Non -Unitarity and Non-Standard Neutrino Interactions · Neutrino masses in the SM All SM fermions...
Transcript of 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
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
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
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
Effective Lagrangian
( ) ( ) .....cos
..2
++−+−+∂/= + chPZg
chPlWg
MKiL LL αµ
αµαµ
αµβαβαβαβα νγνθ
νγνννν
Diagonal mass and canonical kinetic terms
cos2 Wθ
( ) ( ) .....)(cos
..2
† ++−+−+∂/= + ch��PZg
ch�PlWg
miL jijLi
W
iiLiiiiii νγνθ
νγνννν µµα
µαµ
Effective Lagrangian
( ) ( ) .....cos
..2
++−+−+∂/= + chPZg
chPlWg
MKiL LL αµ
αµαµ
αµβαβαβαβα νγνθ
νγνννν
Diagonal mass and canonical kinetic terms
cos2 Wθ
( ) ( ) .....)(cos
..2
† ++−+−+∂/= + ch��PZg
ch�PlWg
miL jijLi
W
iiLiiiiii νγνθ
νγνννν µµα
µαµ
ii� νν αα = � is not unitary
Effective Lagrangian
( ) ( ) .....cos
..2
++−+−+∂/= + chPZg
chPlWg
MKiL LL αµ
αµαµ
αµβαβαβαβα νγνθ
νγνννν
Diagonal mass and canonical kinetic terms
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
� 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
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 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
Non-unitarity in future facilities
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 =
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 + 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-unitarity and NSI matter effects
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
Non-unitarity and NSI matter effects
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
Non-unitarity and 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?
We found three classes satisfying the requirements:
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?
We found three classes satisfying the requirements:
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?
We found three classes satisfying the requirements:
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?
B. Gavela, D. Hernández, T. Ota and W. Winter 0809.3451
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!!
B. Gavela, D. Hernández, T. Ota and W. Winter 0809.3451
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
B. Gavela, D. Hernández, T. Ota and W. Winter 0809.3451
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
C. Biggio, M. Blennow and EFM 0902.0607
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
C. Biggio, M. Blennow and EFM 0902.0607
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…
C. Biggio, M. Blennow and EFM 0902.0607
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
C. Biggio, M. Blennow and EFM 0902.0607
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,….
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 ��
cannot be disentangled
� 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 ��
cannot be disentangled
� elements from oscillations: e-row
( ) ( )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
→ first degeneracy solved
� elements from oscillations: e-row
( ) ( )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
SNO:
→ first degeneracy solved
( ) 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