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Quarks and Leptons as Nambu-Goldstone Fermions Under E 7 /SO(10) S. K. Mandal Introduction Motivations Coset Spaces E 7 /SO(10) Model Preliminaries Model Aspects GUT model Low Energy Results Experimental constraints LHC 7 TeV Dark Matter Detection Summary Quarks and Leptons as Nambu-Goldstone Fermions Under E 7 /SO(10) arXiv:1109.xxxx w/ M. Nojiri, T. T. Yanagida Sourav K. Mandal [email protected] SUSY 2011 Conference September 1st, 2011
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Page 1: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Quarks and Leptons as Nambu-GoldstoneFermions Under E7/SO(10)

arXiv:1109.xxxx w/ M. Nojiri, T. T. Yanagida

Sourav K. [email protected]

SUSY 2011 ConferenceSeptember 1st, 2011

Page 2: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Outline

1 IntroductionMotivationsCoset Spaces

2 E7/SO(10) ModelPreliminariesModel AspectsGUT modelLow Energy Results

3 Experimental constraintsLHC 7 TeVDark Matter Detection

4 Summary

Page 3: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Hierarchy of Yukawa couplings?

log10(m/GeV)

e µ τ

d

u

s

c

b

t

−3 0−2 −1 1 2

Ad-hoc ⇒ dynamical?

Page 4: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Hierarchy of Yukawa couplings?

log10(m/GeV)

e µ τ

d

u

s

c

b

t

−3 0−2 −1 1 2

Ad-hoc ⇒ dynamical?

Page 5: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Field content of standard model

Gauged adjoint and light chiral fundamentals

Gauge some group H ⊂ G in real representation

Where do light chiral fields in fundamental of H comefrom?

Hint from pions

Take SU(2)/U(1) toy model

Broken X and Y ⇒ Z = X + iY , Z∗ = X − iYSU(2) ∼ S3 =⇒ S3/U(1) ∼ CP1

Gauge U(1), toy pions in fundamental complexrepresentation

Need fermionic analogue

Page 6: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Field content of standard model

Gauged adjoint and light chiral fundamentals

Gauge some group H ⊂ G in real representation

Where do light chiral fields in fundamental of H comefrom?

Hint from pions

Take SU(2)/U(1) toy model

Broken X and Y ⇒ Z = X + iY , Z∗ = X − iYSU(2) ∼ S3 =⇒ S3/U(1) ∼ CP1

Gauge U(1), toy pions in fundamental complexrepresentation

Need fermionic analogue

Page 7: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Field content of standard model

Gauged adjoint and light chiral fundamentals

Gauge some group H ⊂ G in real representation

Where do light chiral fields in fundamental of H comefrom?

Hint from pions

Take SU(2)/U(1) toy model

Broken X and Y ⇒ Z = X + iY , Z∗ = X − iYSU(2) ∼ S3 =⇒ S3/U(1) ∼ CP1

Gauge U(1), toy pions in fundamental complexrepresentation

Need fermionic analogue

Page 8: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Strategy

Coset spaces

Assuming gravity mediation

MΛ > MP (∼MGUT )MSUSY

Pseudo-Nambu-Goldstone fermions

1st and 2nd generation Standard Model fermions =SUSY partners of NG bosons

Assert 3rd generation as matter fields ∼MSUSY

⇒ Need SUSY nonlinear σ model!

Page 9: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Strategy

Coset spaces

Assuming gravity mediation

MΛ > MP (∼MGUT )MSUSY

Pseudo-Nambu-Goldstone fermions

1st and 2nd generation Standard Model fermions =SUSY partners of NG bosons

Assert 3rd generation as matter fields ∼MSUSY

⇒ Need SUSY nonlinear σ model!

Page 10: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Strategy

Coset spaces

Assuming gravity mediation

MΛ > MP (∼MGUT )MSUSY

Pseudo-Nambu-Goldstone fermions

1st and 2nd generation Standard Model fermions =SUSY partners of NG bosons

Assert 3rd generation as matter fields ∼MSUSY

⇒ Need SUSY nonlinear σ model!

Page 11: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Strategy

Coset spaces

Assuming gravity mediation

MΛ > MP (∼MGUT )MSUSY

Pseudo-Nambu-Goldstone fermions

1st and 2nd generation Standard Model fermions =SUSY partners of NG bosons

Assert 3rd generation as matter fields ∼MSUSY

⇒ Need SUSY nonlinear σ model!

Page 12: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Formulation of SUSY nonlinear σ model

Supergravity action

In supergravity component Lagrangian,

∆LNLNGB = − (∂µπi) gij (∂µπj)

∆LNLNGF = cijkl(ψiγ

µψj) (ψkγµψl

)gij and cijkl exhibit shift symmetry for d.o.f.’s innonlinear realization.

Complex extension of G

Symmetry breaking is no G→ H, but GC → H

If G/H Kahler, then G/H ' GC/H

Otherwise, need extra “quasi-Nambu-Goldstonebosons” to preserve supersymmetry

Page 13: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Formulation of SUSY nonlinear σ model

Supergravity action

In supergravity component Lagrangian,

∆LNLNGB = − (∂µπi) gij (∂µπj)

∆LNLNGF = cijkl(ψiγ

µψj) (ψkγµψl

)gij and cijkl exhibit shift symmetry for d.o.f.’s innonlinear realization.

Complex extension of G

Symmetry breaking is no G→ H, but GC → H

If G/H Kahler, then G/H ' GC/H

Otherwise, need extra “quasi-Nambu-Goldstonebosons” to preserve supersymmetry

Page 14: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Restrictions on G/H

Non-compactness

Shown by Bagger and Witten, Phys. Lett. B 118 103(1982) for CP1.

Gauging on compact coset induces finite D-term,breaking SUSY

No U(1)’s in H

Shown by Kugo and Yanagida, Prog. Theor. Phys 124,555 (2010).

Kahler transformation in flat space

K(Φ,Φ†)→ K(Φ,Φ†) + F (Φ) + F †(Φ†)

Page 15: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Restrictions on G/H

Non-compactness

Shown by Bagger and Witten, Phys. Lett. B 118 103(1982) for CP1.

Gauging on compact coset induces finite D-term,breaking SUSY

No U(1)’s in H

Shown by Kugo and Yanagida, Prog. Theor. Phys 124,555 (2010).

Kahler transformation in flat space

K(Φ,Φ†)→ K(Φ,Φ†) + F (Φ) + F †(Φ†)

Page 16: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Restrictions on G/H (cont’d)

No U(1)’s in H (cont’d)

Under supergravity,

L =[ΣΣ†e−K(Φ,Φ†)

]D

+[Σ3W (Φ)

]F

For finite W , Σ→ ΣeF not sufficient, breakingG-invariance of theory, giving O(m3/2) masses to N-Gfields

F (†) must vanish

If H ⊃ U(1), global G transformation induces localU(1), generating Fayet-Iliopoulos D-term −gtrV .

H 6⊃ U(1), then Lagrangian G-invariant

Summary: G/H Kahler and non-compact, H 6⊃ U(1)

Page 17: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Restrictions on G/H (cont’d)

No U(1)’s in H (cont’d)

Under supergravity,

L =[ΣΣ†e−K(Φ,Φ†)

]D

+[Σ3W (Φ)

]F

For finite W , Σ→ ΣeF not sufficient, breakingG-invariance of theory, giving O(m3/2) masses to N-Gfields

F (†) must vanish

If H ⊃ U(1), global G transformation induces localU(1), generating Fayet-Iliopoulos D-term −gtrV .

H 6⊃ U(1), then Lagrangian G-invariant

Summary: G/H Kahler and non-compact, H 6⊃ U(1)

Page 18: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Choosing G = E7

Formal motivations for E7

Appears in N = 8 supergravity

Nonlinear realization gives the “simplest field theory”[Arkani-Hamed, Cachazo, Kaplan arXiv:0808.1446]

GUT-like representations

SU(5) ⊃ (5 + 5∗)H⊕

10⊕

5∗

SO(10) ⊃ 10H⊕

16→ (5 + 5∗)H⊕

10⊕

5∗⊕

1E7 gives right flavor cosets:

E7/[SU(5)× U(1)3]→ (10⊕

5∗)× 3 + 5H

E7/[SO(10)× U(1)2]→ (10⊕

5∗)× 2 + (5 + 5∗)H

E6 too small, E8 gives mirror families

Page 19: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Choosing G = E7

Formal motivations for E7

Appears in N = 8 supergravity

Nonlinear realization gives the “simplest field theory”[Arkani-Hamed, Cachazo, Kaplan arXiv:0808.1446]

GUT-like representations

SU(5) ⊃ (5 + 5∗)H⊕

10⊕

5∗

SO(10) ⊃ 10H⊕

16→ (5 + 5∗)H⊕

10⊕

5∗⊕

1E7 gives right flavor cosets:

E7/[SU(5)× U(1)3]→ (10⊕

5∗)× 3 + 5H

E7/[SO(10)× U(1)2]→ (10⊕

5∗)× 2 + (5 + 5∗)H

E6 too small, E8 gives mirror families

Page 20: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Choosing G = E7

Formal motivations for E7

Appears in N = 8 supergravity

Nonlinear realization gives the “simplest field theory”[Arkani-Hamed, Cachazo, Kaplan arXiv:0808.1446]

GUT-like representations

SU(5) ⊃ (5 + 5∗)H⊕

10⊕

5∗

SO(10) ⊃ 10H⊕

16→ (5 + 5∗)H⊕

10⊕

5∗⊕

1

E7 gives right flavor cosets:

E7/[SU(5)× U(1)3]→ (10⊕

5∗)× 3 + 5H

E7/[SO(10)× U(1)2]→ (10⊕

5∗)× 2 + (5 + 5∗)H

E6 too small, E8 gives mirror families

Page 21: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Choosing G = E7

Formal motivations for E7

Appears in N = 8 supergravity

Nonlinear realization gives the “simplest field theory”[Arkani-Hamed, Cachazo, Kaplan arXiv:0808.1446]

GUT-like representations

SU(5) ⊃ (5 + 5∗)H⊕

10⊕

5∗

SO(10) ⊃ 10H⊕

16→ (5 + 5∗)H⊕

10⊕

5∗⊕

1E7 gives right flavor cosets:

E7/[SU(5)× U(1)3]→ (10⊕

5∗)× 3 + 5H

E7/[SO(10)× U(1)2]→ (10⊕

5∗)× 2 + (5 + 5∗)H

E6 too small, E8 gives mirror families

Page 22: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Choosing G = E7

Formal motivations for E7

Appears in N = 8 supergravity

Nonlinear realization gives the “simplest field theory”[Arkani-Hamed, Cachazo, Kaplan arXiv:0808.1446]

GUT-like representations

SU(5) ⊃ (5 + 5∗)H⊕

10⊕

5∗

SO(10) ⊃ 10H⊕

16→ (5 + 5∗)H⊕

10⊕

5∗⊕

1E7 gives right flavor cosets:

E7/[SU(5)× U(1)3]→ (10⊕

5∗)× 3 + 5H

E7/[SO(10)× U(1)2]→ (10⊕

5∗)× 2 + (5 + 5∗)H

E6 too small, E8 gives mirror families

Page 23: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Light 5∗, Light 10 (3rd generation)

0 200 400 600 800 1000MHu

[GeV]

0

200

400

600

800

1000

MHd [

GeV

]

ΩDM 3σ-allowed (MHu,MHd

)

Page 24: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Heavy 5∗, Heavy 10

0 200 400 600 800 1000MHu

[GeV]

0

200

400

600

800

1000

MHd [

GeV

]

ΩDM 3σ-allowed (MHu,MHd

)

Page 25: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Heavy 5∗, Heavy 10 (Minput = MP )

0 200 400 600 800 1000MHu

[GeV]

0

200

400

600

800

1000

MHd [

GeV

]

ΩDM 3σ-allowed (MHu,MHd

)

Page 26: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

GUT-less E7/SO(10) model

Global symmetry must be gauged anyway ⇒ gaugeSU(3)C × SU(2)L × U(1)Y ⊂ SO(10)Don’t need universal Ma

Explicitly break U(1)2 for coupling to supergravity,gives two “novinos” N1, N2 ∼MP

Superpotential:

W = WY +WS +WH

where

WY = Yu · 10 · 10 · 5H + Yd · 10 · 5∗ · 5∗HWS = Mν · 1 · 1 +MN ·N ·NWH = µ · 5H · 5H∗

Page 27: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

GUT-less E7/SO(10) model

Global symmetry must be gauged anyway ⇒ gaugeSU(3)C × SU(2)L × U(1)Y ⊂ SO(10)Don’t need universal Ma

Explicitly break U(1)2 for coupling to supergravity,gives two “novinos” N1, N2 ∼MP

Superpotential:

W = WY +WS +WH

where

WY = Yu · 10 · 10 · 5H + Yd · 10 · 5∗ · 5∗HWS = Mν · 1 · 1 +MN ·N ·NWH = µ · 5H · 5H∗

Page 28: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

GUT superpotential

Additions to superpotential

∆W = WΣ +WH′

where

WΣ = MΣTr Σ2 + λTr Σ3

WH′ = λ1 · 5H · Σ · 5∗H

Outstanding issues

Set right boundary conditions for ΩDM

Evade LHC bounds?

Page 29: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

GUT superpotential

Additions to superpotential

∆W = WΣ +WH′

where

WΣ = MΣTr Σ2 + λTr Σ3

WH′ = λ1 · 5H · Σ · 5∗H

Outstanding issues

Set right boundary conditions for ΩDM

Evade LHC bounds?

Page 30: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Making MGUT ≈MP

Σ ∼ 24 ⊃ (8, 1)⊕ (1, 3)⊕ (1, 1)⊕ (3, 2)⊕ (3∗, 2)

Since gauging anyway, gauge un-Higgsed part of 24

R-charge of Tr Σ3 6= 2 =⇒ λ 1 natural =⇒m3,8 MGUT

Choose: ∼ 1012 GeV

109 1011 1013 1015 1017 1019

50

20

30

15

Μ @GeVD

Α-

1

Page 31: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Making MGUT ≈MP

Σ ∼ 24 ⊃ (8, 1)⊕ (1, 3)⊕ (1, 1)⊕ (3, 2)⊕ (3∗, 2)

Since gauging anyway, gauge un-Higgsed part of 24R-charge of Tr Σ3 6= 2 =⇒ λ 1 natural =⇒m3,8 MGUT

Choose: ∼ 1012 GeV

109 1011 1013 1015 1017 1019

50

20

30

15

Μ @GeVD

Α-

1

Page 32: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Making MGUT ≈MP

Σ ∼ 24 ⊃ (8, 1)⊕ (1, 3)⊕ (1, 1)⊕ (3, 2)⊕ (3∗, 2)

Since gauging anyway, gauge un-Higgsed part of 24R-charge of Tr Σ3 6= 2 =⇒ λ 1 natural =⇒m3,8 MGUT

Choose: ∼ 1012 GeV

109 1011 1013 1015 1017 1019

50

20

30

15

Μ @GeVD

Α-

1

Page 33: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Solving the double-triplet splitting problem

Missing partner mechanism

50 of SU(5) contains color (3, 1), not weak (1, 2)Explicit triplet Higgs 5H + 5∗H to 50 + 50∗ coupling

WT = λT · 5H · 〈75〉 · 50 + c.c.

Huge threshold corrections?

Product group unification

SU(5)G → SU(5)G × SU(3)H × U(1)HDiagonal

SU(3)c ⊂ SU(3)G × SU(3)H

U(1)Y ⊂ U(1)G × U(1)H

Page 34: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Solving the double-triplet splitting problem

Missing partner mechanism

50 of SU(5) contains color (3, 1), not weak (1, 2)Explicit triplet Higgs 5H + 5∗H to 50 + 50∗ coupling

WT = λT · 5H · 〈75〉 · 50 + c.c.

Huge threshold corrections?

Product group unification

SU(5)G → SU(5)G × SU(3)H × U(1)HDiagonal

SU(3)c ⊂ SU(3)G × SU(3)H

U(1)Y ⊂ U(1)G × U(1)H

Page 35: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Product group unification (1/2)

Breaking

Q(m+ λΣ)Q+12mΣTr(Σ2) + hHQq + c.c.

whereQ ∼ (5∗, 3, 1) , q ∼ (1, 3, 1)

and〈Q〉 ∼ vI3 , 〈Σ〉 ∼ diag(3, 3,−2,−2,−2)

Gaugino mass splitting

Modified soft breaking

∆LSSB = − 12MGλGλG −

12MH3λH3λH3

− 12MH1λH1λH1 + c.c.

Page 36: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Product group unification (1/2)

Breaking

Q(m+ λΣ)Q+12mΣTr(Σ2) + hHQq + c.c.

whereQ ∼ (5∗, 3, 1) , q ∼ (1, 3, 1)

and〈Q〉 ∼ vI3 , 〈Σ〉 ∼ diag(3, 3,−2,−2,−2)

Gaugino mass splitting

Modified soft breaking

∆LSSB = − 12MGλGλG −

12MH3λH3λH3

− 12MH1λH1λH1 + c.c.

Page 37: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Product gauge unification (2/2)

Gaugino mass splitting

Re-weighted SM gaugino soft masses:

M3 =⇒ g23

(MH3

g2H3

+MG

g2G

)

M1 =⇒ g21

(MH1

15g2H1

+MG

g2G

)Changes in low-energy phenomenology:

M3 = M1/2 =⇒M3 ∼ 2×M1/2

M1 ∼M1/2

Page 38: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

MSSM analysis

Soft masses

m3/2 = m0(3) = 1 TeV

m0(1,2) = 0A0 = 0, mHu = mHd

= 0Minput = MP

Uncertainties in tan β

With finite µ term, b commonly of the same order(connected through hidden sector)

Spectrum unaffected, except for small shift in t, bmasses

Direct detection cross section varies from 4× 10−47 cm2

(tanβ = 10) to 4× 10−46 cm2 (tanβ = 50) due to Hd

contribution to χ01.

Page 39: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

MSSM analysis

Soft masses

m3/2 = m0(3) = 1 TeV

m0(1,2) = 0A0 = 0, mHu = mHd

= 0Minput = MP

Uncertainties in tan β

With finite µ term, b commonly of the same order(connected through hidden sector)

Spectrum unaffected, except for small shift in t, bmasses

Direct detection cross section varies from 4× 10−47 cm2

(tanβ = 10) to 4× 10−46 cm2 (tanβ = 50) due to Hd

contribution to χ01.

Page 40: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Spectra

Choose SPS1a for comparison since slepton/light gauginospectra similar:

Field SPS1a M3 = M1/2 M3 =500 GeV

χ01 100 100 100

χ02, χ±1 180 230 230

lR(1,2) 140 120 120

lL(1,2) 200 200 200

H0, A0, H± 400 970 1100χ±2 , χ0

3,4 380 960 1100

τ ,ντ 200 1000 1000t1 550 920 1200g 600 789 1250

q1,2 550 680 1100

Page 41: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Newest model-independent constraints

Page 42: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Constraint on model points

Jets + missing ET≥ 3-jet signal region only 10± 2 SM events at 165pb−1:

SPS1a M3 = M1/2 M3 =500 GeV

Prod. σ 4.5 pb 0.6 pb 16 fb

Efficiency 12% 28% 29%

L(2σ) 7 pb−1 15 pb−1 10 fb−1

Multiplicities

Mistag rates: τ -jet (8%), b-jet (5%)

SPS1a M3 = M1/2 M3 =500 GeV

b-jets 18% 5% 5%

τ -jets 8% 9% 9%

nl ≥ 2 8% 14% 14%

Page 43: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Constraint on model points

Jets + missing ET≥ 3-jet signal region only 10± 2 SM events at 165pb−1:

SPS1a M3 = M1/2 M3 =500 GeV

Prod. σ 4.5 pb 0.6 pb 16 fb

Efficiency 12% 28% 29%

L(2σ) 7 pb−1 15 pb−1 10 fb−1

Multiplicities

Mistag rates: τ -jet (8%), b-jet (5%)

SPS1a M3 = M1/2 M3 =500 GeV

b-jets 18% 5% 5%

τ -jets 8% 9% 9%

nl ≥ 2 8% 14% 14%

Page 44: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Dark matter phenomenology

Detection

σχN excludable by XENON100/1T

χ01 mostly bino, < σv >χχ is p-wave suppressed

Page 45: Quarks and Leptons as Nambu-Goldstone 7 Fermions Under E ...

Quarks andLeptons as

Nambu-GoldstoneFermions UnderE7/SO(10)

S. K. Mandal

Introduction

Motivations

Coset Spaces

E7/SO(10)Model

Preliminaries

Model Aspects

GUT model

Low Energy Results

Experimentalconstraints

LHC 7 TeV

Dark MatterDetection

Summary

Summary

Created consistent E7/SO(10) coset model withdistinctive collider signatures

Can be ruled out by DM direct detection in 1–5 yearsdepending on tan β

Can be ruled out by LHC Higgs search in ∼ 10 fb−1

(by end of 2011 at ∼ 80 pb−1/day)


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