Post on 02-Sep-2019
transcript
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:
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 3 / 42
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?
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 4 / 42
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?
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 5 / 42
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 6 / 42
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 7 / 42
From the top down - GUTs and E6
From the Top Down: E6 based unification
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 8 / 42
From the top down - GUTs and E6
What is a GUT?
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 9 / 42
From the top down - GUTs and E6
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 10 / 42
From the top down - GUTs and E6
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 11 / 42
From the top down - GUTs and E6
1) Coupling unification
The gauge coupling constants in the SM are vastly different......but QFT parameters are distance(Energy)-dependent via RGE!
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 12 / 42
From the top down - GUTs and E6
1) Coupling unification
The gauge coupling constants in the SM are vastly different......but QFT parameters are distance(Energy)-dependent via RGE!
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 12 / 42
From the top down - GUTs and E6
2) Unified Gauge Group
Finite Simple Lie Algebras (Cartan):
An : SU(N)...,Bn,Dn : SO(N)...,Cn : Sp(N)...,G2,F4,E6,E7,E8
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 13 / 42
From the top down - GUTs and E6
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!
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 14 / 42
From the top down - GUTs and E6
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 15 / 42
From the top down - GUTs and E6
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!
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 16 / 42
From the top down - GUTs and E6
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!
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 17 / 42
From the top down - GUTs and E6
Already strong (fatal?) constraints on conventional GUTs, newexperiments running!
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 18 / 42
From the top down - GUTs and E6
E6 inspired Models
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 19 / 42
From the top down - GUTs and E6
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...
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 20 / 42
From the top down - GUTs and E6
The 78fold Way (Reuter, Mallot 09)
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 21 / 42
From the top down - GUTs and E6
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...
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 22 / 42
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...
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 23 / 42
E6 GUTs with light exotics
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...
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 24 / 42
E6 GUTs with light exotics
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...
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 24 / 42
E6 GUTs with light exotics
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])
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 25 / 42
Orbifold GUTs
String Inspired Scenarios
The Heterotic String (HE):E8 × E8 gauge theory in 10D coupled to sugra (anomaly free!)
R4 CY 3
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 26 / 42
Orbifold GUTs
Flat 6D Geometry
We consider a simple 6D limit with E6 gauge invariance (anomaly free!)
R4 T2
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 27 / 42
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 28 / 42
Orbifold GUTs
Idea: Introduce symmetry breaking singularities using a quotient space
17 Wallpaper groups, R2/Γ
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 29 / 42
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 30 / 42
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 31 / 42
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 32 / 42
Orbifold GUTs
Further breaking and unification
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 33 / 42
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 34 / 42
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 35 / 42
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
UH1L�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
UH1L�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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 36 / 42
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
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 37 / 42
From the bottom up - Alternative Supersymmetric Spectra
From the Bottom Up: MSSM extensions
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 38 / 42
From the bottom up - Alternative Supersymmetric Spectra
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!
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 39 / 42
From the bottom up - Alternative Supersymmetric Spectra
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]
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 40 / 42
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)
A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 41 / 42