Non -Unitarity and Non-Standard Neutrino Interactions · Neutrino masses in the SM All SM fermions...

Non-Unitarity and Non-Unitarity and Non-Standard Neutrino Interactions

Enrique Fernández-Martínez

MPI für Physik MunichMPI für Physik Munich

Based on collaborations with:

S. Antusch, J. Baumann, C. Biggio, M. Blennow,S. Antusch, J. Baumann, C. Biggio, M. Blennow,

B. Gavela and J. López Pavón

Outline

� Non-unitary lepton mixing matrix� Neutrino masses and non-unitarity� Neutrino masses and non-unitarity

� Effects of non-unitarity in present oscillation data

� Measurements of non-unitarity in future oscillation � Measurements of non-unitarity in future oscillation experiments

� Non-unitarity as NSI

� Non Standard neutrino InteractionsConditions to realize large NSI� Conditions to realize large NSI

� Avoiding constraints without cancellations

� Avoiding constraints with cancellations� Avoiding constraints with cancellations

� NSI in loops

Neutrino masses in the SM

All SM fermions acquire Dirac masses via Yukawa couplings

ffY φSSB Y v vY

RLf ffY φSSB

2

v=φ

RL

fff

Y

2

v

2

vff

Ym =

Adding νR to the SM, a Majorana mass is also allowed

R

C

RM νν

The only d = 5 operator is a Majorana mass for neutrinos

L

C

LM

ννφφ1

This operator cannot be generated in the SM since it violates B – L, an accidental, non anomalous SM symmetry

LLM

ννφφ

B – L, an accidental, non anomalous SM symmetry

Hints that this symmetry is broken at a scale M beyond the SM

The Type I Seesaw Model

The SM is extended by:

If the right-handed neutrino �R is heavy it can be integrated out:If the right-handed neutrino �R is heavy it can be integrated out:

SSB( )( ) SSB

2

v=φ

( )( )αβ σφφσ LiiL tc

22

SSB

Weinberg 1979

( ) ( )αβ σφφσ LiiiL t

2

*

2 ∂/SSB

2

v=φ

βαβα νν Ki ∂/

2

A. Broncano, M. B. Gavela and E. Jenkins hep-ph/0210192

Effective Lagrangian

( ) ( ) .....cos

..2

++−+−+∂/= + chPZg

chPlWg

MKiL LL αµ

αµαµ

αµβαβαβαβα νγνθ

νγννννcos2 Wθ


( ) ( ) .....cos

..2

++−+−+∂/= + chPZg

chPlWg

MKiL LL αµ

αµαµ


νγνννν

Diagonal mass and canonical kinetic terms

cos2 Wθ

( ) ( ) .....)(cos

..2

† ++−+−+∂/= + ch��PZg

ch�PlWg

miL jijLi

W

iiLiiiiii νγνθ

νγνννν µµα

µαµ


( ) ( ) .....cos

..2

++−+−+∂/= + chPZg

chPlWg

MKiL LL αµ

αµαµ


νγνννν


cos2 Wθ

( ) ( ) .....)(cos

..2

† ++−+−+∂/= + ch��PZg

ch�PlWg

miL jijLi

W

iiLiiiiii νγνθ

νγνννν µµα

µαµ

ii� νν αα = � is not unitary


( ) ( ) .....cos

..2

++−+−+∂/= + chPZg

chPlWg

MKiL LL αµ

αµαµ


νγνννν


cos2 Wθ

( ) ( ) .....)(cos

..2

† ++−+−+∂/= + ch��PZg

ch�PlWg

miL jijLi

W

iiLiiiiii νγνθ

νγνννν µµα

µαµ

ii� νν αα =unchanged

δνν =

� is not unitary

ijji δνν =Zero-distance effect:

( ) ∑2

( ) αββαβα δνν ≠∝→ ∑ *0;i

ii��P

The general idea…

13 12 12 13 13

i

i i

c c s c s eδ

δ δ− −

= − − −12 23 23 13 12 12 23 23 13 12 23 13

23 12 23 13 12 23 12 23 13 12 23 13

i i

i i

U s c s s c e c c s s s e s c

s s c s c e s c c s s e c c

δ δ

δ δ

− −

− −

= − − − − − −

1 2 3e e e� � �

1 2 3

1 2 3

e e e� � �

� � � �

� � �

µ µ µ

= 1 2 3� � �τ τ τ

� elements from oscillations only

( ) ( ) ( ) ( )23

2

3

2

2

2

1

4

3

22

2

2

1 cos2ˆ ∆++++≅→ µµµµµµµµ νν ��P

Atmospheric + K2K + MINOS: Δ12≈0

without unitarityOSCILLATIONS

( )

−−=+

<−−

= 86.057.086.057.0

34.066.045.089.075.0

][2/12

2

2

1 µµ ��

( ) ( ) ( )23321321 µµµµµµµµ

OSCILLATIONS( )

−−=+=

???

86.057.086.057.0 ][ 21 µµ ��

3σ

−−−

<−−

= 82.058.073.042.052.019.0

20.061.047.088.079.0

Uwith unitarity

3σ

−−−

−−−=

81.056.074.044.053.020.0

82.058.073.042.052.019.0Uwith unitarity

OSCILLATIONS

M. C. González García hep-ph/0410030

(��†) from decays

Wνi ( )

( ) ( )αα

††

†

��

��→• W decays W

lα ( ) ( )µµ††

�� ee

→

νiZ

( )αβ†��∑

• W decays

Info onνiZ

νj ( ) ( )µµ

αβαβ

††

�� ee

∑→• Invisible Z

( )†��

Info on

(��†)αα

γ

• Universality tests

( )( )ββ

αα†

†

��

��→

• Rare leptons decays( )

( ) ( )ββαα

αβ

††

2†

��

��→

W

νilα lβ

γ

( ) ( )ββαα ��νilα lβ

Info on (��†)αβ

(��†) and (�†�) from decays

⋅<⋅<± −− 106.1100.7005.0994.0 25

±⋅<⋅<

⋅<±⋅<

⋅<⋅<±

≈−−

−−

−−

005.0995.0100.1106.1

100.1005.0995.0100.7

106.1100.7005.0994.0

22

25

25

†��

Experimentally ±⋅<⋅< 005.0995.0100.1106.1 Experimentally

E. Nardi, E. Roulet and D. Tommasini hep-ph/9503228D. Tommasini, G. Barenboim, J. Bernabeu and C. Jarlskog hep-ph/9503228

The diagonal elements are somewhat smaller than 1 due to the

D. Tommasini, G. Barenboim, J. Bernabeu and C. Jarlskog hep-ph/9503228S. Antusch, C. Biggio, EFM, B. Gavela and J. López Pavón hep-ph/0607020

The diagonal elements are somewhat smaller than 1 due to thenearly 2σ deviation from 3 in the number of ν measured by the Z width

009.0984.2 ±=� 009.0984.2 ±=ν�

� elements from oscillations & decays

without unitarity

<−− 20.065.045.089.075.0

without unitarityOSCILLATIONS

+DECAYS

−−−

−−−=

82.054.075.036.056.013.0

82.057.074.042.055.019.0�

3σ

S. Antusch, C. Biggio, EFM, B. Gavela and J. López Pavón hep-ph/0607020

<−− 20.061.047.088.079.0

with unitarity

3σ

−−−

−−−=

81.056.074.044.053.020.0

82.058.073.042.052.019.0Uwith unitarity

OSCILLATIONS

M. C. González García hep-ph/0410030

Non-unitarity in future facilities

If we parametrize U� ⋅+= )1( ε withPM�SUU ≈

and εεεand

= µτµµµ

τµ

εεε

εεε

ε *

e

eeee 22

4sin)2sin(2

∆

−≈E

LmiP θεαβαβ

ττµττ

µτµµµ

εεε **

e

e

4sin)2sin(2

−≈E

iP θεαβαβ

If L/E smallIf L/E small


If we parametrize U� ⋅+= )1( ε withPM�SUU ≈

and εεεand

= µτµµµ

τµ

εεε

εεε

ε *

e

eeee 22

4sin)2sin(2

∆

−≈E

LmiP θεαβαβ

ττµττ

µτµµµ

εεε **

e

e

4sin)2sin(2

−≈E

iP θεαβαβ

If L/E small

222 ∆ ∆ LmLm

If L/E small

222

22 42

sin)2sin()Im(24

sin)2(sin αβαβαβ εθεθ +

∆−

∆=

E

Lm

E

LmP

SM CP violatinginterference

Zero dist.effect


222

22 42

sin)2sin()Im(24

sin)2(sin αβαβαβ εθεθ +

∆

−

∆

=E

Lm

E

LmP 4

2sin)2sin()Im(2

4sin)2(sin αβαβαβ εθεθ +

−

=EE

P

SM CP violating Zero dist.SM CP violatinginterference

Zero dist.effect

At a Neutrino Factory of 50 GeV with L = 130 Km

2 ∆ Lm The SM background 03.0

2sin

2

23 ≈

∆

E

Lm The SM background is suppressed

Measuring unitarity deviations

In Pµτ there is no

θ ∆13sinθ 12∆or

suppression

The CP phase δThe CP phase δµτcan be measured

EFM, B. Gavela, J. López Pavón EFM, B. Gavela, J. López Pavón and O. Yasuda hep-ph/0703098

See also S. Goswami and T. Ota 0802.1434

Non-Unitarity at a NF

Golden channel at NF is sensitive to ετe

νµ disappearance channel linearly sensitive to ετµ through matter effectsνµ disappearance channel linearly sensitive to ετµ through matter effects

Near τ detectors can improve the bounds on ετe and ετµ

Combination of near and far detectors sensitive to the new CP phases

S. Antusch, M. Blennow, EFM and J. López-pavón 0903.3986See also EFM, B. Gavela, J. López Pavón and O. Yasuda hep-ph/0703098;

S. Goswami and T. Ota 0802.1434; G. Altarelli and D. Meloni 0809.1041,….

Non-unitarity and NSI

Generic new physics affecting ν oscillations can beparameterized as 4-fermion Non-Standard Interactions:parameterized as 4-fermion Non-Standard Interactions:

Production or detection of a νβ associated to a lα

π µ +ν( )( )fPflPG RLLF′

,22 µαµ

βαβ γγνε π → µ +νβ

n +ν → p + lSo that

The general matrix � can be parameterized as:

n +νβ → p + lαThe general matrix � can be parameterized as:

( )U� ε+= 1 where †εε =

Also gives but with *

βααβ εε =


Generic new physics affecting ν oscillations can beparameterized as 4-fermion Non-Standard Interactions:parameterized as 4-fermion Non-Standard Interactions:

Production or detection of a νβ associated to a lα

π µ +ν( )( )fPflPG RLLF′

,22 µαµ

βαβ γγνε π → µ +νβ

n +ν → p + l

The general matrix � can be parameterized as:

So that n +νβ → p + lαThe general matrix � can be parameterized as:

( )U� ε+= 1 where †εε =

Also gives but with *

βααβ εε =

Non-unitarity and NSI matter effects

Non-Standard ν scattering off matter can also be parameterized as 4-fermion Non-Standard Interactions:parameterized as 4-fermion Non-Standard Interactions:

( )( )fPfPG RLL

m

F ,22 µαµ

βαβ γνγνε

so that

Integrating out the W and Z, 4-fermion operators are

so that

Integrating out the W and Z, 4-fermion operators are obtained also for the non-unitary mixing matrix

They are related to the production and detection NSIThey are related to the production and detection NSI


Non-Standard ν scattering off matter can also beparameterized as 4-fermion Non-Standard Interactions:parameterized as 4-fermion Non-Standard Interactions:

( )( )fPfPG RLL

m

F ,22 µαµ

βαβ γνγνε

so that

Integrating out the W and Z, 4-fermion operators are

so that

Integrating out the W and Z, 4-fermion operators are obtained also for the non-unitary mixing matrix

They are related to the production and detection NSIThey are related to the production and detection NSI


Integrating out the W and Z, 4-fermion operators Integrating out the W and Z, 4-fermion operators for matter NSI are obtained from non-unitary mixing matrix

( )( )fPfPG RLL

m

F ,22 µαµ

βαβ γνγνε

( ) ( ) ( )

−−− eneeneenee nnnnnn τµ εεε 112( ) ( ) ( )

( )( )

−

−

−−−

=

enenene

enenene

eneeneenee

m

nnnnnn

nnnnnn

nnnnnn

ττµττ

µτµµµ

τµ

εεε

εεε

εεε

ε

1

1

112

They are related to the production and detection NSI

They are related to the production and detection NSI


The bounds on

εε 21)1( 2† +≈+=��Also apply to εAlso apply to ε

⋅<⋅<⋅< −−− 353 100.8106.3105.2

⋅<⋅<⋅<

⋅<⋅<⋅<

⋅<⋅<⋅<

≈−−−

−−−

333

335

105.2100.5100.8

100.5105.2106.3

100.8106.3105.2

ε

Very strong bounds for NSI from non-unitarity…

…also for the related NSI in matter

Direct bounds on prod/det NSI

From µ, β, π decays and zero distance oscillations

( )( )dPuPlG RLL

ud

F ,22 µαµ

βαβ γνγε ( )( )ePPG LL

e

F µαβµµ

αβ γννγµε22

⋅< − 013.01.0106.2

042.0025.0042.05udε

< 03.003.0025.0

03.003.0025.0eµε

⋅<

13.0013.0087.0

013.01.0106.2ε

<

03.003.0025.0

03.003.0025.0ε

Bounds order ~10-2

C. Biggio, M. Blennow and EFM 0907.0097

Direct bounds on matter NSI

If matter NSI are uncorrelated to production and detectiondirect bounds are mainly from ν scattering off e and nucleidirect bounds are mainly from ν scattering off e and nuclei

( )( )fPfPG RLL

m

F ,22 µαµ

βαβ γνγνε

⋅

⋅

< −

−

33.0064.0108

1.31088.34

4

mε

0.330.33

⋅<

2133.01.3

33.0064.0108ε

Rather weak bounds…

0.33

Rather weak bounds… …can they be saturated avoiding additional constraints?

S. Davidson, C. Peña garay, N. Rius and A. Santamaria hep-ph/0302093J. Barranco, O. G. Miranda, C. A. Moura and J. W. F. Valle hep-ph/0512195J. Barranco, O. G. Miranda, C. A. Moura and J. W. F. Valle hep-ph/0512195

J. Barranco, O. G. Miranda, C. A. Moura and J. W. F. Valle 0711.0698C. Biggio, M. Blennow and EFM 0902.0607

Huge effects in ν oscillations

With ε and ε ∼1With εττ and εeτ ∼1

N. Kitazawa, H. Sugiyama and O. Yasuda hep-ph/0606013N. Kitazawa, H. Sugiyama and O. Yasuda hep-ph/0606013See also M. Blennow, T. Ohlsson and J. Skrotzki hep-ph/0702059

Gauge invariance

However ( )( )fPfPG RLL

m

F ,22 µαµ

βαβ γνγνε

is related to ( )( )fPflPlG RLL

m

F ,22 µαµ

βαβ γγε

by gauge invariance and very strong bounds exist

<m

eµε 610−∼

<m

eτε 210−∼µ→ e γµ → e in nucleaiτ decays

<eτε 10∼

<m

µτε 210−∼τ decays

S. Bergmann et al. hep-ph/0004049S. Bergmann et al. hep-ph/0004049Z. Berezhiani and A. Rossi hep-ph/0111147

Large NSI?

We search for gauge invariant SM extensions satisfying:

� Matter NSI are generated at tree level

� 4-charged fermion ops not generated at the same level

� No cancellations between diagrams with different messenger particles to avoid constraints

� The Higgs Mechanism is responsible for EWSB

S. Antusch, J. Baumann and EFM 0807.1003

Large NSI?

At d=6 only one possibility: charged scalar singlet

Present in Zee model orPresent in Zee model orR-parity violating SUSY

( )( )cc LiLLiL δγβα σσ 22

M. Bilenky and A. Santamaria hep-ph/9310302

Large NSI?

Since λαβ = -λβα only εµµ , εµτ and εττ ≠0

Very constrained:

µ → e γµ → e γµ decaysτ decaysτ decaysCKM unitarity

F. Cuypers and S. Davidson hep-ph/9310302S. Antusch, J. Baumann and EFM 0807.1003S. Antusch, J. Baumann and EFM 0807.1003

Large NSI?

At d=8 more freedom

Can add 2 H to break the symmetry between ν and l with the vevCan add 2 H to break the symmetry between ν and l with the vev

-v2/2 ( )( )ff µαµ

β γνγν( ) ( )( )ffLiHHiL t

µαµ

β γσγσ 2

*

2

There are 3 topologies to induce effective d=8 ops with HHLLff legs:

Z. Berezhiani and A. Rossi hep-ph/0111147; S. Davidson et al hep-ph/0302093

There are 3 topologies to induce effective d=8 ops with HHLLff legs:

Large NSI?

We found three classes satisfying the requirements:

Large NSI?


1

Just contributes to the scalar propagator after EWSBJust contributes to the scalar propagator after EWSB

v2/2 ( )( )cc LiLLiL δγβα σσ 22

Same as the d=6 realization with the scalar singlet

( )( )δγβα 22

Large NSI?


2

The Higgs coupled to the selects ν after EWSBThe Higgs coupled to the �R selects ν after EWSB

-v2/2 ( )( )ff µαµ

β γνγν( ) ( )( )ffLiHHiL t

µαµ

β γσγσ 2

*

2-v /2 ( )( )ff µαβ γνγν( ) ( )( )ffLiHHiL µαβ γσγσ 22

Large NSI?

But can be related to non-unitarity and constrained

2

Fij G10<≡ ρ

( )2

2

∑ ∑YvYv ( )

22

∑ ∑YvYv( )αα

αα 122

†2

−=<∑ ∑ ��M

Yv

M

Yv

i i i

i

i

i ( )ββ

ββ1

22

†2

−=<∑ ∑ ��M

Yv

M

Yv

j j j

j

j

j

Large NSI?

For the matter NSI

Where is the largest eigenvalue of

And additional source, detector and matter NSI are

generated through non-unitarity by the d=6 op generated through non-unitarity by the d=6 op

Large NSI?


3

Mixed case, Higgs selects one ν and scalar singlet S the other

Large NSI?

Can be related to non-unitarity and the d=6 antisymmetric op

3

Fij G10<≡ ρ

( )2

2

∑ ∑YvYv

∑ ∑jj

2

λλ( )αααα 1

22

†2

−=<∑ ∑ ��M

Yv

M

Yv

i i i

i

i

i ∑ ∑<j j Sj

j

Sj

j

Mv

Mv 2 γδγδ λλ

Large NSI?

At d=8 we found no new ways of selecting ν

The d=6 constraints on non-unitarity and the scalar singlet

apply also to the d=8 realizationsapply also to the d=8 realizations

What if we allow for cancellations among diagrams?What if we allow for cancellations among diagrams?

B. Gavela, D. Hernández, T. Ota and W. Winter 0809.3451

Large NSI?


Large NSI?

tick means selects ν at d=8 without 4-charged fermion

bold means induces 4-charged fermionat d=6, have to cancel it!!


without 4-charged fermion

Large NSI?

There is always a 4 charged fermion op that needs canceling

Toy model

Cancelling the 4-charged fermion ops.

( ) ( )( )δµγβµ

α γσγσ EELiHHiL t

2

*

2


NSI in loops

Even if we arrange to have

( ) ( )( )O ( ) ( )( )δµγβµ

α γσγσ EELiHHiLM

O t

2

*

24

( )( ) ( )( )[ ]( )µµ γττγγ EEHHLLHHLLO rr †† −=

We can close the Higgs loop, the triplet terms vanishes and

( )( ) ( )( )[ ]( )δµγβµ

αβµ

α γττγγ EEHHLLHHLLM

O rr ††

42−=

We can close the Higgs loop, the triplet terms vanishes and

( )( )µ γγ EELLkO 2Λ

NSIs and 4 charged fermion ops induced with equal strength

( )( )δµγβµ

α γγπ

EELLM 24 162

NSIs and 4 charged fermion ops induced with equal strength


NSI in loops

This loop has to be added to:

++

Used to set loop bounds on εeµ through the log divergence

However the log cancels when adding the diagrams…


NSI in loops

( )( )δµγβµ

α γγπ

EELLk

M

O2

2

4 162

Λ

πM 24 162

The loop contribution is a quadratic divergence

The coefficient k depends on the full theory completion

If no new physics below NSI scale Λ = M

Extra fine-tuning required at loop level to have k=0 or loop contribution dominates when 1/16π2 > v2/M2


Conclusions: non-unitarity

� SM extensions to accommodate ν masses often lead to a non-unitary lepton mixing matrix

� Present oscillation data can only measure half the matrix elementsmatrix elements

� Deviations from unitarity tightly constrained by decays

� All matrix elements can be measured� All matrix elements can be measured

� Future facilities still sensitive to unitary deviations

� Non-unitarity is a particular realization of NSI, but very constrained

Conclusions: NSI

� Models leading “naturally” to NSI imply:

� O(10-2-10-3) bounds on the NSI

Relations between matter and production/detection NSI� Relations between matter and production/detection NSI

Probing O(10-3) NSI at future facilities very challenging but � Probing O(10-3) NSI at future facilities very challenging but not impossible, near detectors excellent probes

� Saturating the mild model-independent bounds on matter NSI and decoupling them from production/detectionrequires strong fine tuningrequires strong fine tuning

Other models for ν masses

Type I seesawMinkowski, Gell-Mann, Ramond, Slansky, Yanagida, Glashow, Mohapatra, Senjanovic, …Glashow, Mohapatra, Senjanovic, …

�R fermionic singlet

Type II seesawMagg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle, …Senjanovic, Schecter, Valle, …

∆ scalar triplet

Type III seesawFoot, Lew, He, Joshi, Ma, Roy, Hambye et al., Bajc et al., Dorsner, Fileviez-PerezDorsner, Fileviez-Perez

ΣR fermionic triplet

Different d=6 ops

Type I:• non-unitary mixing in CC• FCNC for ν

Type III:• non-unitary mixing in CC• FCNC for ν

• LFV 4-fermions

Type III: • FCNC for ν• FCNC for charged leptons

Type II:• LFV 4-fermions

interactions

A. Abada, C. Biggio, F. Bonnet, B. Gavela and T. Hambye 0707.4058

Types II and III induce flavour violation in the charged lepton sectorTypes II and III induce flavour violation in the charged lepton sectorStronger constraints than in Type I

Low scale seesaws

ButBut

D�

t

D mMmmd 1

5

−== ν soD�D mMmmd5 == ν

m

so

D�DM

mmMmd ν≈= −2†

6!!!

�M

Low scale seesaws

The d=5 and d=6 operators are independent

Approximate U(1)L symmetry can keep d=5 (neutrino mass) Approximate U(1)L symmetry can keep d=5 (neutrino mass) small and allow for observable d=6 effects

See e.g. A. Abada, C. Biggio, F. Bonnet, B. Gavela and T. Hambye 0707.4058See e.g. A. Abada, C. Biggio, F. Bonnet, B. Gavela and T. Hambye 0707.4058

Inverse (Type I) seesaw Type II seesaw L= 1 -1 1

µ << M

4 ∆∆=Y

d µ†

∆∆=YY

d

D��

t

D mMMmd 11

5

−−= µ

D�D mMmd 2†

6

−=

25 4∆

∆∆=M

d µ26

∆

∆∆=M

YYd

Magg, Wetterich, Lazarides, Shafi, D�D mMmd6 = Magg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle,…Wyler, Wolfenstein, Mohapatra, Valle, Bernabeu,

Santamaría, Vidal, Mendez, González-García, Branco, Grimus, Lavoura, Kersten, Smirnov,….

� elements from oscillations: µ-row

Atmospheric + K2K: Δ12≈0

( ) ( ) ( ) ( )23

2

3

2

2

2

1

4

3

22

2

2

1 cos2ˆ ∆++++≅→ µµµµµµµµ νν ��P

1. Degeneracy

UNITARITY

2

3

2

2

2

1 µµµ �� ↔+

2.

cannot be disentangled

2

2

2

1 , µµ ��


� elements from oscillations: e-row

Only disappearance exps → information only on |�αi|2

CHOOZ: Δ12≈0 ELmijij 22∆=∆

( ) ( ) ( ) ( )23

2

3

2

2

2

1

4

3

22

2

2

1 cos2ˆ ∆++++≅→ eeeeeeee ��P νν

CHOOZ: Δ12≈0 ELmijij 2∆=∆

K2K (νµ→νµ ): Δ23

1. Degeneracy1. Degeneracy

2

3

2

2

2

1 eee �� ↔+

UNITARITY

2. 2

2

2

1 , ee ��



( ) ( )22444cos2ˆ ∆+++≅→ ��P νν

KamLAND: Δ23>>1

( ) ( )12

2

2

2

1

4

3

4

2

4

1 cos2ˆ ∆+++≅→ eeeeeee ��P νν

≈+ 1

2

2

2

1 ee ��

≈ 02

3

21

e

ee

�

→ first degeneracy solved

KamLAND+CHOOZ+K2K



( ) ( )22444cos2ˆ ∆+++≅→ ��P νν

KamLAND: Δ23>>1

( ) ( )12

2

2

2

1

4

3

4

2

4

1 cos2ˆ ∆+++≅→ eeeeeee ��P νν

≈+ 1

2

2

2

1 ee ��

≈ 02

3

21

e

ee

�


KamLAND+CHOOZ+K2K

SNO:


( ) 2

2

2

1 9.01.0ˆeeee ��P +≅→νν SNO

→ all |�ei|2 determined

(NN†) from decays: GF

Wνi

lα

( )( ) ( )µµ

αα

++

+

→��

��

ee

• W decayslα ( ) ( )µµ�� ee

νiZ

( )

( ) ( )

+∑→

��ij

ij

• Invisible ZInfos on

†Z

νj ( ) ( )µµ++

→�� ee

ij • Invisible Z

( )( )

αα+

→��

(NN†)αα

• Universality tests

( )( )ββ

αα+

→��

��

is measured in µ-decayGF is measured in µ-decay

µ νiNµi

∑∑=ΓF

��mG 2252

µ

∑∑=

F

F

GG

22

2

exp,2

jν

W¯ e

N*ej

∑∑=Γj

ej

i

i

F��

3192µ

µ

π ∑∑=

j

ej

i

i

F

��G

22

µ

Unitarity in the quark sector

Quarks are detected as mass eigenstates

→ we can directly measure |Vab|

ex: |Vus| from K0 →π - e+ νe

uK0 π -

d d

s+

Vus*

sW+

νi

e+ Uei

→ ∑i|Uei|2 =1 if U unitary→ ∑i|Uei| =1 if U unitary

With Vab we check unitarity conditions:

ex: |Vud|2+|Vus|

2+|Vub|2 -1 = -0.0008±0.0011

→ Measurements of VCKM elements relies on UPMNS unitarity

Unitarity in the quark sector

Quarks are detected as mass eigenstates

→ we can directly measure |Vab|

ex: |Vus| from K0 →π - e+ νe

uK0 π -

d d

s+

Vus*

sW+

νe

e+

With Vab we check unitarity conditions:

ex: |Vud|2+|Vus|

2+|Vub|2 -1 = -0.0008±0.0011

→ Measurements of VCKM elements relies on UPMNS unitarity

• decays → only (NN†) and (N†N)• decays → only (NN†) and (N†N)

• N elements → we need oscillations

• to study the unitarity of N: no assumptions on VCKM

With leptons:

ν oscillation in matter

∑−=−α

αα νγννγν 00int

2

12 nFeeeF nGnGL

VCC V�C

2 families

VCC V�C

−

−+

=

ν

ν

ν

ν e�CCCte VVU

EU

di

001*

−

+

=

µµ νν

�CVU

EU

dti

00 2

ν oscillation in matter

∑−=−α

αα νγννγν 00int

2

12 nFeeeF nGnGL

VCC V�C

2 families

VCC V�C

−

−+

=

ν

ν

ν

ν e�CCCte VVU

EU

di

001*

∑ �2

−

+

=

µµ νν

�CVU

EU

dti

00 2

( )

( )

−−

+

=

∑

∑∑

∑∑

−

µ

µ

µ

µ νν

νν

e

iiei

iei

ii

�Ci

ei�CCC

e

�

��

�V�VV

�E

E�

dt

di

2

*

2

2

1*1*

0

0

( )

−−

∑∑∑

∑ µ

µµ

µ

µ νν

ii�C

iiei

ii

iei

�CCC�V��

�

�VV

Edt2

*

2

22

0

1. non-diagonal elements 2. NC effects do not disappear

Large NSI?

General basis for d=8 ops. with two fermions and two H

2 left + 2 right

4 left4 left

Z. Berezhiani and A. Rossi hep-ph/0111147Z. Berezhiani and A. Rossi hep-ph/0111147B. Gavela, D. Hernández, T. Ota and W. Winter 0809.3451

Large NSI?

To cancel the 4-charged fermion ops:

but

�

and

( ) ( )( )δµγβµ

α γσγσ EELiHHiL t

2

*

2�R

( )( )( )HHLiLLiL cc †

22 δγβα σσ

( ) ( )( )δµγβµ

α γσγσ LLLiHHiL t

2

*

2�R

scalar singlet

( ) ( )( )δµγβα γσγσ LLLiHHiL 22

( )( ) ( )δµ

γβµα σγσγ LiHHiLLL t

2

*

2

�R

�R

after a Fierz transformationafter a Fierz transformation

Non -Unitarity and Non-Standard Neutrino Interactions · Neutrino masses in the SM All SM fermions...

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Transcript of Non -Unitarity and Non-Standard Neutrino Interactions · Neutrino masses in the SM All SM fermions...