“What isν ?”GGI Workshop – Arcetri, Firenze – July 13, 2012
LFV in Minimal Flavor Violationextensions of the seesaw
(Type-I seesaw with 3 RH neutrinos)
Enrico NardiINFN – Laboratori Nazionali di Frascati, Italy
Based mainly on:– R. Alonso, G. Isidori, L. Merlo, L. A. Mu noz, EN JHEP06(2011)037 [arXiv:1103.5461]– V. Cirigliano, B. Grinstein, G. Isidori, M. B. Wise, NPB728(2005) [hep-ph/0507001]– EN, NPB (Pr. S.) 2257(2012)236 [arXiv:1112.4418]
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 1
Why Charged Lepton Flavor Violation (cLFV)?
• ν-oscillations indisputably signal LFV in the neutral sector.
• In extensions of the SM that can account for ν-oscillationsit is natural to expect also cLFV.
• However, in the simplest extensions (Dirac ν, SM+seesaw)cLFV remains unobservable (below the O(10−50) level).
• Dirac ν: no new scale. Seesaw: large new scale Λ6L∼ΛGUT
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 2
Why Charged Lepton Flavor Violation (cLFV)?
• ν-oscillations indisputably signal LFV in the neutral sector.
• In extensions of the SM that can account for ν-oscillationsit is natural to expect also cLFV.
• However, in the simplest extensions (Dirac ν, SM+seesaw)cLFV remains unobservable (below the O(10−50) level).
• Dirac ν: no new scale. Seesaw: large new scale Λ6L∼ΛGUT
However, according to an old theoretical prejudice:
there 6is was New Physics around the TeV scale
since NP is needed to cure the SM naturalness problem.
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 2
The flavor problem
If NP has a generic flavor structure, then FCNCconstraints require ΛNP > O(105) TeV (≫ ΛEW )
Possible ways out (apart from ΛNP>∼ O(10
5) TeV)
NP is Flavor BlindHowever, complete blindness is difficult to realize,it is theoretically unmotivated, (is boring), etc.
NP (TeV) should (approximately) conserve B, B-L, CP (SM).No reason for conserving flavor, that is not a SM symmetry.
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 3
The flavor problem
If NP has a generic flavor structure, then FCNCconstraints require ΛNP > O(105) TeV (≫ ΛEW )
Possible ways out (apart from ΛNP>∼ O(10
5) TeV)
NP is Flavor BlindHowever, complete blindness is difficult to realize,it is theoretically unmotivated, (is boring), etc.
NP (TeV) should (approximately) conserve B, B-L, CP (SM).No reason for conserving flavor, that is not a SM symmetry.
NP Violates Flavor Minimally The only sources of flavor viola-tion are the SM Yukawa couplings
Ansatz: TeV-scale NP violates flavor“as much”as the SM does“What isν ?” - LFV in MLFV extensions of the seesaw – p. 3
MFV in the Quark Sector[G D’Ambrosio et al., NPB 645 (2002) 155, hep-ph/0207036]
Gauge invariant kinetic terms vs. Yukawa interactions
Qi 6DQQi + ui 6Duui + di 6Dddi︸ ︷︷ ︸U(3)Q×U(3)u×U(3)d=GF×U(1)B×U(1)Y ×U(1)qR
+ QiYiju uj H + QiY
ijd dj H︸ ︷︷ ︸
×GF
GF = SU(3)Q × SU(3)u × SU(3)d
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 4
MFV in the Quark Sector[G D’Ambrosio et al., NPB 645 (2002) 155, hep-ph/0207036]
Gauge invariant kinetic terms vs. Yukawa interactions
Qi 6DQQi + ui 6Duui + di 6Dddi︸ ︷︷ ︸U(3)Q×U(3)u×U(3)d=GF×U(1)B×U(1)Y ×U(1)qR
+ QiYiju uj H + QiY
ijd dj H︸ ︷︷ ︸
×GF
GF = SU(3)Q × SU(3)u × SU(3)d
To construct the MFV NP Operators ⇒ Spurion Technique:
• Introduce Yukawa formal transformations Yu,d → VQYu,dV†u,d
• Require formal invariance under the flavor group GF .
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 4
MFV in the Quark Sector[G D’Ambrosio et al., NPB 645 (2002) 155, hep-ph/0207036]
Gauge invariant kinetic terms vs. Yukawa interactions
Qi 6DQQi + ui 6Duui + di 6Dddi︸ ︷︷ ︸U(3)Q×U(3)u×U(3)d=GF×U(1)B×U(1)Y ×U(1)qR
+ QiYiju uj H + QiY
ijd dj H︸ ︷︷ ︸
×GF
GF = SU(3)Q × SU(3)u × SU(3)d
To construct the MFV NP Operators ⇒ Spurion Technique:
• Introduce Yukawa formal transformations Yu,d → VQYu,dV†u,d
• Require formal invariance under the flavor group GF .
Dipole Contact Suppressed byYd
1Λ2
NP
× Q YuY†u Q·(DµF
µν); Q YuY†u Q·(QQ); d Y †
d YuY†u Q·(QQ)
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 4
MFV in the Lepton Sector[V. Cirigliano et al. NPB 728 (2005) 121; V. Cirigliano and B. Grinstein, NPB752, 18 (2006) ]
[R. Alonso et al., JHEP 1106, 037 (2011), [arXiv:1103.5461].]
SM: ℓi 6Dℓℓi + ei 6Deei︸ ︷︷ ︸U(3)ℓ×U(3)e=GSM
F ×U(1)L
+ ℓi Yije ej H︸ ︷︷ ︸
=⇒ U(1)e×U(1)µ×U(1)τ
The SM Lepton sector is incomplete[no ν-masses
no ν-oscillat.
]. A choice for
a specific SM extension must be made:
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 5
MFV in the Lepton Sector[V. Cirigliano et al. NPB 728 (2005) 121; V. Cirigliano and B. Grinstein, NPB752, 18 (2006) ]
[R. Alonso et al., JHEP 1106, 037 (2011), [arXiv:1103.5461].]
SM: ℓi 6Dℓℓi + ei 6Deei︸ ︷︷ ︸U(3)ℓ×U(3)e=GSM
F ×U(1)L
+ ℓi Yije ej H︸ ︷︷ ︸
=⇒ U(1)e×U(1)µ×U(1)τ
The SM Lepton sector is incomplete[no ν-masses
no ν-oscillat.
]. A choice for
a specific SM extension must be made: SM + seesaw:
ℓ 6Dℓℓ + e6Dee +
Kinetic︷ ︸︸ ︷N 6∂N︸ ︷︷ ︸
U(3)ℓ×U(3)e×U(3)N=GF×U(1)L
+ ℓi Yije ej H+
Yukawa︷ ︸︸ ︷ℓiY
ijν Nj H︸ ︷︷ ︸
×GF
+12 µL
Majorana︷ ︸︸ ︷N c
i YijM Nj︸ ︷︷ ︸
U(1)L��
�PP
P
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 5
MFV in the Lepton Sector[V. Cirigliano et al. NPB 728 (2005) 121; V. Cirigliano and B. Grinstein, NPB752, 18 (2006) ]
[R. Alonso et al., JHEP 1106, 037 (2011), [arXiv:1103.5461].]
SM: ℓi 6Dℓℓi + ei 6Deei︸ ︷︷ ︸U(3)ℓ×U(3)e=GSM
F ×U(1)L
+ ℓi Yije ej H︸ ︷︷ ︸
=⇒ U(1)e×U(1)µ×U(1)τ
The SM Lepton sector is incomplete[no ν-masses
no ν-oscillat.
]. A choice for
a specific SM extension must be made: SM + seesaw:
ℓ 6Dℓℓ + e6Dee +
Kinetic︷ ︸︸ ︷N 6∂N︸ ︷︷ ︸
U(3)ℓ×U(3)e×U(3)N=GF×U(1)L
+ ℓi Yije ej H+
Yukawa︷ ︸︸ ︷ℓiY
ijν Nj H︸ ︷︷ ︸
×GF
+12 µL
Majorana︷ ︸︸ ︷N c
i YijM Nj︸ ︷︷ ︸
U(1)L��
�PP
P
3 spurions Ye, Yν, YM ⇒ The leading MLFV effective terms:
∆(1)8 =YνY
†ν , ∆6 =YνY
†MY T
ν , ∆(2)8 =YνY
†MYMY †
ν , Ye∆, . . .
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 5
Predictivity: Yν, YM (18) ⇔ mν, UPMNS (9)
Two ansatzs can match No. LFV paramts to No. observables:
1) YM ∝ I3×3 Reduced symmetry: SU(3)N → SO(3)N×CP[V. Cirigliano, B. Grinstein, G. Isidori, M.B. Wise, NPB 728 (2005) 121]
∆6 =∆(1)8 =∆
(2)8 = YνY
Tν = µL
v2 UmνUT mν =diag(m1, m2, m3)
U = UPMNS
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 6
Predictivity: Yν, YM (18) ⇔ mν, UPMNS (9)
Two ansatzs can match No. LFV paramts to No. observables:
1) YM ∝ I3×3 Reduced symmetry: SU(3)N → SO(3)N×CP[V. Cirigliano, B. Grinstein, G. Isidori, M.B. Wise, NPB 728 (2005) 121]
∆6 =∆(1)8 =∆
(2)8 = YνY
Tν = µL
v2 UmνUT mν =diag(m1, m2, m3)
U = UPMNS
2) Yν ∝ UY (Unitary) Symmetry: SU(3)N × SU(3)ℓ → SU(3)N+ℓ
[R. Alonso, G. Isidori, L. Merlo, L. A. Munoz, EN, JHEP 1106, 037 (2011)]
∆6 = v2
µLU 1
mνUT ; ∆
(2)8 =∆6 · ∆
†6 = v4
µ2
L
U 1m
2νU † ∆
(1)8 = I3×3
− This second scenario (2) allows for CP�� .− Non-Abelian symmetries (⇒TBM) imply Y 0
ν ∝ UY at LO.[E. Bertuzzo, P. Di Bari, F. Feruglio, EN, JHEP 0911:036, (2009)]
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 6
MLFV Operators: ℓ→ℓ′γ; µ+A→e+A; ℓ→3ℓ′
ℓ → ℓ′γ (µ−e; ℓ → 3ℓ′) (On-shell photonic operators only)
O(1)RL = g′H†eRσµνλe∆ ℓL · Bµν
O(2)RL = gH†eRσµντaλe∆ ℓL · W a
µν
B(µ → eee) ≃1
160B(µ → eγ)
Γ(µ T i → e T i)
Γ(µ T i → capt)≃
1
240B(µ → eγ)
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 7
MLFV Operators: ℓ→ℓ′γ; µ+A→e+A; ℓ→3ℓ′
ℓ → ℓ′γ (µ−e; ℓ → 3ℓ′) (On-shell photonic operators only)
O(1)RL = g′H†eRσµνλe∆ ℓL · Bµν
O(2)RL = gH†eRσµντaλe∆ ℓL · W a
µν
B(µ → eee) ≃1
160B(µ → eγ)
Γ(µ T i → e T i)
Γ(µ T i → capt)≃
1
240B(µ → eγ)
µ+A → e+A (off-shell photonic; 4-fermions contact, LO)O
(1)LL = ℓLγµ∆ ℓL ·
(H†iDµH
)
O(2)LL = ℓLγµτa∆ ℓL ·
(H†τaiDµH
)
O(3)LL = ℓLγµ∆ ℓL ·
(QLγµQL
)
O(4d)LL = ℓLγµ∆ ℓL ·
(dRγµdR
)
O(4u)LL = ℓLγµ∆ ℓL · (uRγµuR)
O(5)LL = ℓLγµτa∆ ℓL ·
(QLγµτ
aQL
)
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 7
MLFV Operators: ℓ→ℓ′γ; µ+A→e+A; ℓ→3ℓ′
ℓ → ℓ′γ (µ−e; ℓ → 3ℓ′) (On-shell photonic operators only)
O(1)RL = g′H†eRσµνλe∆ ℓL · Bµν
O(2)RL = gH†eRσµντaλe∆ ℓL · W a
µν
B(µ → eee) ≃1
160B(µ → eγ)
Γ(µ T i → e T i)
Γ(µ T i → capt)≃
1
240B(µ → eγ)
µ+A → e+A (off-shell photonic; 4-fermions contact, LO)O
(1)LL = ℓLγµ∆ ℓL ·
(H†iDµH
)
O(2)LL = ℓLγµτa∆ ℓL ·
(H†τaiDµH
)
O(3)LL = ℓLγµ∆ ℓL ·
(QLγµQL
)
O(4d)LL = ℓLγµ∆ ℓL ·
(dRγµdR
)
O(4u)LL = ℓLγµ∆ ℓL · (uRγµuR)
O(5)LL = ℓLγµτa∆ ℓL ·
(QLγµτ
aQL
)
ℓ → ℓ′ℓ′′ℓ′′′ (4-leptons contact, LO)
O(1)4L = ℓLγµ∆ ℓL ·
(ℓLγµℓL
)
O(2)4L = ℓLγµτa∆ ℓL ·
(ℓLγµτ
aℓL
) O(3)4L = ℓLγµ∆ ℓL · (eRγµeR)
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 7
MLFV Predictions: ℓ→ℓ′γ; µ+A→e+A; ℓ→3ℓ′
Case 1. Bτ→µγ and Bµ→eγ for vµL/Λ2NP = 5× 107 as a function of s13.
0 0.05 0.1 0.15 0.2
10-8
10-10
10-12
10-140 0.05 0.1 0.15 0.2
10-8
10-10
10-12
10-140 0.05 0.1 0.15 0.2
10-8
10-10
10-12
10-140 0.05 0.1 0.15 0.2
10-8
10-10
10-12
10-14
NORMAL INVERTED
s13s13
Bτ→µγ Bτ→µγ
δ = π
δ = 0
Bexp limitµ→eγ B
exp limitµ→eγ
δ = 0
δ = πBµ→eγ Bµ→eγ
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 8
MLFV Predictions: ℓ→ℓ′γ; µ+A→e+A; ℓ→3ℓ′
Case 1. Bτ→µγ and Bµ→eγ for vµL/Λ2NP = 5× 107 as a function of s13.
0 0.05 0.1 0.15 0.2
10-8
10-10
10-12
10-140 0.05 0.1 0.15 0.2
10-8
10-10
10-12
10-140 0.05 0.1 0.15 0.2
10-8
10-10
10-12
10-140 0.05 0.1 0.15 0.2
10-8
10-10
10-12
10-14
NORMAL INVERTED
s13s13
Bτ→µγ Bτ→µγ
δ = π
δ = 0
Bexp limitµ→eγ B
exp limitµ→eγ
δ = 0
δ = πBµ→eγ Bµ→eγ
0 0.05 0.1 0.15 0.2 0.250
5
10
15
20
25
30
35
0 0.05 0.1 0.15 0.2 0.250
0.05
0.1
0.15
0.2
0.25
0.3
0.35
mlightestν = 0 m
lightestν = 0.2 eV
RAuµ→e
Rµ→eγ
RAlµ→e
RAuµ→e
Rµ→eγ
RAlµ→e
s13s13Veritical units × ∼ 2 · 10−12 (δ = 0) (Ti 4 · 10−12; Au 7 · 10−13)“What isν ?” - LFV in MLFV extensions of the seesaw – p. 8
MLFV Predictions (Case 2): Bµ→eγ
Bτ→µγ;
Bµ→eγ
Bτ→eγ
10-3 10-2 10-110-4
10-3
10-2
10-1
100
101
102
103
Bµ→
eγ
Bτ→
µγ
mνl [eV℄Hierar hyNormalInverted
10-3 10-2 10-110-4
10-3
10-2
10-1
100
101
102
103
Bµ→
eγ
Bτ→
eγ
mνl [eV℄
Hierar hyNormalInverted
0 0.05 0.1 0.15 0.2
Hierar hyNormalInverted
0 0.05 0.1 0.15 0.2
Hierar hyNormalInverted
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 9
MLFV Predictions (Case 2): Bµ→eγ
Bτ→µγ;
Bµ→eγ
Bτ→eγ
10-3 10-2 10-110-4
10-3
10-2
10-1
100
101
102
103
Bµ→
eγ
Bτ→
µγ
mνl [eV℄Hierar hyNormalInverted
10-3 10-2 10-110-4
10-3
10-2
10-1
100
101
102
103
Bµ→
eγ
Bτ→
eγ
mνl [eV℄
Hierar hyNormalInverted
0 0.05 0.1 0.15 0.210-4
10-3
10-2
10-1
100
101
102
103
Bµ→
eγ
Bτ→
µγ
sin θ13
Hierar hyNormalInverted0 0.05 0.1 0.15 0.2
10-4
10-3
10-2
10-1
100
101
102
103
Bµ→
eγ
Bτ→
eγ
sin θ13
Hierar hyNormalInverted
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 9
MLFV Predictions (Case 1): Γµ→3e
Γµ→eνν
Γµ→3e
Γµ→eνν= (Wilson Coeff.)×
(vµL
Λ2
NP
)2
×|beµ|2 ∼
(1014−1016
)×|beµ|
2
0 0.05 0.1 0.15 0.2 0.25s13
10-26
10-28
10-30
ÈbeΜÈ2
∆=0
0 0.05 0.1 0.15 0.2 0.25s13
10-26
10-28
10-30
ÈbeΜÈ2
∆=0
0 0.05 0.1 0.15 0.2 0.25s13
10-26
10-28
10-30
ÈbeΜÈ2
∆=Π
0 0.05 0.1 0.15 0.2 0.25s13
10-26
10-28
10-30
ÈbeΜÈ2
∆=Π
Bµ→3e for normal neutrino mass hierarchy and δ = 0, π.
Shaded band: 0 ≤ mminν ≤ 0.2 eV (Upper edge: mmin
ν = 0)
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 10
CONCLUSIONS• MFV is a guess about the behaviour of NP with respect to FV.
• MLFV is a double guess: a specific extension of the SM to accountfor mν 6= 0 has to be assumed first.
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 11
CONCLUSIONS• MFV is a guess about the behaviour of NP with respect to FV.
• MLFV is a double guess: a specific extension of the SM to accountfor mν 6= 0 has to be assumed first.
• MLFV does not necessarily imply suppression of the LFVprocesses involving the lightest generations.
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 11
CONCLUSIONS• MFV is a guess about the behaviour of NP with respect to FV.
• MLFV is a double guess: a specific extension of the SM to accountfor mν 6= 0 has to be assumed first.
• MLFV does not necessarily imply suppression of the LFVprocesses involving the lightest generations.
• This is because a theory that is MFV in the UV ingeneral is not MFV in the IR (CCB) .
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 11
CONCLUSIONS• MFV is a guess about the behaviour of NP with respect to FV.
• MLFV is a double guess: a specific extension of the SM to accountfor mν 6= 0 has to be assumed first.
• MLFV does not necessarily imply suppression of the LFVprocesses involving the lightest generations.
• This is because a theory that is MFV in the UV ingeneral is not MFV in the IR (CCB) .
• UV-MFV =⇒ IR-MFV only if after sending spurions → 0 the onlyfields that become massless are the SM fields.
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 11
CONCLUSIONS• MFV is a guess about the behaviour of NP with respect to FV.
• MLFV is a double guess: a specific extension of the SM to accountfor mν 6= 0 has to be assumed first.
• MLFV does not necessarily imply suppression of the LFVprocesses involving the lightest generations.
• This is because a theory that is MFV in the UV ingeneral is not MFV in the IR (CCB) .
• UV-MFV =⇒ IR-MFV only if after sending spurions → 0 the onlyfields that become massless are the SM fields.
• Even with MFV, experimental constraints on FCNC & LFV implyΛNP > (≫)10 TeV. (Is the original motivation for MFV matched ?)
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 11
CONCLUSIONS• MFV is a guess about the behaviour of NP with respect to FV.
• MLFV is a double guess: a specific extension of the SM to accountfor mν 6= 0 has to be assumed first.
• MLFV does not necessarily imply suppression of the LFVprocesses involving the lightest generations.
• This is because a theory that is MFV in the UV ingeneral is not MFV in the IR (CCB) .
• UV-MFV =⇒ IR-MFV only if after sending spurions → 0 the onlyfields that become massless are the SM fields.
• Even with MFV, experimental constraints on FCNC & LFV implyΛNP > (≫)10 TeV. (Is the original motivation for MFV matched ?)
• As a general remark, the LFV processes ℓ → ℓ′γ, µ-e conversion,ℓ → 3ℓ′, are sensitive to different NP operators, and thus providecomplementary informations.
“What isν ?” - LFV in MLFV extensions of the seesaw – p. 11