Neutrino Oscillation WorkshopConca Specchiulla (Otranto, Italy)

September 9-16, 2012

Minimal Flavor Violating extensionsof 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]

NOW-2012- 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

NOW-2012- 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 is New Physics around the TeV scale

since NP is needed to cure the SM naturalness problem.

NOW-2012- 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 accepting ΛNP>∼ O(10

5) TeV)

NP is Flavor BlindHowever, complete blindness is difficult to realize,it is theoretically unmotivated, (is boring), etc.

TeV-NP should (approximately) conserve B, B-L, CP (SM).No reason for conserving flavor, that is not a SM symmetry.

NOW-2012- 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 accepting ΛNP>∼ O(10

5) TeV)

NP is Flavor BlindHowever, complete blindness is difficult to realize,it is theoretically unmotivated, (is boring), etc.

TeV-NP 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

NOW-2012- 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 accepting ΛNP>∼ O(10

5) TeV)

NP is Flavor BlindHowever, complete blindness is difficult to realize,it is theoretically unmotivated, (is boring), etc.

TeV-NP 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 doesG. D’Ambrosio, G.F. Giudice, G. Isidori, A. Strumia, Nucl. Phys. B 645 (2002) 155, hep-ph/0207036.V. Cirigliano, B. Grinstein, G. Isidori, M.B. Wise, Nucl. Phys. B 728 (2005) 121, hep-ph/0507001.V. Cirigliano, B. Grinstein, Nucl. Phys. B752, 18 (2006), [hep-ph/0601111].B. Grinstein, V. Cirigliano, G. Isidori, M. B. Wise, Nucl. Phys. B763, 35 (2007), [hep-ph/0608123].S. Davidson, F. Palorini, Phys.Lett. B642 (2006) 72,hep-ph/0607329.. . .

NOW-2012- 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)u×U(1)d

+ QiYiju uj H + QiY

ijd dj H︸ ︷︷ ︸

×GF , ×U(1)u, ×U(1)d U(1)B

GF = SU(3)Q × SU(3)u × SU(3)d

NOW-2012- 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)u×U(1)d

+ QiYiju uj H + QiY

ijd dj H︸ ︷︷ ︸

×GF , ×U(1)u, ×U(1)d U(1)B

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 .

NOW-2012- 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)u×U(1)d

+ QiYiju uj H + QiY

ijd dj H︸ ︷︷ ︸

×GF , ×U(1)u, ×U(1)d U(1)B

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 .

NP Opts.: Dipole Contact Suppressed byYd

1Λ2

NP

× Q σµνYuY†u Q·(F µν); Q YuY

†u Q·(QQ); d Y †

d YuY†u Q·(QQ)

NOW-2012- 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, G. Isidori, L. Merlo, L. A. Munoz, EN, JHEP 1106, 037 (2011).

SM: ℓi 6Dℓℓi + ei 6Deei︸ ︷︷ ︸U(3)ℓ×U(3)e=GSM

F ×U(1)ℓ×U(1)e

+ 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:

NOW-2012- 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, G. Isidori, L. Merlo, L. A. Munoz, EN, JHEP 1106, 037 (2011).

SM: ℓi 6Dℓℓi + ei 6Deei︸ ︷︷ ︸U(3)ℓ×U(3)e=GSM

F ×U(1)ℓ×U(1)e

+ 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)2ℓ,e×U(3)N=GF×U(1)L×U(1)2e,N

+ ℓi Yije ej H+

Yukawa︷ ︸︸ ︷ℓiY

ijν Nj H︸ ︷︷ ︸

×GF , ×U(1)2e,N

+12 µL

Majorana︷ ︸︸ ︷N c

i YijM Nj︸ ︷︷ ︸

U(1)L��

�PP

P×U(1)2N

Role of U(1)2e,N

see: R. Alonso et al., JHEP 1106 037 (2011); D. Aristizabal et al., JHEP 1207 135 (2012).

NOW-2012- 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, G. Isidori, L. Merlo, L. A. Munoz, EN, JHEP 1106, 037 (2011).

SM: ℓi 6Dℓℓi + ei 6Deei︸ ︷︷ ︸U(3)ℓ×U(3)e=GSM

F ×U(1)ℓ×U(1)e

+ 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)2ℓ,e×U(3)N=GF×U(1)L×U(1)2e,N

+ ℓi Yije ej H+

Yukawa︷ ︸︸ ︷ℓiY

ijν Nj H︸ ︷︷ ︸

×GF , ×U(1)2e,N

+12 µL

Majorana︷ ︸︸ ︷N c

i YijM Nj︸ ︷︷ ︸

U(1)L��

�PP

P×U(1)2N

Role of U(1)2e,N

see: R. Alonso et al., JHEP 1106 037 (2011); D. Aristizabal et al., JHEP 1207 135 (2012).

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∆, . . .NOW-2012- 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

NOW-2012- 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)]

NOW-2012- 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)

NOW-2012- 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

)

NOW-2012- 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)

NOW-2012- 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

NOW-2012- 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)NOW-2012- 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

NOW-2012- 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

NOW-2012- 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)

NOW-2012- 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.

NOW-2012- 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.

NOW-2012- 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 it canwell be non-MFV in the IR (C.C.B.) .

NOW-2012- 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 it canwell be non-MFV in the IR (C.C.B.) .

• UV-MFV =⇒ IR-MFV only if after sending spurions → 0 the onlyfields that become massless are the SM fields.

NOW-2012- 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 it canwell be non-MFV in the IR (C.C.B.) .

• UV-MFV =⇒ IR-MFV only if after sending spurions → 0 the onlyfields that become massless are the SM fields.

• Even with MFV, exp. constraints on FCNC imply ΛNP > (≫)10 TeV.(Is the original motivation for MFV matched ? Flavor is a real puzzle !)

NOW-2012- 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 it canwell be non-MFV in the IR (C.C.B.) .

• UV-MFV =⇒ IR-MFV only if after sending spurions → 0 the onlyfields that become massless are the SM fields.

• Even with MFV, exp. constraints on FCNC imply ΛNP > (≫)10 TeV.(Is the original motivation for MFV matched ? Flavor is a real puzzle !)

• As a general remark, the LFV processes ℓ → ℓ′γ, µ-e conversion,ℓ → 3ℓ′, are sensitive to different NP operators. They are allimportant since can provide complementary informations.

NOW-2012- MLFV extensions of the seesaw – p. 11