neutrino masses and unitarity of the leptonic mixing...
TRANSCRIPT
Carla BiggioUniversidad Autónoma de Madrid
Neutrino masses and unitarity of the leptonic mixing matrix
Padova, 20/XI/2006
Carla BiggioUniversidad Autónoma de Madrid
Neutrino masses and unitarity of the leptonic mixing matrix
Padova, 20/XI/2006
1. ν physics in the “standard” scenario:• in the SM: exactly massless• experimentally: oscillations → ν are massive
leptonic flavour mixing• ν masses beyond the SM: see-saw mechanisms→ low energy effects of high energy models:
unitarity violations arise…
2. ν physics without unitarity• oscillation probabilities and decay rates• determining the elements of leptonic mixing matrix
Outline:
ν in the SM: exactly massless
..~ chlHY RL +νν
( )LRRLDm νννν +No Dirac mass:
• No right-handed νR → no
• No scalar triplets Δ → no
• SM is renormalizable → no dim5
• U(1)B-L non-anomalous global symmetry → no radiatively generated
ν in the SM: exactly massless
..~ chlHY RL +νν
..chllY Lc
L +ΔΔ
( )( ) ..~~ † chlHHlY Lc
L +∗βααβ
( )LRRLDm νννν +
( )cLLL
cLMm νννν +
No Dirac mass:
• No right-handed νR → no
No Majorana mass:
• No scalar triplets Δ → no
• SM is renormalizable → no dim5
• U(1)B-L non-anomalous global symmetry → no radiatively generated
ν in the SM: exactly massless
..~ chlHY RL +νν
..chllY Lc
L +ΔΔ
( )( ) ..~~ † chlHHlY Lc
L +∗βααβ
( )LRRLDm νννν +
( )cLLL
cLMm νννν +
No Dirac mass:
• No right-handed νR → no
No Majorana mass:
Massless neutrinos → neither mixing nor CP violation in the leptonic sector
But experimentally…
Experiments on SOLAR, ATMOSPHERIC and TERRESTRIAL νhave shown that ν oscillate
→ ν are massive and there is flavour mixing in the lepton sector too
But experimentally…
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−=
−−
−−
132313231223121323121223
132313231223121323122312
1313121312
ccescsscesccsscsesssccessccsescscc
Uii
ii
i
δδ
δδ
δ
Experiments on SOLAR, ATMOSPHERIC and TERRESTRIAL νhave shown that ν oscillate
→ ν are massive and there is flavour mixing in the lepton sector too
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛×
Φ
Φ
2
1
0000001
i
i
ee
m1, m2, m3
Majorana phases
But experimentally…
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−=
−−
−−
132313231223121323121223
132313231223121323122312
1313121312
ccescsscesccsscsesssccessccsescscc
Uii
ii
i
δδ
δδ
δ
m1, m2, m3
Experiments on SOLAR, ATMOSPHERIC and TERRESTRIAL νhave shown that ν oscillate
→ ν are massive and there is flavour mixing in the lepton sector too
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛×
Φ
Φ
2
1
0000001
i
i
ee
Oscillation experimentsθ12 , θ23 , Δm2
12 , |Δm223|
Majorana phases
But experimentally…
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−=
−−
−−
132313231223121323121223
132313231223121323122312
1313121312
ccescsscesccsscsesssccessccsescscc
Uii
ii
i
δδ
δδ
δ
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛×
Φ
Φ
2
1
0000001
i
i
ee
m1, m2, m3
Experiments on SOLAR, ATMOSPHERIC and TERRESTRIAL νhave shown that ν oscillate
→ ν are massive and there is flavour mixing in the lepton sector too
Oscillation experimentsθ12 , θ23 , Δm2
12 , |Δm223|
0νββ decay
Majorana phases
( )( )21.0
26.0232
223
2
2521
22
2
1104.2
09.011092.7+−
−
−
⋅=−=Δ
±⋅=−=Δ
eVmmm
eVmmm
atm
sun
Fogli et al. 05
• Sign (Δm223) ?
m
NORMAL INVERTED
ν3
ν2ν1
ν1
ν2
ν3
Mass spectrum: present status
( )( )21.0
26.0232
223
2
2521
22
2
1104.2
09.011092.7+−
−
−
⋅=−=Δ
±⋅=−=Δ
eVmmm
eVmmm
atm
sun
Fogli et al. 05
• Sign (Δm223) ?
• Absolute mass scale?
m
NORMAL INVERTED
ν3
ν2ν1
ν1
ν2
ν3
Mass spectrum: present status
( )( )21.0
26.0232
223
2
2521
22
2
1104.2
09.011092.7+−
−
−
⋅=−=Δ
±⋅=−=Δ
eVmmm
eVmmm
atm
sun
eVmUm ieiie 2.2 2 <= ∑
eVmUm ieiiee 6.14.0 2 −<= ∑
Fogli et al. 05
• Sign (Δm223) ?
• Absolute mass scale?
m
NORMAL INVERTED
ν3
ν2ν1
ν1
ν2
ν3
• Tritium β decay
• 0νββ decay
• Cosmology ∑⎪⎩
⎪⎨
⎧
−−−
<68.042.07.10.11.36.1
ii mCMB
CMB + LSS
CMB + LSS + Lyman-α
Mainz, Troitsk
Heidelberg-Moscow
modeldependent
Mass spectrum: present status
Mixing angles: present status
047.0sin
38.023.0sin
68.034.0sin
132
122
232
≤
−=
−=
θ
θ
θ
Maltoni, Schwetz, Tortola, Valle 04
Mixing angles: present status
047.0sin
38.023.0sin
68.034.0sin
132
122
232
≤
−=
−=
θ
θ
θ
FUTURE:- Dirac phase δ → appearance experiments- Majorana phases φ1 , φ2 → 0νββ decay
Maltoni, Schwetz, Tortola, Valle 04
ν masses beyond the SM
• right-handed νR →
Why ν are so light?Why νR does not acquire large Majorana mass?
.. .. ~ chmchlHY RLDRL +→+ νννν
1. Adding “light” fields
ν masses beyond the SM
• right-handed νR →
Why ν are so light?Why νR does not acquire large Majorana mass?
• scalar triplet Δ →
Why <Δ> « <H> ?
.. .. ~ chmchlHY RLDRL +→+ νννν
( ) ( )cLLL
cLM
cLLL
cL mllllY νννν +→+ΔΔ
1. Adding “light” fields
ν masses beyond the SM
• right-handed νR →
Why ν are so light?Why νR does not acquire large Majorana mass?
• scalar triplet Δ →
Why <Δ> « <H> ?
→ maybe there are better solutions…
.. .. ~ chmchlHY RLDRL +→+ νννν
( ) ( )cLLL
cLM
cLLL
cL mllllY νννν +→+ΔΔ
1. Adding “light” fields
ν masses beyond the SM
2. Adding heavy fields
Heavy fields manifest in the low energy effective theory (SM)via higher dimensional operators
ν masses beyond the SM
2. Adding heavy fields
Heavy fields manifest in the low energy effective theory (SM)via higher dimensional operators
Dimension 5 operator:
†* ~~ HHllM L
cL βα
αβλ
lα
lβ Mαβλ
ν masses beyond the SM
2. Adding heavy fields
Heavy fields manifest in the low energy effective theory (SM)via higher dimensional operators
Dimension 5 operator:
†* ~~ HHllM L
cL βα
αβλβα
αβ ννλ
Lc
LM v2→
lα
lβ Mαβλ
ν masses beyond the SM
2. Adding heavy fields
Heavy fields manifest in the low energy effective theory (SM)via higher dimensional operators
Dimension 5 operator:
This mass term violates lepton number→ neutrinos must be Majorana fermions
It’s unique → very special role of ν masses:lowest-order effect of higher energy physics
→
lα
lβ Mαβλ
†* ~~ HHllM L
cL βα
αβλβα
αβ ννλ
Lc
LM v2
ν masses beyond the SM
Tree-level realizations
Type I See-SawMinkowski, Gell-Mann, Ramond, Slansky, Yanagida, Glashow, Mohapatra, Senjanovic
NR fermion singlet
NR
NR
ν masses beyond the SM
Tree-level realizations
μ
Type II See-SawMagg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle
Δ scalar triplet
Type I See-SawMinkowski, Gell-Mann, Ramond, Slansky, Yanagida, Glashow, Mohapatra, Senjanovic
NR fermion singlet
NR
NR
ν masses beyond the SM
Tree-level realizations
μ
Type II See-SawMagg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle
Δ scalar triplet
Type III See-SawMa, Hambye et al., …
tR fermion triplettR
tRMt
Yt
Yt
Type I See-SawMinkowski, Gell-Mann, Ramond, Slansky, Yanagida, Glashow, Mohapatra, Senjanovic
NR fermion singlet
NR
NR
ν masses beyond the SM
• radiative mechanisms: ex.) 1 loop:
Other realizations
ν masses beyond the SM
• radiative mechanisms: ex.) 1 loop:
Other realizations
• SUSY models with R-parity violation
ν masses beyond the SM
• radiative mechanisms: ex.) 1 loop:
Other realizations
• SUSY models with R-parity violation
• (models with large extra dimensions)
SMRνψ ⊃Dirac mass suppressed by (2πR)d/2
ν masses beyond the SM
• radiative mechanisms: ex.) 1 loop:
Other realizations
• SUSY models with R-parity violation
• (models with large extra dimensions)
• …
SMRνψ ⊃Dirac mass suppressed by (2πR)d/2
Low-energy effects of see-saw: type I
( ) ( )cRRR
cRLRRLRRSM NMNMNNlHYNNYHlNNiLL ∗+−+−∂/+=
21~~ ††
νν
...11 62
5 +Λ
+Λ
+= == ddSM
eff LLLLIntegrate out NR
Low-energy effects of see-saw: type I
...11 62
5 +Λ
+Λ
+= == ddSM
eff LLLLIntegrate out NR
( ) ( )cRRR
cRLRRLRRSM NMNMNNlHYNNYHlNNiLL ∗+−+−∂/+=
21~~ ††
νν
d=5 operatorit gives mass to ν
( ) ..~~41 ††* chHHlY
MYl LL +⎟
⎟⎠
⎞⎜⎜⎝
⎛⎥⎦⎤
⎢⎣⎡− τητ β
αβννα
rr
Mm
2v≈ν
Low-energy effects of see-saw: type I
...11 62
5 +Λ
+Λ
+= == ddSM
eff LLLLIntegrate out NR
( ) ( )βαβ
ννα LL lHYM
YiHl ††2
~1~⎥⎦⎤
⎢⎣⎡∂/
d=5 operatorit gives mass to ν
d=6 operatorit renormalises kinetic energy
Broncano, Gavela, Jenkins 02
( ) ( )cRRR
cRLRRLRRSM NMNMNNlHYNNYHlNNiLL ∗+−+−∂/+=
21~~ ††
νν
( ) ..~~41 ††* chHHlY
MYl LL +⎟
⎟⎠
⎞⎜⎜⎝
⎛⎥⎦⎤
⎢⎣⎡− τητ β
αβννα
rr
Mm
2v≈ν
Low-energy effects of see-saw: type I
( )
( ) ( ) .....cos
..2
..21
++−+−
++−∂/=
+ chPZgchPlWg
chMKiL
LW
L
c
αμ
αμαμ
αμ
βαβαβαβα
νγνθ
νγ
νννν
αβνναβαβ δ ⎟
⎠⎞
⎜⎝⎛+= †
2
2 12v Y
MYK
αβνναβ
η⎟⎠⎞
⎜⎝⎛= †*
2
2v Y
MYM
After EWSB:
Low-energy effects of see-saw: type I
( )
( ) ( ) .....cos
..2
..21
++−+−
++−∂/=
+ chPZgchPlWg
chMKiL
LW
L
c
αμ
αμαμ
αμ
βαβαβαβα
νγνθ
νγ
νννν
αβνναβαβ δ ⎟
⎠⎞
⎜⎝⎛+= †
2
2 12v Y
MYK
αβνναβ
η⎟⎠⎞
⎜⎝⎛= †*
2
2v Y
MYM
After EWSB:
Mαβ → diagonalized → unitary transformation
Kαβ → diagonalized and normalized → unitary transf. + rescaling
Low-energy effects of see-saw: type I
( )
( ) ( ) .....cos
..2
..21
++−+−
++−∂/=
+ chPZgchPlWg
chMKiL
LW
L
c
αμ
αμαμ
αμ
βαβαβαβα
νγνθ
νγ
νννν
αβνναβαβ δ ⎟
⎠⎞
⎜⎝⎛+= †
2
2 12v Y
MYK
αβνναβ
η⎟⎠⎞
⎜⎝⎛= †*
2
2v Y
MYM
After EWSB:
( ) ( ) ( ) .....)(cos22
1 † ++−−−∂/= + chNNPZgNPlWgmiL jijLiW
iiLiiiic
ii νγνθ
νγνννν μμα
μαμ
Mαβ → diagonalized → unitary transformation
Kαβ → diagonalized and normalized → unitary transf. + rescaling
iiN νν αα = N non-unitary
Low-energy effects of see-saw: type II & IIIAbada, CB, Bonnet, Gavela, in progress
type II (scalar triplet)
d=5 2
2v
Δ
≈M
m μν
Low-energy effects of see-saw: type II & IIIAbada, CB, Bonnet, Gavela, in progress
type II (scalar triplet)
d=5
d=6
2
2v
Δ
≈M
m μν
• 4 Higgs interaction• 6 Higgs interaction• 4 fermions interaction
no correction to kinetic terms
→ no deviations from unitarity
Low-energy effects of see-saw: type II & IIIAbada, CB, Bonnet, Gavela, in progress
type II (scalar triplet) type III (fermion triplet)
d=5
d=6
2
2v
Δ
≈M
m μν
tMm
2v≈ν
• 4 Higgs interaction• 6 Higgs interaction• 4 fermions interaction
no correction to kinetic terms
→ no deviations from unitarity
Low-energy effects of see-saw: type II & III
corrections to
• kinetic terms for neutrinos• kinetic terms for charged
fermions• interactions with gauge bosons
→ deviations from unitarity
Abada, CB, Bonnet, Gavela, in progress
type II (scalar triplet) type III (fermion triplet)
d=5
d=6
2
2v
Δ
≈M
m μν
tMm
2v≈ν
• 4 Higgs interaction• 6 Higgs interaction• 4 fermions interaction
no correction to kinetic terms
→ no deviations from unitarity
Low energy effects of a model with xdimDe Gouvea, Giudice, Strumia, Tobe 01
( )[ ]∫∫ +−+/= ..~44 chHYlLdxDidydxS RLSM βαβαααδ νψψ
Low energy effects of a model with xdimDe Gouvea, Giudice, Strumia, Tobe 01
⎟⎠⎞
⎜⎝⎛ ⋅
= ∑ Rynix
Ryx
n n
rrrrr
r r exp)()2(
1),( ,2/ αδα ψπ
ψDevelope in KK modes and perform ∫ δdy
( )[ ]∫∫ +−+/= ..~44 chHYlLdxDidydxS RLSM βαβαααδ νψψ
Low energy effects of a model with xdimDe Gouvea, Giudice, Strumia, Tobe 01
⎟⎠⎞
⎜⎝⎛ ⋅
= ∑ Rynix
Ryx
n n
rrrrr
r r exp)()2(
1),( ,2/ αδα ψπ
ψDevelope in KK modes and perform ∫ δdy
( )[ ]∫∫ +−+/= ..~44 chHYlLdxDidydxS RLSM βαβαααδ νψψ
∫ ∑⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎭⎬⎫
⎩⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛+−⎟
⎠⎞
⎜⎝⎛ ⋅
−∂/+=n RnLnnSM chH
RY
lR
niLdxS r rrr
rr
..~)2( 2/
4βδ
αβααα ν
πψγψ
Dirac mass 2/
2
)2(v
δν πλR
m ≈
Low energy effects of a model with xdimDe Gouvea, Giudice, Strumia, Tobe 01
⎟⎠⎞
⎜⎝⎛ ⋅
= ∑ Rynix
Ryx
n n
rrrrr
r r exp)()2(
1),( ,2/ αδα ψπ
ψDevelope in KK modes and perform ∫ δdy
( )[ ]∫∫ +−+/= ..~44 chHYlLdxDidydxS RLSM βαβαααδ νψψ
∫ ∑⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎭⎬⎫
⎩⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛+−⎟
⎠⎞
⎜⎝⎛ ⋅
−∂/+=n RnLnnSM chH
RY
lR
niLdxS r rrr
rr
..~)2( 2/
4βδ
αβααα ν
πψγψ
Dirac mass 2/
2
)2(v
δν πλR
m ≈
Integrate out the heavy modes: ( ) [ ] ( )βαβαδδ LL
d lHYYiHlL ††26 ~~ ∂/Λ∝ −=
→ deviations from unitarity
A general statement…
We have unitarity violation whenever we integrate out heavy fermions:
A general statement…
We have unitarity violation whenever we integrate out heavy fermions:
...112 +
/−−=
−/ MDi
MMDi
v
v
A general statement…
We have unitarity violation whenever we integrate out heavy fermions:
...112 +
/−−=
−/ MDi
MMDi
v
v
It connects fermions withopposite chirality → mass term
A general statement…
We have unitarity violation whenever we integrate out heavy fermions:
...112 +
/−−=
−/ MDi
MMDi
v
vThere’s a γμ: it connects fermionswith the same chirality → correction to the kinetic terms
It connects fermions withopposite chirality → mass term
A general statement…
We have unitarity violation whenever we integrate out heavy fermions:
...112 +
/−−=
−/ MDi
MMDi
v
vThere’s a γμ: it connects fermionswith the same chirality → correction to the kinetic terms
It connects fermions withopposite chirality → mass term
The propagator of a scalar field does not contain γμ → if it generates neutrino mass, it cannot correct the kinetic term
Neutrino physics without unitarity
• Unitarity violations arise in models for ν masses with heavy fermions
• They can arise from other new physics
Neutrino physics without unitarity
• Unitarity violations arise in models for ν masses with heavy fermions
• They can arise from other new physics
→ worthwhile studying neutrino physics relaxing the hypothesisof unitarity of the leptonic mixing matrix
Neutrino physics without unitarity
• Unitarity violations arise in models for ν masses with heavy fermions
• They can arise from other new physics
Antusch, CB, Fernández-Martínez, Gavela, López-PavónJHEP 0610:084,2006 [hep-ph/0607020]
we constrain the matrix elements
• first only with present oscillation experiments and • then by combining them with other electroweak data
→ worthwhile studying neutrino physics relaxing the hypothesisof unitarity of the leptonic mixing matrix
Minimal Unitarity Violation Scheme
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−=
−−
−−
132313231223121323121223
132313231223121323122312
1313121312
ccescsscesccsscsesssccessccsescscc
Uii
ii
i
δδ
δδ
δ
( ) ( ) ( ) .....cos22
1++−−−∂/= + chPZgUPlWgmiL iLi
WiiLiiii
cii νγν
θνγνννν μ
μαμ
αμ
Minimal Unitarity Violation Scheme
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−=
−−
−−
132313231223121323121223
132313231223121323122312
1313121312
ccescsscesccsscsesssccessccsescscc
Uii
ii
i
δδ
δδ
δ
( ) ( ) ( ) .....)(cos22
1 † ++−−−∂/= + chNNPZgNPlWgmiL jijLiW
iiLiiiic
ii νγνθ
νγνννν μμα
μαμ
( ) ( ) ( ) .....cos22
1++−−−∂/= + chPZgUPlWgmiL iLi
WiiLiiii
cii νγν
θνγνννν μ
μαμ
αμ
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
321
321
321
τττ
μμμ
NNNNNNNNN
Neee
Minimal Unitarity Violation Scheme
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−=
−−
−−
132313231223121323121223
132313231223121323122312
1313121312
ccescsscesccsscsesssccessccsescscc
Uii
ii
i
δδ
δδ
δ
( ) ( ) ( ) .....)(cos22
1 † ++−−−∂/= + chNNPZgNPlWgmiL jijLiW
iiLiiiic
ii νγνθ
νγνννν μμα
μαμ
( ) ( ) ( ) .....cos22
1++−−−∂/= + chPZgUPlWgmiL iLi
WiiLiiii
cii νγν
θνγνννν μ
μαμ
αμ
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
321
321
321
τττ
μμμ
NNNNNNNNN
Neee
This is completely general and model independent
• 3 light ν• all unitarity violation from NP @ E > ΛSM
Unique assumptions:
The effective Lagrangian in the MUV
( ) ( ) ( ) .....)(cos22
1 † ++−−−∂/= + chNNPZgNPlWgmiL jijLiW
iiLiiiic
ii νγνθ
νγνννν μμα
μαμ
The effective Lagrangian in the MUV
unchanged
⇓
( ) ( ) ( ) .....)(cos22
1 † ++−−−∂/= + chNNPZgNPlWgmiL jijLiW
iiLiiiic
ii νγνθ
νγνννν μμα
μαμ
ijji δνν =
The effective Lagrangian in the MUV
unchanged
⇓
Non-unitarity effects appear in the interaction:
( ) ii
iii
i NNNN
ννν αα
αα
α ∑∑ ∗∗ ≡= ~1†
⇓
( ) αβαβαβ δνν ≠= ∗ tNN ~~
( ) ( ) ( ) .....)(cos22
1 † ++−−−∂/= + chNNPZgNPlWgmiL jijLiW
iiLiiiic
ii νγνθ
νγνννν μμα
μαμ
ijji δνν =
The effective Lagrangian in the MUV
unchanged
⇓
Non-unitarity effects appear in the interaction:
( ) ii
iii
i NNNN
ννν αα
αα
α ∑∑ ∗∗ ≡= ~1†
⇓
( ) αβαβαβ δνν ≠= ∗ tNN ~~
( ) ( ) ( ) .....)(cos22
1 † ++−−−∂/= + chNNPZgNPlWgmiL jijLiW
iiLiiiic
ii νγνθ
νγνννν μμα
μαμ
ijji δνν =
This affects both electroweak decays and oscillation probabilities…
ν oscillations in vacuum
iijj
freeiji
freei EHH
dtdi νννν === ∑ˆ• mass basis 0)(
i
itiEi et νν −=
ν oscillations in vacuum
ββ
αβαα ννν ∑== freefree EHdtdi ˆ• flavour basis
iijj
freeiji
freei EHH
dtdi νννν === ∑ˆ• mass basis 0)(
i
itiEi et νν −=
( ) 1** ~~ −= βααβ j
freeiji
free NHNEwith tj
freeiji
free NHNH βααβ~~*=≠
ν oscillations in vacuum
ββ
αβαα ννν ∑== freefree EHdtdi ˆ• flavour basis
iijj
freeiji
freei EHH
dtdi νννν === ∑ˆ• mass basis 0)(
i
itiEi et νν −=
( ) 1** ~~ −= βααβ j
freeiji
free NHNEwith tj
freeiji
free NHNH βααβ~~*=≠
( ) ( ) ( )ββαα
βα
αβ ††
2*
,NNNN
NeNLEP i
iLiP
ii∑
=
ν oscillations in vacuum
ββ
αβαα ννν ∑== freefree EHdtdi ˆ• flavour basis
( ) ( ) ( )ββαα
βα
αβ ††
2*
,NNNN
NeNLEP i
iLiP
ii∑
=
Zero-distance effect:
iijj
freeiji
freei EHH
dtdi νννν === ∑ˆ• mass basis 0)(
i
itiEi et νν −=
( )( )
( ) ( )ββαα
αβαβ ††
2†
0,NNNN
NNEP =
( ) 1** ~~ −= βααβ j
freeiji
free NHNEwith tj
freeiji
free NHNH βααβ~~*=≠
ν oscillations in matter
2 families
∑−=−α
αα νγννγν 00int
212 nFeeeF nGnGL
VCC VNC
⎟⎟⎠
⎞⎜⎜⎝
⎛⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−
−+⎟⎟
⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
μμ νν
νν e
NC
NCCCte
VVV
UE
EU
dtdi
00
00
2
1*
ν oscillations in matter
2 families
∑−=−α
αα νγννγν 00int
212 nFeeeF nGnGL
VCC VNC
⎟⎟⎠
⎞⎜⎜⎝
⎛⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−
−+⎟⎟
⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
μμ νν
νν e
NC
NCCCte
VVV
UE
EU
dtdi
00
00
2
1*
( )( )( ) ( )
( ) ( )
( ) ( )( ) ( ) ( )
⎟⎟⎠
⎞⎜⎜⎝
⎛
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
−−
−−+⎟⎟
⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛ −
μμμμ
μμ
μμμ
μ νν
νν e
NCeee
NCCC
eee
NCeeNCCCe
NNVNNNNNNVV
NNNNNN
VNNVVN
EE
Ndtdi
†††
†
††
††
1*
2
1*
00
1. non-diagonal elements 2. NC effects do not disappear
N elements from oscillations: e-row
( ) ( ) ( ) ( )232
32
22
14
3
222
21 cos2ˆ Δ++++≅→ eeeeeeee NNNNNNP νν
Only disappearance exps → informations only on |Nαi|2
CHOOZ: Δ12≈0
K2K (νμ→νμ ): Δ23
1. Degeneracy
2.
cannot be disentangled
23
22
21 eee NNN ↔+
22
21 , ee NN
ELmijij 22Δ=Δ
UNITARITY
N elements from oscillations: e-row
( ) ( )122
22
14
34
24
1 cos2ˆ Δ+++≅→ eeeeeee NNNNNP νν
⎪⎩
⎪⎨⎧
≈
≈+
01
23
22
21
e
ee
NNN
→ first degeneracy solved
KamLAND: Δ23>>1
KamLAND+CHOOZ+K2KKamLAND+CHOOZ+K2K
N elements from oscillations: e-row
( ) ( )122
22
14
34
24
1 cos2ˆ Δ+++≅→ eeeeeee NNNNNP νν
⎪⎩
⎪⎨⎧
≈
≈+
01
23
22
21
e
ee
NNN
KamLAND: Δ23>>1
SNO:
( ) 22
21 9.01.0ˆ
eeee NNP +≅→νν
→ first degeneracy solved
→ all |Nei|2 determined
KamLAND+CHOOZ+K2K
SNO
N elements from oscillations: μ-row
( ) ( ) ( ) ( )23
2
3
2
2
2
1
4
3
22
2
2
1 cos2ˆ Δ++++≅→ μμμμμμμμ νν NNNNNNP
1. Degeneracy
2.
cannot be disentangled
2
3
2
2
2
1 μμμ NNN ↔+
2
2
2
1 , μμ NN
Atmospheric + K2K: Δ12≈0
UNITARITY
N elements from oscillations only
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−
<−−=
81.056.074.044.053.020.082.058.073.042.052.019.0
20.061.047.088.079.0U
González-García 04
with unitarityOSCILLATIONS
without unitarityOSCILLATIONS
3σ
( )⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛−−=+
<−−=
???86.057.086.057.0
34.066.045.089.075.0][ 2/12
22
1 μμ NNN
…adding near detectors…
Test of zero-distance effect: ( ) ( ) αβαβαβ δ≠=2†0, NNEP
• KARMEN: (NN†)μe <0.05
• NOMAD: (NN†)μτ <0.09 (NN†)eτ <0.013• MINOS: (NN†)μμ =1±0.05
• BUGEY: (NN†)ee =1±0.04
…adding near detectors…
Test of zero-distance effect: ( ) ( ) αβαβαβ δ≠=2†0, NNEP
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛−−−
<−−=
???85.057.081.022.069.000.0
27.066.045.089.075.0N
→ also all |Nμi|2 determined
• KARMEN: (NN†)μe <0.05
• NOMAD: (NN†)μτ <0.09 (NN†)eτ <0.013• MINOS: (NN†)μμ =1±0.05
• BUGEY: (NN†)ee =1±0.04
Electroweak decays
( )ijNN † ≈νi
Z
νj
iNα ≈W νi
lα
( )ααα†2 NNN SM
iiSM Γ=Γ=Γ ∑
( )∑Γ=Γij
ijSM NN2†
Electroweak decays
νiZ
νj
iNα ≈W νi
lα
( )ααα†2 NNN SM
iiSM Γ=Γ=Γ ∑
With decays we can only constrain (NN†) and (N†N) ,we cannot extract the matrix elements
→ we need oscillations!
Different from quark sector…
( )ijNN † ≈ ( )∑Γ=Γij
ijSM NN2†
(NN†) from decays
( )( ) ( )μμ
αᆆ
†
NNNN
NN
ee
→• W decays
( )( ) ( )μμ
αβαβ
††
†
NNNN
NN
ee
∑→• Invisible Z
• Universality tests( )( )ββ
αα†
†
NNNN
→
Infos on(NN†)αα
(NN†) from decays
( )( ) ( )μμ
αᆆ
†
NNNN
NN
ee
→• W decays
( )( ) ( )μμ
αβαβ
††
†
NNNN
NN
ee
∑→• Invisible Z
• Universality tests( )( )ββ
αα†
†
NNNN
→
Infos on(NN†)αα
GF is measured in μ-decay
jν
W¯
μ
e
νiNμi
N*ej
( ) ( )μμμ
π††
3
52
192NNNN
mGee
F=Γ ( ) ( )μ솆
2exp,2
NNNNG
Gee
FF =
(NN†) from decays
• Rare leptons decays Infos on (NN†)αβW
νi
lα lβ
γ
Nαi N*βi
(NN†) from decays
• Rare leptons decays Infos on (NN†)αβ
SM → GIM suppression: 54
3,22
21 10
323) −
=
∗ <Δ
=→ ∑i W
iii M
mUUlBr(l βαβα παγ
( )( ) ( )ββαα
αↆ
2†
NNNN
NN→
Now → no suppression:→ constant term leading
W
νi
lα lβ
γ
Nαi N*βi
(NN†) from decays
• Rare leptons decays Infos on (NN†)αβ
• μ-e conversion in nuclei• μ → e+e-e
SM → GIM suppression: 54
3,22
21 10
323) −
=
∗ <Δ
=→ ∑i W
iii M
mUUlBr(l βαβα παγ
( )( ) ( )ββαα
αↆ
2†
NNNN
NN→
Now → no suppression:→ constant term leading
W
νi
lα lβ
γ
Nαi N*βi
(NN†) and (N†N) from decays
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
±⋅<⋅<⋅<±⋅<⋅<⋅<±
≈−−
−−
−−
005.0003.1103.1106.1103.1005.0003.1102.7106.1102.7005.0002.1
22
25
25
†NNExperimentally
(NN†) and (N†N) from decays
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
±⋅<⋅<⋅<±⋅<⋅<⋅<±
≈−−
−−
−−
005.0003.1103.1106.1103.1005.0003.1102.7106.1102.7005.0002.1
22
25
25
†NNExperimentally
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
±<<<±<<<±
≈032.000.1032.0032.0
032.0032.000.1032.0032.0032.0032.000.1
†NNEstimation
(the most conservative)
→ N is unitary at % level
†2† with 1 εεε =+== HNN
'1 1 †† εε +=+= VVNN 03.0'2
≈≤ ∑αβ
αβεε ij
HVN =
N elements from oscillations & decays
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−
<−−=
81.056.074.044.053.020.082.058.073.042.052.019.0
20.061.047.088.079.0U
González-García 04
with unitarityOSCILLATIONS
without unitarityOSCILLATIONS
+DECAYS3σ
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−
<−−=
82.054.075.036.056.013.082.057.073.042.054.019.0
20.065.045.089.076.0N
In the future…
MEASUREMENT OF MATRIX ELEMENTS
• |Ne3|2 , μ-row → MINOS, T2K, Superbeams, NUFACTs…• τ-row → high energies: NUFACTs• phases → appearance experiments: NUFACTs, β-beams
In the future…
MEASUREMENT OF MATRIX ELEMENTS
• |Ne3|2 , μ-row → MINOS, T2K, Superbeams, NUFACTs…• τ-row → high energies: NUFACTs• phases → appearance experiments: NUFACTs, β-beams
Rare leptons decays
• μ→eγ
• τ→eγ
• τ→μγ
TESTS OF UNITARITY
( ) 016.0† <τeNN
( ) 013.0† <μτNN
( ) 5† 102.7 −⋅<μeNN
PRESENT
In the future…
MEASUREMENT OF MATRIX ELEMENTS
• |Ne3|2 , μ-row → MINOS, T2K, Superbeams, NUFACTs…• τ-row → high energies: NUFACTs• phases → appearance experiments: NUFACTs, β-beams
Rare leptons decays
• μ→eγ
• τ→eγ
• τ→μγ
TESTS OF UNITARITY
( ) 016.0† <τeNN
( ) 013.0† <μτNN
( ) 5† 102.7 −⋅<μeNN
PRESENT FUTURE
~ 10-6 MEG
~ 10-7 NUFACT
In the future…
MEASUREMENT OF MATRIX ELEMENTS
• |Ne3|2 , μ-row → MINOS, T2K, Superbeams, NUFACTs…• τ-row → high energies: NUFACTs• phases → appearance experiments: NUFACTs, β-beams
Rare leptons decays
• μ→eγ
• τ→eγ
• τ→μγ
TESTS OF UNITARITY
( ) 016.0† <τeNN
( ) 013.0† <μτNN
( ) 5† 102.7 −⋅<μeNN
PRESENT FUTURE
~ 10-6 MEG
~ 10-7 NUFACT
ZERO-DISTANCE EFFECT40Kt Iron calorimeter @ NUFACT
• νe→νμ
4Kt OPERA-like @ NUFACT
• νe→ντ
• νμ→ντ ( ) 3† 106.2 −⋅<μτNN
( ) 3† 109.2 −⋅<τeNN
( ) 4† 103.2 −⋅<μeNN
In the future…
MEASUREMENT OF MATRIX ELEMENTS
• |Ne3|2 , μ-row → MINOS, T2K, Superbeams, NUFACTs…• τ-row → high energies: NUFACTs• phases → appearance experiments: NUFACTs, β-beams
Rare leptons decays
• μ→eγ
• τ→eγ
• τ→μγ
TESTS OF UNITARITY
( ) 016.0† <τeNN
( ) 013.0† <μτNN
( ) 5† 102.7 −⋅<μeNN
PRESENT FUTURE
~ 10-6 MEG
~ 10-7 NUFACT
ZERO-DISTANCE EFFECT40Kt Iron calorimeter @ NUFACT
• νe→νμ
4Kt OPERA-like @ NUFACT
• νe→ντ
• νμ→ντ ( ) 3† 106.2 −⋅<μτNN
( ) 3† 109.2 −⋅<τeNN
( ) 4† 103.2 −⋅<μeNN
Conclusions
• ν oscillations are an indication of ν masses
• ν masses require new physics beyond the SM
• model for ν masses involving heavy fermions produce violationsof unitarity at low energy
• unitarity violation can be a general effect of new physics
→ we studied ν physics relaxing the hypothesis of unitarity
If we don’t assume unitarity for the leptonic mixing matrix
• Present oscillation experiments alone can only measure the e-row and part of the μ-row
• EW decays probes unitarity at % level
• Combining oscillations and EW decays we obtain values forthe leptonic mixing matrix comparable with the ones obtainedwith the unitary analysis