

emτ

ε

μτm

ε

5 .

< 0

emμ

ε

1 .

< 0

emμ

ε

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Ribeiro-Kajita-Ko-Minakata-Nakayama- Nunokawa, PRD77:073007,’08

Sensitivity to

ε

_μτ and

ε

_ττ at T2KK truncation

03 .

< 0

ε

μτ

3 .

< 0

ε

ττ Statistical +

systematic errors

some correlations of

errors

ε

ττ

ε

μτ

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Esteban-Pretel, Valle, Huber, arXiv:0803.1790 [hep-ph]

Sensitivity of MINOS+OPERA+DCHOOZ

Statistics at OPERA: too small to be significant to constrain

ε

_e_τ

Does OPERA help to resolve

θ

₁₃ -

ε

_eτ degeneracy?

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Kopp-Ota-Winter, 0804.2261v1 [hep-ph]

Sensitivity at

ν

factory Statistical + systematic errors + some correlations of errors + some correlations of errors

eem

ε

emτ

ε

μτm

ε

ττm

ε

αβm

ε

) 3 (@ σ

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Blennow-Meloni-Ohlsson-Terranova- Westerberg, 0804.2744v1 [hep-ph]

ν ν +

( ) ε

_μτ

Re

( ) ε

_μτ

Im

ν only

( ) ε

_μτ

Re

Sensitivity at OPERA

ε

_μτ : important at shorter baseline length

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6. Violation of unitarity w/o light ν

_s

In generic see-saw models, after integrating out ν_R, the kinetic term gets modified, and unitarity is

expected to be violated.

J The nontrivial issue is the magnitude of violation.

Some of see-saw models (e.g., inverse see-saw) do have two scales, one to produce small neutrino mass and another which may not be extremely different

from M_W. Then magnitude of violation may not be extremely small.

J Unitarity of the lepton sector is worth checking.

Antusch, Biggio, Fernandez-Martinez, Gavela, Lopez-Pavon, JHEP0610,084, ‘06

( ) ( )

^...

2 2

1 ∂/ − − +

= ci _ii _i ⁺ _L _i _i

i

i g W l P N

m i

L ν ν ν ν _μ _αγ ^μ _αν

( ) (

^. ^.

)

^...

2 2

1 ∂/ − − + +

= g W ⁺l P hc

M K

i

L να αβνβ ν ^cα _αβν_β _μ _αγ ^μ _Lν_α

N: non-unitary rescaling ν

(45)

J

Deviation from unitarity < O(1%) unitarity from

deviation :

−1 NN†

5 2

† 5 2

2 2

0.994 0.005 7.1 10 1.6 10 7.1 10 0.995 0.005 1.0 10 1.6 10 1.0 10 0.995 0.005 NN

− −

⎛ ± < ⋅ < ⋅ ⎞

⎜ ⎟

≈ ⎜ < ⋅ ± < ⋅ ⎟

⎜ < ⋅ < ⋅ ± ⎟

⎝ ⎠ ^{90% C.L.}

HU N ≡

Constraints from weak decays turned out to be more stringent than ν oscillation:

mostly from rare decays

Oscillation probability is similar to but different from that of NP:

H: close to identity

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Sensitivity to

arg(η_μτ)

Sensitivity to

|η_μτ^|

Present bound from τ ^→ μ γ

|

η

_μτ |

τ

μ

ν

^→

Sensitivity at

ν

factory

• 4kt OPERA-like near detector @100 m

0.016) :

(present 10

2.9 × ⁻³

∑

<

i

*i

ei N

N _τ

0.013) :

(present 10

2.6 × ⁻³

∑

<

i

*i

i N

N _μ _ٛ _τ

• 5kt OPERA-like far detector @130 km

ν

τ

ν

_e ^→

τ

μ

ν

^→

For non-trivial arg(η_μτ) ^,

one order of magnitude improvement for |

η

_μτ |

arg(η_μτ)

Antusch et al, JHEP0610,084, ‘06

Fernandez-Martinez, et al, PLB649:427,’07

η +

≡ 1

H

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7. Summary

z

Violation of 3 flavor unitarity

• Current bounds on

ε

_αβ are typically of order 10^-3 for production and detection

•

ε

_αβ for propagation have bounds typically of order 10^-2 but

ε

_ee ^{, |}

ε

_eτ^|,

ε

_ττ ^<^~O(1) and it is difficult to give strong constraints on these three from the present data.

•

ν

factory may be able to improve bounds on

ε

_αβ ^for

propagation dramatically.

Deviation from unitarity is expected in generic models (e.g., see-saw) but phenomenologically its magnitude is less than O(1%). Further studies are necessary.

z

New physics

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There are a lot of problems to be worked out:

z Correlations of errors, degeneracies, etc. in the presence of all new physics parameters ε

_αβ

z Distinction between the new physics effects

(e.g., 4-fermi interactions vs. unitarity violation

due to modification in the kinetic term)

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Backup slides

(50)

In the present case 1-P_μμ can be expressed as

(51)

Analytical formula for the oscillation probability in matter with New Physics in the limit Δm²₂₁ → ⁰

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +

=

ττ τ

τ

ε ε

0 0 0 0

0 1

*

e

A ee

A

OY arXiv:0704.1531 [hep-ph]

depends only on arg(

ε

_e_τ)+

δ

(52)

Features of the probability

A) It depends only on arg(

ε

_e_τ)+

δ.

J

This is approximately the case also for . B) Each term gives a large contribution (See Fig. below).

J

Interpretation of behavior of probability is not obvious.

0) (in thelimit Δm²₂₁ →

2 0

Δm21 ≠

cf In standard 3 flavor case, only one term dominates: