Signature of the MSSM with s in a long baseline...

Signature of the MSSM with νRsin a long baseline experiment

Results are shown in part in the proceedings for the conference NuFACT04,[arXiv:hep-ph/0410408]

Paper is in progress [arXiv:hep-ph/0502***]

Toshihiko Ota

in collaboration with Joe Sato∗

Osaka University Japan, ∗TUM, Munich, Germany

Signature of the MSSM with νRs in a long baseline experiment – p.1/20

Contents

IntroductioncLFV: lepton flavor violation in charged lepton sectornLFV: lepton flavor violation with neutrinos

Model independent analysis

Feasibility study to detect nLFV signalsbased on TO Sato Yamashita, Phys. Rev. D65 (2002) 093015.

In the MSSM with νRs,not only cLFV but also nLFV are induced.

Correlation between cLFV and nLFV

Size of nLFV couplings. — Detectable or not?

Summary


Introduction


Introduction: LFV

In the SM, there is no LFV. In the SM with mν , it is small.

-lα q-να

(m2ν)β

αq-νβ q -lβ

W

γ

Br(lα → lβγ) '3α

32π

∣

∣

∣

∣

∣

Uµi

m2νi

m2W

U†ie

∣

∣

∣

∣

∣

2

Cheng Li (1977), Petcov (1977),Marciano Sandra (1977), Shrock Lee (1977)

In the MSSM with νRs, it can be large

-lα q-l̃α

(m2

L̃)β

αq-l̃β q -lβ

-χ̃0

γ

The large mixings of neutrinos mayimply the large cLFV ...

(

m2

L̃

)

β

α' −

(6 + a20)m2

0

16π2

(

Y †ν Yν

)

β

αln

MX

MR,

Br(lα → lβγ) 'α3

G2F

∣

∣

∣

∣

(

m2

L̃

)

β

α∣

∣

∣

∣

2

m8SUSY

tan2 β.

Borzumati Masiero (1986),Hisano Moroi Tobe Yamaguchi (1995)


LFV in charged lepton sector (cLFV)

M = 150 GeV m = 300 GeV a = 0 > 0

tan

2 0Le~

β

µ

LMASMALOW

10 10 10 1010

10

10

10

10-11-12-13-14

-10

-11

-12

-13

Br( )e

Br(

)τ

µ

γµ

γ

= 5

-15

One examplenumerical study

Sato Tobe (2000)

The future experimentsBr(µ → eγ) > 10−14,Br(τ → µγ) > 10−8,Br(µ → e conv.) > 10−18.

The search for the cLFV is promising experiments.— However, we here consider an alternative process.


LFV interaction with neutrinos (nLFV)

We here discuss a process with the neutrino flavor violation,such as

µ− → ντe−ν̄e, ναe− → νβe−, ναd → `βu.

These processes affect the neutrino oscillation experiments.Gonzalez-Garcia Grossman Gusso Nir (2001)

Gago Guzzo Nunokawa Teves Zukanovich Funchal (2001)

Huber Schwetz Valle (2002)

Fogli Lisi Mirizzi Montanino (2002)

Can we detect these effects in oscillation experiments?— Yes, we can, but it depends on the type and size of nLFV

interaction. TO Sato Yamashita (2001)

In the MSSM+νR, what is the typical size of nLFVcouplings?

— We show the correlation between nLFV and cLFV.


Model independentapproach


Standard Oscillation νµ → ντ

s sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

XXXXs

��XXXX

��XXXXs

µ− τ−W W

ν̄ee−

e− e−

d u

- - - - - -

�z

: z

: z

νµoscillation−−−−−→ ντ

‖∣

∣

∣A(µ → νµν̄ee) ×A(νµ

osc−−→ ντ ) ×A(ντd → τu)

∣

∣

∣

2

‖ΓSM(µ → νµν̄ee) × Pνµ→ντ × σSM(ντd → τu)




XXXXs

��XXXX

��XXXXs

µ− τ−W W

ν̄ee−

e− e−

d u

- - - - - -

�z

: z

: z


‖A(µ → νµν̄ee) ×A(νµ


‖∣

∣



∣

∣

∣

2




2s sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

XXXXs

��XXXX

��XXXXs

µ− τ−W W

ν̄ee−

e− e−

d u

- - - - - -

�z

: z

: z


‖∣

∣



∣

∣

∣

2



Oscillation with nLFV interactions


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µ− τ−W W

ν̄ee−

e− e−

d u

- - - - - -

�z

: z

: z


~ sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

XXXXs

��XXXX

��XXXXs

µ− τ−

W W

ν̄ee−

e− e−

d u

- - - -

�z

: z

: z

nLFV interactionντ

no oscillation−−−−−−−→ ντ


XXXXs

��XXXX

��XXXXs

µ− τ−W W

ν̄ee−

e− e−

d u

- - - - - -

�z

: z

: z


+~ sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

XXXXs

��XXXX

��XXXXs

µ− τ−

W W

ν̄ee−

e− e−

d u

- - - -

�z

: z

: z


no oscillation−−−−−−−→ ντ 2




XXXXs

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��XXXXs

µ− τ−W W

ν̄ee−

e− e−

d u

- - - - - -

�z

: z

: z


+~ sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

XXXXs

��XXXX

��XXXXs

µ− τ−

W W

ν̄ee−

e− e−

d u

- - - -

�z

: z

: z


no oscillation−−−−−−−→ ντ 2



∣

∣

∣

∣

p pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppHHp �� HH �� XXp

- - - -�j

* j: z

νµosc−−→ ντ

∣

∣

∣

∣

2

+ 2Re

[

( p pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppHHp �� HH �� XXp

- - - -�j

* j: z

νµosc−−→ ντ

)∗( u pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp

HHp�� HH

��XXp- - - -

�j* j

:z

nLFV ντno osc−−−→ ντ

)

]

= ΓSM ×(

Pνµ→ντ + 2Re[

εsµτA

∗(νµosc−−→ ντ )A(ντ

no osc−−−→ ντ )

])

× σSM,

where εsµτ ≡ A(µ→ντ ν̄ee)

ASM.

The oscillation probability is modified by the interferenceterm due to the nLFV interaction.

The size of the interference term is O(εsµτ ), not O(|εs

µτ |2).

— This interference effect can occure only in the oscillatonprocess.


Search for the effect of εsµτ in νµ → ντ

10 20 30 40 50 60250500

1000

1500

2000

2500

3000

3500

4000

Eµ[GeV]

L[k

m]

10.

50.

10.

050.0

1

TO JS Yamashita (2002)Necessary (muon)×(detector size)for 90% CL detection of nLFV.

normalized at 1021× 100[kton]

νµ → ντ channel

εsµτ = 3 × 10−3eiπ

2

10% ambiguity is considered in the oscillation

parameters, ∆m2s and θs, and the CP-phase δ is

treated as a free parameter.

µ− GF−−−−→ νµosc.−−−→ ντ → τ−

µ−εsµτGF

−−−−→ ντno osc.−−−→ ντ → τ−

The energy dependence of this signal is 1/Eν .

It is quite different from the standard oscillation effect(∝ 1/E2ν ).



The other diagrams which contribute to A(µ + I → τ + F )

s ~ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

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µ− τ−

W W

ν̄ee−

e− e−

d u

- - - -

�z

: z

: z

nLFV at detection∝ εdµτGFνµ

no oscillation−−−−−−−→ νµ

s s~

XXXXs

��XXXXs

��XXXXs

µ− τ−

W WZ

ν̄ee−

e− e−

d u

νµ ντ- - - -

�z

: z

: z

nLFV in matter effect∝ εmµτGF

not oscillation


Summary of the model independent analysis

Detectable signal ...In να → νβ channel, we can extract the nLFV signals only

with εs,m,dαβ .

— by using its characteristic energy dependence.— the nLFV amplitude does not include neutrino oscillation

but its final states are the same as the standard one.

We here deal with εs,m,dµτ in the νµ → ντ channel.

At a neutrino factory (1021 muons ×100 kt detector), wehave a chance to detect the signal of |εs,m,d

αβ | ∼ O(10−4).

We make a numerical calculation for the size of nLFVcouplings εs,m,d

µτ in the MSSM with νRs.


Summary of the model independent analysis

Detectable signal ...In να → νβ channel, we can extract the nLFV signals only

with εs,m,dαβ .

— by using its characteristic energy dependence.— the nLFV amplitude does not include neutrino oscillation

but its final states are the same as the standard one.We here deal with εs,m,d

µτ in the νµ → ντ channel.

At a neutrino factory (1021 muons ×100 kt detector), wehave a chance to detect the signal of |εs,m,d

αβ | ∼ O(10−4).

We make a numerical calculation for the size of nLFVcouplings εs,m,d

µτ in the MSSM with νRs.


In the MSSM with νRs


Estimation of εsµτ in MSSM+νR

-µ r-χ̃− r-χ̃0 r -ντ

r(m2

L̃)3

2

ν̃µ ν̃τ� U

W

XXXXr �z

ν̄e

e

∼g2

(4π)2

(m2L̃)3

2

m2SUSY

GF ∼ εsµτGF

The origin of the nLFV is the same as that of the cLFV:slepton mixing

Naively, εsµτ ∼ O(10−4) in nLFV corresponds to

Br(τ → µγ) ∼ O(10−8) in cLFV.

— However, for quantitative analysis, it is necessary to makea numerical calculation ...


Numerical evaluation of εsµτ in MSSM+νR

-µ q-l̃Y q-̃νX q -ντ

-̃χ0A

W

-µ q -l̃X τ qq -ντ-

-̃χ0A

W

-µ νµ- q -̃νXq q ντ-

-̃χ0A

W

-µ q -̃νX τ qq -ντ-

-̃χ−

A

W

-µ νµ- q -l̃Xq q ντ-

-̃χ+A

W

-µ q-̃χ−B q-̃χ0

A q -ντ

zν̃X

W

-µ q-̃χ0B q-̃χ+

A q -ντ

zl̃X

W

and box diagrams ...


Numerical evaluation of εmµτ in MSSM+νR

-να q-̃νY q-̃νX q -νβ

-̃χ0A

Z

-να q -̃νX νβqq -νβ-

-̃χ0A

Z

-να να- q -̃νXq q νβ-

-̃χ0A

Z

-να q-l̃Y q-l̃X q -νβ

-̃χ+A

Z

-να q -l̃X νβqq -νβ-

-̃χ+A

Z

-να να- q -l̃Xq q νβ-

-̃χ+A

Z

-να q-̃χ+

B q-̃χ+

A q -νβ

zl̃X

Z

-να q-̃χ0B q-̃χ0

A q -νβ

zν̃X

Z

and box diagrams ...


Numerical evaluation of εs,m,dµτ in MSSM+νR

~ ~ ~

XXXXs

��XXXXs

��XXXXs

µ− τ−

W WZ

ν̄ee−

e− e−

d u

- - - - - - - -

�z

: z

: z

Source Matter Detection

10-710-810-910-1010-1110-1210-1310-14

10-5

10-6

10-7

10-8

10-9

10-10

εsµτ

|ε|

Br(τ → µγ)10-710-810-910-1010-1110-1210-1310-14

10-5

10-6

10-7

10-8

10-9

10-10

εmµτ

Br(τ → µγ)10-710-810-910-1010-1110-1210-1310-14

10-4

10-5

10-6

10-7

10-8

εdµτ

Br(τ → µγ)


Correlation between nLFV and cLFV

10-710-810-910-1010-1110-1210-1310-14

10-5

10-6

10-7

10-8

10-9

10-10

BR(τ → µγ)

|εsµτ |

��

��

��

��

��

��

��3

|εsµτ| ∝

√ Br(τ→

µγ)

Correlation between thenLFV coupling εs

µτ andcLFV process τ → µγ.

With some different Yνs, we scan

the m0-M1/2 space with a0 = 0,

tan β = 10, and µ > 0.

The parameter εsµτ is

constrained at O(10−5) bythe current bound ofτ → µγ.

It is smaller than the naiveestimation because of can-cellation among diagrams.


Summary


Summary

The large neutrino mixings may imply the sizable effect notonly for cLFV but also nLFV.

The oscillation enhances the nLFV effect due to interference.

We evaluate the effective couplings of nLFV which arerelevant to νµ → ντ in the MSSM with νRs.

εsµτ , εm

µτ , εdµτ where εs,m,d

µτ ≡ exotic/standard

Detectable size: |εs,m,dµτ | & O(10−4)

In the MSSM with νRs, these couplings are constrained bythe process τ → µγ as |εs,m,d

µτ | . O(10−5).

Other model? — R-parity violation ...— CPV MSSM ...— SU(5) GUT ...


Signature of the MSSM with s in a long baseline...

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