Flavour scenarios from 5D SO(10): order and anarchy interplay - - PowerPoint PPT Presentation

Denise Vicino, University of Padova

Based on:

arXiv: 1507.00669

and JHEP 1409(2014)095 - arXiv: 1407.2913

21-25 Jul 2015

Flavour scenarios from 5D SO(10):

• rder and anarchy interplay

in collaboration with:

• F. Feruglio and K. Patel

Nu@Fermilab 2015

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Unification of Forces:

Gravity Weak EM Strong

1016 1018 100

Energy (GeV) GUT?

TOE?

E l e c t r

• w

e a k

SM BSM

SUSY?

Grand Unification

String theory? SU(3)C×SU(2)L×U(1)Y

Grand Unification and the Flavour puzzle

2

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Unification of Forces:

Gravity Weak EM Strong

1016 1018 100

Energy (GeV) GUT?

TOE?

E l e c t r

• w

e a k

SM BSM

SUSY?

Grand Unification

String theory? SU(3)C×SU(2)L×U(1)Y SU(5) ?

Grand Unification and the Flavour puzzle

2

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Unification of Forces:

Gravity Weak EM Strong

1016 1018 100

Energy (GeV) GUT?

TOE?

E l e c t r

• w

e a k

SM BSM

SUSY?

Grand Unification

String theory? SU(3)C×SU(2)L×U(1)Y SU(5) ?

Grand Unification and the Flavour puzzle

2

⊂ SO(10)?

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Unification of Forces:

Gravity Weak EM Strong

1016 1018 100

Energy (GeV) GUT?

TOE?

E l e c t r

• w

e a k

SM BSM

SUSY?

Grand Unification

String theory? SU(3)C×SU(2)L×U(1)Y SU(5) ?

}

• Explain the origin of SM gauge

structure: but which symmetry breaking down to the SM?

• Unified description of SM fermions:

a single SO(10) representation: SM fermions + RH neutrinos

16i=1,2,3

Grand Unification and the Flavour puzzle

2

⊂ SO(10)?

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Grand Unification and the Flavour puzzle

Why this peculiar structure of the Yukawa couplings?

3

SO(10) GUT: which advantages? Masses

∆S ∆A ≈ λ2

• Charged Fermions
• Neutrinos

mu : mc : mt ≈ λ8 : λ4 : 1 md : ms : mb ≈ λ5 : λ3 : 1 me : mµ : mτ ≈ λ6 : λ2 : 1

mν ≤ O(eV)

∆S ≡ ∆A ≡ m2

ν2 − m2 ν1

• m2

ν3 − m2 ν2

• Mixing
• Quark sector
• Lepton sector

|VCKM| ≈   1 λ λ3 λ 1 λ2 λ3 λ2 1  

|UPMNS| ≈   0.8 0.5 0.2 0.5 0.6 0.6 0.3 0.6 0.7  

• RH neutrinos, natural implementation of (type I)
• Embedding SU(5) SO(10): explain similar hierarchy in down quarks

⊂

and charged leptons

[Minkowski (1977), Yanagida (1979), Gell-Mann,Ramond, Slansky (1979), Mohapatra and Senjanovic (1980)] [Georgi-Glashow (1974)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Grand Unification and the Flavour puzzle

Why this peculiar structure of the Yukawa couplings?

3

SO(10) GUT: which advantages? Masses

∆S ∆A ≈ λ2

• Charged Fermions
• Neutrinos

mu : mc : mt ≈ λ8 : λ4 : 1 md : ms : mb ≈ λ5 : λ3 : 1 me : mµ : mτ ≈ λ6 : λ2 : 1

mν ≤ O(eV)

∆S ≡ ∆A ≡ m2

ν2 − m2 ν1

• m2

ν3 − m2 ν2

• Mixing
• Quark sector
• Lepton sector

|VCKM| ≈   1 λ λ3 λ 1 λ2 λ3 λ2 1  

|UPMNS| ≈   0.8 0.5 0.2 0.5 0.6 0.6 0.3 0.6 0.7  

• RH neutrinos, natural implementation of (type I) See-Saw mechanism
• RH neutrinos, natural implementation of (type I)
• Embedding SU(5) SO(10): explain similar hierarchy in down quarks

⊂

and charged leptons

[Minkowski (1977), Yanagida (1979), Gell-Mann,Ramond, Slansky (1979), Mohapatra and Senjanovic (1980)] [Georgi-Glashow (1974)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Grand Unification and the Flavour puzzle

Why this peculiar structure of the Yukawa couplings?

3

SO(10) GUT: which advantages? Masses

∆S ∆A ≈ λ2

• Charged Fermions
• Neutrinos

mu : mc : mt ≈ λ8 : λ4 : 1 md : ms : mb ≈ λ5 : λ3 : 1 me : mµ : mτ ≈ λ6 : λ2 : 1

mν ≤ O(eV)

∆S ≡ ∆A ≡ m2

ν2 − m2 ν1

• m2

ν3 − m2 ν2

• Mixing
• Quark sector
• Lepton sector

|VCKM| ≈   1 λ λ3 λ 1 λ2 λ3 λ2 1  

|UPMNS| ≈   0.8 0.5 0.2 0.5 0.6 0.6 0.3 0.6 0.7  

• RH neutrinos, natural implementation of (type I) See-Saw mechanism
• Embedding SU(5) SO(10): explain similar hierarchy in down quarks

⊂

and charged leptons

• RH neutrinos, natural implementation of (type I)
• Embedding SU(5) SO(10): explain similar hierarchy in down quarks

⊂

and charged leptons

[Minkowski (1977), Yanagida (1979), Gell-Mann,Ramond, Slansky (1979), Mohapatra and Senjanovic (1980)] [Georgi-Glashow (1974)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Grand Unification and the Flavour puzzle

4

• No minimal coupling

quarks and leptons);

• Large representations;
• Lots of parameters,

16 × 16 = 10 + 120 + 126

Yij

1016i16j10H + 3 possible Higgs representations

+...

SO(10) GUT: which disadvantages?

Structure of the Yukawa couplings:

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Grand Unification and the Flavour puzzle

4

• No minimal coupling

quarks and leptons);

• Large representations;
• Lots of parameters,

16 × 16 = 10 + 120 + 126

Yij

1016i16j10H + 3 possible Higgs representations

+...

SO(10) GUT: which disadvantages?

Structure of the Yukawa couplings:

• No minimal coupling is possible (more then one Higgs, necessary to distinguish

quarks and leptons);

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Grand Unification and the Flavour puzzle

4

• No minimal coupling

quarks and leptons);

• Large representations;
• Lots of parameters,

16 × 16 = 10 + 120 + 126

Yij

1016i16j10H + 3 possible Higgs representations

+...

SO(10) GUT: which disadvantages?

Structure of the Yukawa couplings:

• No minimal coupling is possible (more then one Higgs, necessary to distinguish

quarks and leptons);

• Large representations; Doublet-Triplet splitting problem;

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Grand Unification and the Flavour puzzle

4

• No minimal coupling

quarks and leptons);

• Large representations;
• Lots of parameters,

16 × 16 = 10 + 120 + 126

Yij

1016i16j10H + 3 possible Higgs representations

+...

SO(10) GUT: which disadvantages?

Structure of the Yukawa couplings:

• No minimal coupling is possible (more then one Higgs, necessary to distinguish

quarks and leptons);

• Large representations; Doublet-Triplet splitting problem;
• Lots of parameters, hierarchical and fine-tuned (as much as in the SM)

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Grand Unification and the Flavour puzzle

4

• No minimal coupling

quarks and leptons);

• Large representations;
• Lots of parameters,

16 × 16 = 10 + 120 + 126

Yij

1016i16j10H + 3 possible Higgs representations

+...

SO(10) GUT: which disadvantages?

Structure of the Yukawa couplings:

• No minimal coupling is possible (more then one Higgs, necessary to distinguish

quarks and leptons);

• Large representations; Doublet-Triplet splitting problem;
• Lots of parameters, hierarchical and fine-tuned (as much as in the SM)

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

Grand Unification and the Flavour puzzle

4

• No minimal coupling

quarks and leptons);

• Large representations;
• Lots of parameters,

16 × 16 = 10 + 120 + 126

Yij

1016i16j10H + 3 possible Higgs representations

+...

SO(10) GUT: which disadvantages?

Structure of the Yukawa couplings:

Are ANARCHICAL O(1) Yukawas allowed? Can any mechanism ORDER the parameters and create the hierarchies? Is this compatible with unified description of fermions in SO(10)?

• No minimal coupling is possible (more then one Higgs, necessary to distinguish

quarks and leptons);

• Large representations; Doublet-Triplet splitting problem;
• Lots of parameters, hierarchical and fine-tuned (as much as in the SM)

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5

Anarchy and order interplay: the basic idea

Yu = FQ Yu Fuc Yd = FQ Yd Fdc

FQ1 ⌧ FQ2 ⌧ FQ3

Fd1 . Fd2 . Fd3

Fu1 < Fu2 < Fu3

}

Ye = FL Ye Fec

FL1 ≈ FL2 ≈ FL3 Fe1 ⌧ Fe2 ⌧ Fe3

}

Anarchical

O(1)

Hierarchical

[Kawamura, (2001

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5

Anarchy and order interplay: the basic idea

Yu = FQ Yu Fuc Yd = FQ Yd Fdc

FQ1 ⌧ FQ2 ⌧ FQ3

Fd1 . Fd2 . Fd3

Fu1 < Fu2 < Fu3

}

Ye = FL Ye Fec

FL1 ≈ FL2 ≈ FL3 Fe1 ⌧ Fe2 ⌧ Fe3

}

Anarchical

O(1)

Hierarchical Which mechanism can generate these hierarchies ? “Ordering”

[Kawamura, (2001

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5

Anarchy and order interplay: the basic idea

Yu = FQ Yu Fuc Yd = FQ Yd Fdc

FQ1 ⌧ FQ2 ⌧ FQ3

Fd1 . Fd2 . Fd3

Fu1 < Fu2 < Fu3

}

Ye = FL Ye Fec

FL1 ≈ FL2 ≈ FL3 Fe1 ⌧ Fe2 ⌧ Fe3

}

Anarchical

O(1)

Hierarchical Froggatt-Nielsen charges:

Gf = U(1)F N

Which mechanism can generate these hierarchies ? “Ordering”

[Kawamura, (2001

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5

Anarchy and order interplay: the basic idea

Yu = FQ Yu Fuc Yd = FQ Yd Fdc

FQ1 ⌧ FQ2 ⌧ FQ3

Fd1 . Fd2 . Fd3

Fu1 < Fu2 < Fu3

}

Ye = FL Ye Fec

FL1 ≈ FL2 ≈ FL3 Fe1 ⌧ Fe2 ⌧ Fe3

}

Anarchical

O(1)

Hierarchical Froggatt-Nielsen charges:

Gf = U(1)F N

Which mechanism can generate these hierarchies ? “Ordering”

y

L

Higgs Top Up

Extra dimension (ED): different localisation

• f fermions

[Kawamura, (2001

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5

Anarchy and order interplay: the basic idea

Yu = FQ Yu Fuc Yd = FQ Yd Fdc

FQ1 ⌧ FQ2 ⌧ FQ3

Fd1 . Fd2 . Fd3

Fu1 < Fu2 < Fu3

}

Ye = FL Ye Fec

FL1 ≈ FL2 ≈ FL3 Fe1 ⌧ Fe2 ⌧ Fe3

}

Anarchical

O(1)

Hierarchical Froggatt-Nielsen charges:

Gf = U(1)F N

More predictive model

[Kitano, Li (2004)] [Feruglio, Patel, DV (2014)]

New mechanisms of symmetry breaking Solution to Doublet-Triplet splitting problem

Combined with SO(10), N=1 SUSY

Which mechanism can generate these hierarchies ? “Ordering”

y

L

Higgs Top Up

Extra dimension (ED): different localisation

• f fermions

[Kawamura, (2001

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5

Anarchy and order interplay: the basic idea

Yu = FQ Yu Fuc Yd = FQ Yd Fdc

FQ1 ⌧ FQ2 ⌧ FQ3

Fd1 . Fd2 . Fd3

Fu1 < Fu2 < Fu3

}

Ye = FL Ye Fec

FL1 ≈ FL2 ≈ FL3 Fe1 ⌧ Fe2 ⌧ Fe3

}

Anarchical

O(1)

Hierarchical Froggatt-Nielsen charges:

Gf = U(1)F N

More predictive model

[Kitano, Li (2004)] [Feruglio, Patel, DV (2014)]

New mechanisms of symmetry breaking Solution to Doublet-Triplet splitting problem

Combined with SO(10), N=1 SUSY

Which mechanism can generate these hierarchies ? “Ordering” New mechanisms of symmetry breaking

y

L

Higgs Top Up

Extra dimension (ED): different localisation

• f fermions

[Kawamura, (2001

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5

Anarchy and order interplay: the basic idea

Yu = FQ Yu Fuc Yd = FQ Yd Fdc

FQ1 ⌧ FQ2 ⌧ FQ3

Fd1 . Fd2 . Fd3

Fu1 < Fu2 < Fu3

}

Ye = FL Ye Fec

FL1 ≈ FL2 ≈ FL3 Fe1 ⌧ Fe2 ⌧ Fe3

}

Anarchical

O(1)

Hierarchical Froggatt-Nielsen charges:

Gf = U(1)F N

More predictive model

[Kitano, Li (2004)] [Feruglio, Patel, DV (2014)]

New mechanisms of symmetry breaking Solution to Doublet-Triplet splitting problem

Combined with SO(10), N=1 SUSY

Which mechanism can generate these hierarchies ? “Ordering” New mechanisms of symmetry breaking

y

L

Higgs Top Up

Extra dimension (ED): different localisation

• f fermions

[Kawamura, (2001

Solution to Doublet-Triplet splitting problem

[Kawamura, (2001)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5

Anarchy and order interplay: the basic idea

Yu = FQ Yu Fuc Yd = FQ Yd Fdc

FQ1 ⌧ FQ2 ⌧ FQ3

Fd1 . Fd2 . Fd3

Fu1 < Fu2 < Fu3

}

Ye = FL Ye Fec

FL1 ≈ FL2 ≈ FL3 Fe1 ⌧ Fe2 ⌧ Fe3

}

Anarchical

O(1)

Hierarchical Froggatt-Nielsen charges:

Gf = U(1)F N

More predictive model

[Kitano, Li (2004)] [Feruglio, Patel, DV (2014)]

New mechanisms of symmetry breaking Solution to Doublet-Triplet splitting problem

Combined with SO(10), N=1 SUSY

Which mechanism can generate these hierarchies ? “Ordering” New mechanisms of symmetry breaking More predictive model

[Kitano, Li (2004)] [Feruglio, Patel, DV (2014)]

y

L

Higgs Top Up

Extra dimension (ED): different localisation

• f fermions

[Kawamura, (2001

Solution to Doublet-Triplet splitting problem

[Kawamura, (2001)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 6

A 5D SO(10) SUSY model: compactification

• Extra dimension compactified on Orbifold:

& MGUT

1 R

T ≈ 1016 GeV

πR

S1/(Z2 × Z0

2)

πR/2

πR

Z2 : y ↔ −y

Z0

2 : y0 ↔ −y0

y0 ≡ y − πR/2

y

πR 2

All the fields in ED are defined in the fundamental interval:

• Kaluza-Klein expansion: for each field propagating in the ED

H(xµ, y) = X

n

Hn(xµ)fn(y) =

Profile in the extra dimension n=0 mode describes the

massless particle (MSSM field)

with assigned parities ( P , P’ ) under Z2 × Z0

2

with flat metric

[Pati Salam (1974), Kawamura, (2001)] [Pomarol, Quiros (1998), Arkani-Hamed et al. (2002)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 6

A 5D SO(10) SUSY model: compactification

• Extra dimension compactified on Orbifold:

& MGUT

1 R

T ≈ 1016 GeV

πR

S1/(Z2 × Z0

2)

πR/2

πR

Z2 : y ↔ −y

Z0

2 : y0 ↔ −y0

y0 ≡ y − πR/2

y

πR 2

All the fields in ED are defined in the fundamental interval:

• Kaluza-Klein expansion: for each field propagating in the ED

H(xµ, y) = X

n

Hn(xµ)fn(y) =

Profile in the extra dimension n=0 mode describes the

massless particle (MSSM field)

with assigned parities ( P , P’ ) under Z2 × Z0

2

Vanishing of some profiles: in the bulk or in one of the two branes with flat metric

[Pati Salam (1974), Kawamura, (2001)] [Pomarol, Quiros (1998), Arkani-Hamed et al. (2002)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 6

A 5D SO(10) SUSY model: compactification

• Extra dimension compactified on Orbifold:

& MGUT

1 R

T ≈ 1016 GeV

πR

S1/(Z2 × Z0

2)

πR/2

πR

Z2 : y ↔ −y

Z0

2 : y0 ↔ −y0

y0 ≡ y − πR/2

y

πR 2

All the fields in ED are defined in the fundamental interval:

• Kaluza-Klein expansion: for each field propagating in the ED

H(xµ, y) = X

n

Hn(xµ)fn(y) =

Profile in the extra dimension n=0 mode describes the

massless particle (MSSM field)

with assigned parities ( P , P’ ) under Z2 × Z0

2

SYMMETRY BREAKING ! Vanishing of some profiles: in the bulk or in one of the two branes with flat metric

[Pati Salam (1974), Kawamura, (2001)] [Pomarol, Quiros (1998), Arkani-Hamed et al. (2002)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 6

A 5D SO(10) SUSY model: compactification

• Extra dimension compactified on Orbifold:

& MGUT

1 R

T ≈ 1016 GeV

πR

S1/(Z2 × Z0

2)

πR/2

πR

Z2 : y ↔ −y

Z0

2 : y0 ↔ −y0

y0 ≡ y − πR/2

y

πR 2

All the fields in ED are defined in the fundamental interval:

• Kaluza-Klein expansion: for each field propagating in the ED

H(xµ, y) = X

n

Hn(xµ)fn(y) =

Profile in the extra dimension n=0 mode describes the

massless particle (MSSM field)

with assigned parities ( P , P’ ) under Z2 × Z0

2

SYMMETRY BREAKING ! Vanishing of some profiles: in the bulk or in one of the two branes Breaks 5D N=1 SUSY (4D N=2 SUSY) 4D N=1 SUSY with flat metric

[Pati Salam (1974), Kawamura, (2001)] [Pomarol, Quiros (1998), Arkani-Hamed et al. (2002)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 6

A 5D SO(10) SUSY model: compactification

• Extra dimension compactified on Orbifold:

& MGUT

1 R

T ≈ 1016 GeV

πR

S1/(Z2 × Z0

2)

πR/2

πR

Z2 : y ↔ −y

Z0

2 : y0 ↔ −y0

y0 ≡ y − πR/2

y

πR 2

All the fields in ED are defined in the fundamental interval:

• Kaluza-Klein expansion: for each field propagating in the ED

H(xµ, y) = X

n

Hn(xµ)fn(y) =

Profile in the extra dimension n=0 mode describes the

massless particle (MSSM field)

with assigned parities ( P , P’ ) under Z2 × Z0

2

SYMMETRY BREAKING ! Vanishing of some profiles: in the bulk or in one of the two branes Breaks 5D N=1 SUSY (4D N=2 SUSY) 4D N=1 SUSY Breaks SO(10) Pati Salam group:

SU(4)×SU(2)L×SU(2)R

with flat metric

[Pati Salam (1974), Kawamura, (2001)] [Pomarol, Quiros (1998), Arkani-Hamed et al. (2002)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

The model: symmetries

7

N=2 SUSY N=1 SUSY N=1 SUSY

y

πR 2

SO(10) bulk SO(10) brane PS brane

SU(4)×SU(2)L×SU(2)R

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

The model: symmetries

7

N=2 SUSY N=1 SUSY N=1 SUSY

y

πR 2

SO(10) bulk SO(10) brane PS brane

SU(4)×SU(2)L×SU(2)R

45V 45V

(15, 1, 1)

(1, 3, 1)

(1, 1, 3)

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

The model: symmetries

7

N=2 SUSY N=1 SUSY N=1 SUSY

y

πR 2

SO(10) bulk SO(10) brane PS brane

SU(4)×SU(2)L×SU(2)R

45V 45V

(15, 1, 1)

(1, 3, 1)

(1, 1, 3)

16i (4, 2, 1)i →

SM weak doublets: Q, L

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

The model: symmetries

7

N=2 SUSY N=1 SUSY N=1 SUSY

y

πR 2

SO(10) bulk SO(10) brane PS brane

SU(4)×SU(2)L×SU(2)R

45V 45V

(15, 1, 1)

(1, 3, 1)

(1, 1, 3)

16i (4, 2, 1)i →

SM weak doublets: Q, L

(¯ 4, 1, 2)i → 160

i

SM weak singlets + RH neutrinos:

uc

L, dc L, ec L, νc L

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 8

The model: fermions profiles

• Superpotential in the bulk:
• 0-mode profiles:

exponentials modulated by bulk mass parameters:

• bulk masses can be corrected by VEV

+

160c

i

h ˆ m0

i + ∂y −

√ 2g5 45Φ i 160

i

Wbulk = 16c

i

h ˆ mi + ∂y − √ 2g5 45Φ i 16i

f160i(y, m0

i)

h45Φi

f16i(mi, y) = r 2mi 1 − e−miπR e−miy ;

y

m>0 m<0

πR 2

Higgs

• distinguish between doublets and singlets

still leptons + quark unified

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 8

The model: fermions profiles

• Superpotential in the bulk:
• 0-mode profiles:

exponentials modulated by bulk mass parameters:

• bulk masses can be corrected by VEV

+

160c

i

h ˆ m0

i + ∂y −

√ 2g5 45Φ i 160

i

Wbulk = 16c

i

h ˆ mi + ∂y − √ 2g5 45Φ i 16i

f160i(y, m0

i)

bulk masses

h45Φi

f16i(mi, y) = r 2mi 1 − e−miπR e−miy ;

y

m>0 m<0

πR 2

Higgs

• distinguish between doublets and singlets

still leptons + quark unified

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 8

The model: fermions profiles

• Superpotential in the bulk:
• 0-mode profiles:

exponentials modulated by bulk mass parameters:

• bulk masses can be corrected by VEV

+

160c

i

h ˆ m0

i + ∂y −

√ 2g5 45Φ i 160

i

Wbulk = 16c

i

h ˆ mi + ∂y − √ 2g5 45Φ i 16i

f160i(y, m0

i)

bulk masses

h45Φi

f16i(mi, y) = r 2mi 1 − e−miπR e−miy ;

y

m>0 m<0

πR 2

Higgs

• distinguish between doublets and singlets

still leptons + quark unified from gauge interaction in 5D

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 8

The model: fermions profiles

• Superpotential in the bulk:
• 0-mode profiles:

exponentials modulated by bulk mass parameters:

• bulk masses can be corrected by VEV

+

160c

i

h ˆ m0

i + ∂y −

√ 2g5 45Φ i 160

i

Wbulk = 16c

i

h ˆ mi + ∂y − √ 2g5 45Φ i 16i

f160i(y, m0

i)

bulk masses

h45Φi

f16i(mi, y) = r 2mi 1 − e−miπR e−miy ;

y

m>0 m<0

πR 2

Higgs

Q, L

• distinguish between doublets and singlets

still leptons + quark unified from gauge interaction in 5D

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 8

The model: fermions profiles

• Superpotential in the bulk:
• 0-mode profiles:

exponentials modulated by bulk mass parameters:

• bulk masses can be corrected by VEV

+

160c

i

h ˆ m0

i + ∂y −

√ 2g5 45Φ i 160

i

Wbulk = 16c

i

h ˆ mi + ∂y − √ 2g5 45Φ i 16i

f160i(y, m0

i)

bulk masses

h45Φi

f16i(mi, y) = r 2mi 1 − e−miπR e−miy ;

y

m>0 m<0

πR 2

Higgs

Q, L uc

L, dc L, ec L, νc L

• distinguish between doublets and singlets

still leptons + quark unified from gauge interaction in 5D

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 8

The model: fermions profiles

• Superpotential in the bulk:
• 0-mode profiles:

exponentials modulated by bulk mass parameters:

• bulk masses can be corrected by VEV

+

160c

i

h ˆ m0

i + ∂y −

√ 2g5 45Φ i 160

i

Wbulk = 16c

i

h ˆ mi + ∂y − √ 2g5 45Φ i 16i

f160i(y, m0

i)

bulk masses

h45Φi

f16i(mi, y) = r 2mi 1 − e−miπR e−miy ;

y

m>0 m<0

πR 2

Higgs

Q, L uc

L, dc L, ec L, νc L

• distinguish between doublets and singlets

still leptons + quark unified

• distinguish between doublets and singlets

still leptons + quark unified from gauge interaction in 5D

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 8

The model: fermions profiles

• Superpotential in the bulk:
• 0-mode profiles:

exponentials modulated by bulk mass parameters:

• bulk masses can be corrected by VEV

+

160c

i

h ˆ m0

i + ∂y −

√ 2g5 45Φ i 160

i

Wbulk = 16c

i

h ˆ mi + ∂y − √ 2g5 45Φ i 16i

f160i(y, m0

i)

bulk masses

h45Φi

f16i(mi, y) = r 2mi 1 − e−miπR e−miy ;

y

m>0 m<0

πR 2

Higgs

Q, L uc

L, dc L, ec L, νc L

• distinguish between doublets and singlets

still leptons + quark unified

• distinguish between doublets and singlets

still leptons + quark unified from gauge interaction in 5D

• bulk masses can be corrected by VEV h45Φi

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 9

16 = 10−1 + ¯ 53 + 1−5

(Q, uc, ec) (dc, L) (N c)

• in the bulk:

SO(10) − → SU(5) × U(1)X

h45Φi

f16 − → {f10, f¯

5, f1}

The model: quarks-leptons splitting

• Splitting from spontaneous symmetry breaking:

mr

i = mi

p 2g5 Qr

X h45Φi

• bulk mass correction × U(1)X charges:

∝

= mi − →

• decomposition under

SU(5) × U(1)X :

• the same is happening for m0

i

flavour universal due to gauge interaction (SUSY constraint)

[Kitano, Li (2004)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 10

The model: fermions profiles splitting

• Combining SO(10) −

→ PS with SO(10) −

→ SU(5) × U(1)X

h45Φi

Z0

2

:

; aL

i = mi 3

p 2g5h45Φi ; adc

i = m0 i 3

p 2g5h45Φi ; aN c

i = m0 i + 5

p 2g5h45Φi

Q10

X = −1

Q

¯ 5 X = 3

Q1

X = −5

aQ

i = mi +

p 2g5h45Φi ; auc

i = m0 i +

p 2g5h45Φi ; aec

i = m0 i +

p 2g5h45Φi ;

• Globally 3+3+1=7 parameters create 15 different profiles

y

xµ

f16i

fQi fLi

πR 2

f16i

fQi fLi

πR 2

f160i

fuci fdci

y

xµ

πR 2

fN ci

≡ feci

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

+ δ(y)

wπ(H, H0, Σ, Σ, T)

w0(16H, 16H)

+ δ ✓ y − πR 2 ◆

. . .

11

The Higgs sector on the brane

• Yukawa couplings on the PS brane:
• For the Higgs we can select only doublets: no DT splitting problem

H, H0∼ (1, 2, 2)

• lower dimensional representations with respect to SO(10) brane:

less number of 4D fields

1 Λ  Yij16i160

jH + Y 0 ij16i160 jH0 + 1

2Y R

ij 160 i160 j

ΣΣ Λ + ...

• Wbrane = δ

✓ y − πR 2 ◆

• Majorana mass term: Σ, Σ ∼

∼ (4, 1, 2), 2), (4, 1, 2) 2), + . . .

• Superpotential on the branes:

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

+ δ(y)

wπ(H, H0, Σ, Σ, T)

w0(16H, 16H)

+ δ ✓ y − πR 2 ◆

. . .

11

The Higgs sector on the brane

• Yukawa couplings on the PS brane:
• For the Higgs we can select only doublets: no DT splitting problem

H, H0∼ (1, 2, 2)

• lower dimensional representations with respect to SO(10) brane:

less number of 4D fields

1 Λ  Yij16i160

jH + Y 0 ij16i160 jH0 + 1

2Y R

ij 160 i160 j

ΣΣ Λ + ...

• Wbrane = δ

✓ y − πR 2 ◆

• Majorana mass term: Σ, Σ ∼

∼ (4, 1, 2), 2), (4, 1, 2) 2), + . . .

• Superpotential on the branes:

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

+ δ(y)

wπ(H, H0, Σ, Σ, T)

w0(16H, 16H)

+ δ ✓ y − πR 2 ◆

. . .

11

The Higgs sector on the brane

• Yukawa couplings on the PS brane:
• For the Higgs we can select only doublets: no DT splitting problem

H, H0∼ (1, 2, 2)

• lower dimensional representations with respect to SO(10) brane:

less number of 4D fields

1 Λ  Yij16i160

jH + Y 0 ij16i160 jH0 + 1

2Y R

ij 160 i160 j

ΣΣ Λ + ...

• Wbrane = δ

✓ y − πR 2 ◆

• Majorana mass term: Σ, Σ ∼

∼ (4, 1, 2), 2), (4, 1, 2) 2), + . . .

• Superpotential on the branes:

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

+ δ(y)

wπ(H, H0, Σ, Σ, T)

w0(16H, 16H)

+ δ ✓ y − πR 2 ◆

. . .

11

The Higgs sector on the brane

• Yukawa couplings on the PS brane:
• For the Higgs we can select only doublets: no DT splitting problem

H, H0∼ (1, 2, 2)

• lower dimensional representations with respect to SO(10) brane:

less number of 4D fields

1 Λ  Yij16i160

jH + Y 0 ij16i160 jH0 + 1

2Y R

ij 160 i160 j

ΣΣ Λ + ...

• Wbrane = δ

✓ y − πR 2 ◆

• Majorana mass term: Σ, Σ ∼

∼ (4, 1, 2), 2), (4, 1, 2) 2), + . . .

• Superpotential on the branes:

T ∼ (1, 1, 3)

Needed to generate non trivial CKM mixing

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay

+ δ(y)

wπ(H, H0, Σ, Σ, T)

w0(16H, 16H)

+ δ ✓ y − πR 2 ◆

. . .

11

The Higgs sector on the brane

• Yukawa couplings on the PS brane:
• For the Higgs we can select only doublets: no DT splitting problem

H, H0∼ (1, 2, 2)

• lower dimensional representations with respect to SO(10) brane:

less number of 4D fields

1 Λ  Yij16i160

jH + Y 0 ij16i160 jH0 + 1

2Y R

ij 160 i160 j

ΣΣ Λ + ...

• Wbrane = δ

✓ y − πR 2 ◆

• Majorana mass term: Σ, Σ ∼

∼ (4, 1, 2), 2), (4, 1, 2) 2), + . . .

• Superpotential on the branes:

T ∼ (1, 1, 3)

Needed to generate non trivial CKM mixing Needed to preserve SUSY on the branes

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 12

Effective Yukawas

• Effective Yukawa couplings

Profiles

µ1, µ2, µ3, kX

Higgs Mixing Yukawas

0.5 ≤ |Yij| ≤ 1.5

• Parameters counting:

+ +

7 free bulk mass parameters

O(1)

fitting 17

• bservables

(masses and mixing angles of quarks and leptons)

Yu = FQ Yu Fuc Yd = FQ Yd Fdc Ye = FL Yd Fec Yν = FL Yu FN c

Fr ≡   fr1( πR

2 )

fr2( πR

2 )

fr3( πR

2 )

 

MR ⌘ hΣi2 Λ FN cYRFN c Mν ⌘ Λv2 sin2 β hΣi2 FL (YuY −1

R Y T u ) FL

µ0

1, µ0 2, µ0 3

θu, θd Y, Y 0, YR

2 free angles 44 parameters constrained ≈

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 13

Numerical fit

[tanβ=50]

• Agreement is not so trivial: only large tanβ allowed

(unification of the third generation)

Normal ordering Inverted ordering Observable Fitted value Pull Fitted value Pull yt 0.51 0.52 0.33 yb 0.37 0.38 0.50 yτ 0.51 0.51 mu/mc 0.0027 0.0028 0.17 md/ms 0.051 0.052 0.14 me/mµ 0.0048 0.0048 mc/mt 0.0023 0.0023 ms/mb 0.016 0.017 0.50 mµ/mτ 0.050 0.050 |Vus| 0.227 0.227 |Vcb| 0.037 0.037 |Vub| 0.0033 0.0030

• 0.50

JCP 0.000023 0.000023 ∆S/∆A 0.0305 0.0305 sin2 θ12 0.304 0.304 sin2 θ23 0.452 0.442

• 0.20

sin2 θ13 0.0218 0.0218

• 0.10

χ2

min

⇡ 0 ⇡ 0.96

from global

χ2

minimization (including Yukawas)

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 14

Random O(1) Yukawas

Naturalness test

|Yij| ∈ [0.5, 1.5] arg(Yij) ∈ [0, 2π]

• Uniform variation of the parameters:
• Fitting 17 observables

with 9 free parameters (8 d.o.f)

NO IO 1 10 100 1000 0.00 0.05 0.10 0.15 0.20

Χ min

2

ê Ν Probability

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 14

Random O(1) Yukawas

Naturalness test

|Yij| ∈ [0.5, 1.5] arg(Yij) ∈ [0, 2π]

• Uniform variation of the parameters:
• Fitting 17 observables

with 9 free parameters (8 d.o.f)

0.5% of successful cases

NO IO 1 10 100 1000 0.00 0.05 0.10 0.15 0.20

Χ min

2

ê Ν Probability

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 14

Random O(1) Yukawas

Naturalness test

|Yij| ∈ [0.5, 1.5] arg(Yij) ∈ [0, 2π]

• Uniform variation of the parameters:
• Fitting 17 observables

with 9 free parameters (8 d.o.f)

0.5% of successful cases

NO IO 1 10 100 1000 0.00 0.05 0.10 0.15 0.20

Χ min

2

ê Ν Probability

• If the Higgs sector was on SO(10) brane…
• Minimal Higgs content:

10H, 120H 126H

l i g h t h e a v y

• 8 Higgs mixing parameters

PS SOH 10L 1 10 100 0.00 0.05 0.10 0.15 0.20

Χ min

2

ê Ν Probability

• Fitting 17 observables

with 15 free parameters (2 d.o.f)

30% of successful cases

[Feruglio, Patel, DV (2014)]

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 15

Predictions for NO [tanβ=50]

• Predictions result quite stable

with respect to the Higgs dynamics on the branes, they depend almost entirely on the mechanism of lepton-quarks distinction.

10 - 4 0.001 0.01 0.1 10 - 4 0.001 0.01 0.1 1

m n lightest @ eVD »m bb» @ eVD

GERDA-I H CurrentL GERDA-II H FutureL PLANCK H CurrentL KATRIN H FutureL

M N1 M N 2 M N 3 2 4 6 8 10 12 14 16 0.0 0.2 0.4 0.6 0.8

Log10H M N i ê GeVL Probability

• Effective Majorana neutrino mass

and lightest neutrino mass:

• RH neutrinos mass spectrum:

very hierarchical

• and Majorana

phases:

no preferred value

δCP

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 16

Conclusions

• O(1) Anarchical Yukawa matrices for both quarks and leptons can be nicely

reconciled with the observed fermion masses and mixing angles in the framework of extra-dimension, where the hierarchies are created by different localisation of the fermions;

• This scenario can be combined with the unification of one fermion

generation implied by the SO(10) GUT, exploiting a dynamical mechanism for splitting the profiles of quarks and leptons.

• Drawbacks: currently no experimental test can confirm the model.
• Different models can be realised, changing the dynamics on the branes, but

the predictions depend almost entirely on the mechanism of lepton-quarks

• distinction. More free parameters on the branes improve the success rate,
• Both NO and IO are allowed, but NO is more natural with respect to the

random variation of Yukawas.

• Tendency to unify the third generations makes the model compatible only

with large tanβ.

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 16

Conclusions

• O(1) Anarchical Yukawa matrices for both quarks and leptons can be nicely

reconciled with the observed fermion masses and mixing angles in the framework of extra-dimension, where the hierarchies are created by different localisation of the fermions;

• This scenario can be combined with the unification of one fermion

generation implied by the SO(10) GUT, exploiting a dynamical mechanism for splitting the profiles of quarks and leptons.

• Drawbacks: currently no experimental test can confirm the model.

Thank you!

• Different models can be realised, changing the dynamics on the branes, but

the predictions depend almost entirely on the mechanism of lepton-quarks

• distinction. More free parameters on the branes improve the success rate,
• Both NO and IO are allowed, but NO is more natural with respect to the

random variation of Yukawas.

• Tendency to unify the third generations makes the model compatible only

with large tanβ.

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 17

Backup slides

S5 = R d5x[ 1

g2

R d4θ ⇣ ∂5V −

1 √ 2(Φ + ¯

Φ) ⌘2 + 1

4g2

R (d2θ W αWα + h.c.) + R d4θ ¯ He2qQV H + ¯ Hce−2gQV Hc

• +

R d2θ Hc

• m + ∂5 −

√ 2gQΦ

• H + h.c.
• The whole action in abelian theory

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 18

Backup slides

Bulk fields content:

G a u g e f i e l d s

Vector multiplet Hypermultiplet Hypermultiplet

Vector multiplet Chiral multiplet Chiral multiplet Chiral multiplet Chiral multiplet Chiral multiplet

Z0

2

Z2

M a t t e r f i e l d s

Imposed

}

PS Adjoint SO(10) Adjoint SM weak singlets + RH neutrinos:

uc

L, dc L, ec L, νc L SM weak doublets:

Q, L

Consequence of invariance

∂}

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 19

Backup slides

Higgs mass splitting and mixing angles

wπ = MH 2 H2 + MH0 2 H02 + mHH0 + λTHH0 + T(λHH2 + λH0H02) + ...

(Hu H0

u) M

✓Hd H0

d

◆ , with M = ✓ MH m λhTi m + λhTi MH0 ◆ .

θu,d = 1 2 tan−1 ✓ 2MH0(m ⌥ λhTi) M 2

H0 (m ⌥ λhTi)2

◆

hu,d = cos θu,dHu,d + sin θu,dH0

u,d

Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 20

Backup slides

• Profiles parameters distributions (NO)