alexander knochel - tu dresden · e 6 spectra at the tev scale instituts-seminar kerne und...

E6 Spectra at the TeV ScaleInstituts-Seminar Kerne und Teilchen, TU Dresden

Alexander Knochel

Uni Freiburg

24.06.2010

Based on:

F. Braam, AK, J. Reuter, arXiv:1001.4074 [hep-ph], JHEP06(2010)013

Outline

1 Introduction

2 From the top down - GUTs and E6

3 E6 GUTs with light exotics

4 Orbifold GUTs

5 From the bottom up - Alternative Supersymmetric Spectra

6 Outlook

A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 2 / 42

Introduction

The Standard Model - what do we know?

Particle content:


Introduction

The Standard Model - what do we know?

Gauge theory:

Interactions and representations → gauge symmetry

SU(3)× SU(2)L × U(1)Y

Massive W ,Z and fermions → nonlinear realization below ∼ 100 GeV

Sucessful precision fits point to perturbative spontaneous breaking

Perturbative and Renormalizable? −→ elementary scalar Higgs?


Introduction

Questions and Problems of the SM with Higgs

Problems

mH � ΛPlanck : extreme fine tuning

no cold Dark Matter

Dark Energy problem

CP violation and Baryogenesis

Strong CP problem

Open Questions

What types of neutrino masses?

Why three generations?

Where does the flavor structure (mixing, hierarchies) come from?e.g. why is the top yukawa ∼ 1?

Deeper reason behind SU(3)× SU(2)× U(1) and irreps?


Introduction

Supersymmetry

Properties:

only nontrivial 4D extension of Poincare algebra:

{Qα,Q α} = 2Pµσµαα

representations contain equal number of fermion and boson d.o.f.

”Superpartners”[Q,Tgauge ] = 0 → same quantum numbers[Q,P2] = 0 → same mass (spont. breaking!)

Why do we like it?

only nontrivial 4D extension of Poincare algebra

mH stabilized against ΛPlanck

superpartners → Dark Matter candidates

New sources of CP violations

Stabilization of hierarchy → can talk about high scale unification


Introduction

Some problems with SUSY

Existence?

Little hierarchy

MSSM: µ Problem, W ∼ µHuHd , why is µ� ΛPlanck?

How is SUSY broken?

Plethora of ”free” parametersSUSY flavor problem


From the top down - GUTs and E6

From the Top Down: E6 based unification



What is a GUT?



Grand Unified Theories

The interactions of G a,W±,Z , γ with themselves, Higgs and Matter:

defined by gauge invariance

SU(3): Strong color Interactions, coupling strength gs ∼ 1.2

SU(2): Weak Isospin, coupling strength g ∼ 0.65

Charges defined by λa/2 and σi/2

U(1): Hypercharge, coupling strength g ′ ∼ 0.45 in some normaliz.

Hypercharges are numbers



Grand Unified Theories

Gauge Theories based on a simple Algebra have only one coupling constant!GUT Idea: Could the SM be embedded in one simple Lie algebra?

Minimal requirements:

1 Equal couplings for SU(3), SU(2) and U(1)

2 G with SU(3)× SU(2)× U(1) ⊂ G

3 Matter and Higgses must fit in representations of G



1) Coupling unification

The gauge coupling constants in the SM are vastly different......but QFT parameters are distance(Energy)-dependent via RGE!



2) Unified Gauge Group

Finite Simple Lie Algebras (Cartan):

An : SU(N)...,Bn,Dn : SO(N)...,Cn : Sp(N)...,G2,F4,E6,E7,E8



2) Unified Gauge Group

Many interesting groups containing GSM = SU(3)× SU(2)L × U(1)Y .Which one to use?

Search for minimal group

with the right matter representations

From a String Theory perspective: E8 Subgroups

A series of groups of increasing rank containing the SM

GSM ⊂ SU(5) ⊂ SO(10) ⊂ E6 ⊂ E7 ⊂ E8

−→ Look at Representations!



3) Matter Representations

Representations given as (SU(3),SU(2))Y , Q = Y + I 3L

Quarks per generation:

(3, 2)1/6︸︷︷︸Lefthanded

+ (3, 1)−1/3 + (3, 1)2/3︸︷︷︸Righthanded d,u

Leptons per generation:

(1, 2)−1/2︸︷︷︸Lefthanded

+ (1, 1)−1 + (1, 1)0︸︷︷︸Righthanded d,u



3) Matter Representations

Does the Standard Model Matter fit into simple group representations?

The smallest SU(5) irreps

Fundamental (complex) 5 ψi

complex 10 ψ[i ,j]

complex 15 ψ(i ,j)

Adjoint (real) 24 V ji

How does this decompose under SU(5)→ SU(3)× SU(2)× U(1)Y ?

5 −→ (3, 1)−1/3 + (1, 2)1/2

10 −→ (3, 1)−2/3 + (3, 2)1/6 + (1, 1)1

15 −→ (6, 1)−2/3 + (3, 2)1/6 + (1, 3)1

24 −→ (8, 1)0 + (1, 3)0 + (1, 1)0 + (3, 2)−5/6 + (3, 2)5/6

Geogi, Glashow: 10 + 5 correspond exactly to known matter w/o νR!



3) Higgs Representations and Doublet-Triplet Splitting

Unfortunately, this is not true for the electroweak Higgs:

5 + 5 ∼ (1, 2)1/2 + (1, 2)−1/2︸︷︷︸MSSM Higgs candidates

+ (3, 1)−1/3 + (3, 1)1/3︸︷︷︸Triplets

In simple GUTs, the triplets are naturally at M ∼ µWhy is this a problem?

Light triplets skew unification

Yukawas = 5H × 5M × 10M + 5H × 10M × 10M violate B!



Already strong (fatal?) constraints on conventional GUTs, newexperiments running!



E6 inspired Models



E6 representations

Largest En Group with complex irreps

No anomalies in D ≤ 6 (up to GS)

Dimension Real

27 Fundamental rep.

78 X Adjoint

351351′

650 X1728...



The 78fold Way (Reuter, Mallot 09)



Higgs-Matter Unification

The group E6 contains SU(5):

SU(5) ⊂ SO(10) ⊂ E6

Analogous for Matter representations:

10, 5, 1︸︷︷︸Matter

+ 5, 5︸︷︷︸Higgs

⊂ 16︸︷︷︸Matter

+ 10︸︷︷︸Higgs

+ 1︸︷︷︸Singlet

= 27

E6 unifies Higgs and Matter irreps in its fundamental.

However, it does so in every generation separately!Doublet-Triplet-splitting has become Doublet-Triplet-Decouplet splitting...


E6 GUTs with light exotics

E6 has rank 6: E6 ⊃ SM × U(1)× U(1)

Proposition (S.F. King et al.), (W. Kilian, J. Reuter):

If an extra U(1) is only broken at TeV

The exotics in 27 are light

Higgs mass parameter µ is generated dynamically at O(TeV)

Unification can be recovered via an intermediate symmetry breaking

E6 unification is accessible to experiment!

An exciting possibility, but with serious conceptual challenges

1 Can we obtain realistic superpotential and spectrum?

2 How to break E6

3 RGE running and unification...



The renormalizable E6 Superpotential

What is the most general renormalizable superpotential for 27 Matter?

27⊗ 27 = 351 + 351′ + 27, so the only D ≤ 4 singlet is

W = 27⊗ 27⊗ 27

This includes:

273 ∼ SHuHd︸︷︷︸µ Term

+ STT c︸︷︷︸Mass

+ HQLQR + HLLLR︸︷︷︸Matter Mass

+ T cQLLL + TQRLR︸︷︷︸Leptoquark

+ TQLQL + T cQRQR︸︷︷︸Diquark!

Proton decay

FCNCs from extra Higgs multiplets

complete Yukawa unification...



Two ways out

1 Forbid the renormalizable E6 Superpotential 273

(F. Braam, C.Horst, W.Kilian, AK, J.Reuter, in preparation)

Renormalizable superpotential is generated in E6 breaking, e.g. like

W5 =1

Λ650× 273 〈650〉−→ Wren

2 E6 is broken by higher-dimensional geometry (orbifolding), fixedpoints of the orbifold respect subgroups of E6

(F. Braam, AK, J. Reuter, arXiv:1001.4074 [hep-ph])


Orbifold GUTs

String Inspired Scenarios

The Heterotic String (HE):E8 × E8 gauge theory in 10D coupled to sugra (anomaly free!)

R4 CY 3


Orbifold GUTs

Flat 6D Geometry

We consider a simple 6D limit with E6 gauge invariance (anomaly free!)

R4 T2


Orbifold GUTs

Torus compactification preserves too many symmetries

∼

Breaking:

6D N = 1 ∼ 4D N = 2 to 4D N = 1

E6 to G ⊂ E6

Need more structure! −→ Orbifolding


Orbifold GUTs

Idea: Introduce symmetry breaking singularities using a quotient space

17 Wallpaper groups, R2/Γ


Orbifold GUTs

The R2/632 Orbifold

Modding out a 60◦ Z6 rotation:

→θ

Orbifold breaking: Associate θ with a shift V in the gauge group algebra

|µ〉 θ−→ e i V ·H |µ〉

Here: only abelian shifts, rank is preserved


Orbifold GUTs

Orbifold breaking of E6 to LR Symmetric Model

Example: V = (−12 ,

12 ,

13 ,

16 ,

12 , 0)

E6

N = 2

SU(3)× SU(2)2 × U(1)2

N = 1

SO(10)× U(1)

N = 1

SU(3)3

N = 1


Orbifold GUTs

Matter

Three types of matter in 4D:

Massless modes from the bulk N = 2 gauge multiplet 78

Massless modes from bulk hypermultiplets (e.g. 27)

Fixed point localized matter in H ⊂ E6 irreps

Important parities are now allowed:

E6 → SO(10)× U(1): 27→ 16 + 10 + 1, allows H

E6 → SU(3)3: 27→ (3, 3, 1)× (3, 1, 3)× (1, 3, 3), allows B

Leptoquarks!

Have gained (too?) much freedom to place matterAnomaly constraints and unbroken U(1)s: complete 27s at massless level


Orbifold GUTs

Further breaking and unification


Orbifold GUTs

Unification scheme (no intermediate Higgs in RGE)

SUH3L

SUH2LL

UH1LY

UH1LB-L

102 104 106 108 1010 1012 1014 1016 1018 1020

10

20

30

40

50

Μ�GeV

1

Αi

EH6L -> SUH3L ´ SUH2L2´ UH1LB-L@´UH1LΧD -> E6MSSM @´ UH1L’D


Orbifold GUTs

Unification scheme (intermediate Higgs in RGE)

SUH3L

SUH2LL

UH1LY

UH1LB-L

102 104 106 108 1010 1012 1014 1016 1018 1020

10

20

30

40

50

Μ�GeV

1

Αi

EH6L -> SUH3L ´ SUH2L2´ UH1LB-L@´UH1LΧD -> E6MSSM @´ UH1L’D


Orbifold GUTs

Unification scheme (different vectorlike intermediate Higgs)

UH1LY

UH1L’

SUH3L

SUH2LL

UH1L2

UH1L1

UH1LΧ

UH1LB-L

102 104 106 108 1010 1012 1014 1016 1018

10

20

30

40

50

60

Μ�GeV

1

Αi

UH1LY

UH1L’

SUH3L

SUH2LL

UH1L2

UH1L1

UH1LΧ�B-L

102 104 106 108 1010 1012 1014 1016

10

20

30

40

50

60

Μ�GeV

1

Αi

UH1LY

UH1L’

SUH3L

SUH2LL

UH1L2

UH1L1

UH1LΧ�B-L

102 104 106 108 1010 1012 1014 1016

10

20

30

40

50

60

Μ�GeV

1

Αi

UH1LY

UH1L’

SUH3L

SUH2LL

UH1L2

UH1L1

UH1LB-L�Χ

102 104 106 108 1010 1012 1014 1016

10

20

30

40

50

60

Μ�GeV

1

Αi


Orbifold GUTs

Summary so far:

SM is successful but incomplete

GUTs allow unification of matter and interactions

E6 unifies Higgs and Matter states

E6 based models

must give up some aspects of grand unification

Unification in two steps with intermediate Seesaw scale (a good thing!)Matter unification partly due to anomaly cancellation only

appear in string compactifications

improve aspects of the MSSM

give us typical new TeV phenomenology from U(1)′ and 27!

Extended neutralino sector and Z ′

Color charged exotics (can be Leptoquarks or Diquarks)Exotic Higgs-like states

orbifold breaking yields realistic candidates


From the bottom up - Alternative Supersymmetric Spectra

From the Bottom Up: MSSM extensions



Improving the MSSM

The µ Problem: W ∼ µHuHd contains unconstrained scale!

Solution: NMSSM!

1 Introduce SM singlet scalar S

2 Forbid µHuHd and mS2 by Z3 symmetry

3 Scalar potential from λS3

4 〈S〉HuHd → vµ HuHd

New Problem: Z3 domain walls at the electroweak scale!

Better: Forbid µHuHd by gauged U(1)′ ⊃ Z3!Potential from U(1)′ D-Term!

No domain walls

Z ′ boson!



Extra U(1)

Challenge: Choosing U(1)′ charges such that

1 NMSSM Superpotential is still allowed

2 U(1) is anomaly free

3 S does not induce FCNCs (eg by family universality)

4 νR is uncharged (Seesaw, Leptogenesis)

This is nearly impossible! But:

The E6 spectrum and charges satisfy all of the above!

E6 like models are the most natural extra-U(1) extensions!

[Cvetic et al, 1997][Everett et al, 2000][Hambye et al., 2000]

[Suematsu et al, 2000][Han et al, 2004][Demir et al., 2005][Morissey et al., 2007]


Outlook

Outlook and future Projects

Exciting times ahead thanks to LHC and DM searches!

Look for Z ′ and color charged exotics at the LHC!

New states might provide alternative dark matter

Ongoing and future Projects:

E6 inspired Dark Matter

LHC predictions from orbifold threshold corrections

Systematic exotic LHC phenomenology of theintermediate LR model

Heterotic and F-Theory embeddings(in collaboration with Munich and Heidelberg groups)


Outlook

Thank You for Your Attention!


alexander knochel - tu dresden · e 6 spectra at the tev scale instituts-seminar kerne und...

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