E 6 Spectra at the TeV Scale - PDF Free Download

E 6 Spectra at the TeV Scale Instituts-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 E 6 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 m H Λ Planck : 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 Poincaré algebra: {Q α, Q α } = 2P µ σ µ α α representations contain equal number of fermion and boson d.o.f. Superpartners [Q, T gauge ] = 0 same quantum numbers [Q, P 2 ] = 0 same mass (spont. breaking!) Why do we like it? only nontrivial 4D extension of Poincaré algebra m H stabilized against Λ Planck 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 µ H u H d, why is µ Λ Planck? How is SUSY broken? Plethora of free parameters SUSY flavor problem A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 7 / 42

From the top down - GUTs and E 6 From the Top Down: E 6 based unification A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 8 / 42

From the top down - GUTs and E 6 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 E 6 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 g s 1.2 SU(2): Weak Isospin, coupling strength g 0.65 Charges defined by λ a /2 and σ i /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 E 6 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 E 6 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 E 6 2) Unified Gauge Group Finite Simple Lie Algebras (Cartan): A n : SU(N)..., B n, D n : SO(N)..., C n : Sp(N)..., G 2, F 4, E 6, E 7, E 8 A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 13 / 42

From the top down - GUTs and E 6 2) Unified Gauge Group Many interesting groups containing G SM = 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: E 8 Subgroups A series of groups of increasing rank containing the SM G SM SU(5) SO(10) E 6 E 7 E 8 Look at Representations! A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 14 / 42

From the top down - GUTs and E 6 3) Matter Representations Representations given as (SU(3), SU(2)) Y, Q = Y + I 3 L Quarks per generation: (3, 2) 1/6 }{{} + (3, 1) 1/3 + (3, 1) 2/3 }{{} Lefthanded Righthanded d,u Leptons per generation: (1, 2) 1/2 + (1, 1) 1 + (1, 1) }{{}}{{} 0 Lefthanded Righthanded d,u A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 15 / 42

From the top down - GUTs and E 6 3) Matter Representations Does the Standard Model Matter fit into simple group representations? The smallest SU(5) irreps Fundamental (complex) 5 ψ i complex 10 ψ [i,j] complex 15 ψ (i,j) Adjoint (real) 24 V j i 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 ν R! A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 16 / 42

From the top down - GUTs and E 6 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 }{{} + (3, 1) 1/3 + (3, 1) 1/3 }{{} MSSM Higgs candidates Triplets Why is this a problem? In simple GUTs, the triplets are naturally at M µ Light triplets skew unification Yukawas = 5 H 5 M 10 M + 5 H 10 M 10 M violate B! A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 17 / 42

From the top down - GUTs and E 6 Already strong (fatal?) constraints on conventional GUTs, new experiments running! A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 18 / 42

From the top down - GUTs and E 6 E 6 inspired Models A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 19 / 42

E 6 representations From the top down - GUTs and E 6 Largest E n Group with complex irreps No anomalies in D 6 (up to GS) Dimension Real 27 Fundamental rep. 78 Adjoint 351 351 650 1728... A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 20 / 42

From the top down - GUTs and E 6 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 E 6 Higgs-Matter Unification The group E 6 contains SU(5): SU(5) SO(10) E 6 Analogous for Matter representations: 10, 5, 1 }{{} Matter + 5, 5 }{{} 16 + 10 }{{} Higgs Matter }{{} Higgs + 1 = 27 }{{} Singlet E 6 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 E 6 has rank 6: E 6 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 E 6 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 E 6 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 E 6 Superpotential What is the most general renormalizable superpotential for 27 Matter? 27 27 = 351 + 351 + 27, so the only D 4 singlet is This includes: 27 3 SH u H }{{ d } µ Term W = 27 27 27 + STT }{{ c } Mass + HQ L Q R + HL L L R }{{} Matter Mass + T c Q L L L + TQ R L }{{ R + TQ } L Q L + T c Q R Q }{{ R } Leptoquark 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

Two ways out E6 GUTs with light exotics 1 Forbid the renormalizable E 6 Superpotential 27 3 (F. Braam, C.Horst, W.Kilian, AK, J.Reuter, in preparation) Renormalizable superpotential is generated in E 6 breaking, e.g. like W 5 = 1 650 650 273 Wren Λ 2 E 6 is broken by higher-dimensional geometry (orbifolding), fixed points of the orbifold respect subgroups of E 6 (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

String Inspired Scenarios Orbifold GUTs The Heterotic String (HE): E 8 E 8 gauge theory in 10D coupled to sugra (anomaly free!) R 4 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 A. Knochel (Uni Freiburg) T2 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 E 6 to G E 6 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, R 2 /Γ A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 29 / 42

The R 2 /632 Orbifold Orbifold GUTs Modding out a 60 Z 6 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 E 6 to LR Symmetric Model Example: V = ( 1 2, 1 2, 1 3, 1 6, 1 2, 0) E 6 N = 2 SU(3) SU(2) 2 U(1) 2 N = 1 SU(3) 3 N = 1 SO(10) U(1) 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 E 6 irreps Important parities are now allowed: E 6 SO(10) U(1): 27 16 + 10 + 1, allows H E 6 SU(3) 3 : 27 (3, 3, 1) (3, 1, 3) (1, 3, 3), allows B Leptoquarks! Have gained (too?) much freedom to place matter Anomaly 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) E 6 SU 3 SU 2 2 U 1 B L U 1 Χ E 6 MSSM U 1 50 40 U 1 Y 1 Α i 30 SU 2 L U 1 B L 20 SU 3 10 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 Μ GeV A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 34 / 42

Orbifold GUTs Unification scheme (intermediate Higgs in RGE) E 6 SU 3 SU 2 2 U 1 B L U 1 Χ E 6 MSSM U 1 50 40 U 1 Y 1 Α i 30 SU 2 L U 1 B L 20 SU 3 10 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 Μ GeV A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 35 / 42

Orbifold GUTs Unification scheme (different vectorlike intermediate Higgs) 60 U 1 Y U 1 50 U 1 1 60 U 1 U 1 Y 50 U 1 1 40 1 Αi 30 U 1 2 SU 2 L U 1 B L 40 1 Αi 30 U 1 2 SU 2 L 20 U 1 Χ 20 U 1 Χ B L 10 SU 3 10 SU 3 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 Μ GeV 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 Μ GeV 60 U 1 Y 60 U 1 Y U 1 50 U 1 1 U 1 50 U 1 1 40 1 Αi 30 20 U 1 2 SU 2 L U 1 Χ B L 40 1 Αi 30 20 U 1 2 SU 2 L U 1 B L Χ 10 SU 3 10 SU 3 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 Μ GeV 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 Μ GeV 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 E 6 unifies Higgs and Matter states E 6 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 µ H u H d contains unconstrained scale! Solution: NMSSM! 1 Introduce SM singlet scalar S 2 Forbid µ H u H d and ms 2 by Z 3 symmetry 3 Scalar potential from λs 3 4 S H u H d v µ H u H d New Problem: Z 3 domain walls at the electroweak scale! Better: Forbid µ H u H d by gauged U(1) Z 3! 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 ν R is uncharged (Seesaw, Leptogenesis) This is nearly impossible! But: The E 6 spectrum and charges satisfy all of the above! E 6 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: E 6 inspired Dark Matter LHC predictions from orbifold threshold corrections Systematic exotic LHC phenomenology of the intermediate 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

Outlook Thank You for Your Attention! A. Knochel (Uni Freiburg) E6 Spectra at the TeV Scale 24.06.2010 42 / 42