The Big Deal with the Little Higgs

The Big Deal with the Little Higgs Jürgen Reuter DESY Theory Group, Hamburg Seminar Dresden, 16.Dec.2005

Outline Hierarchy Problem, Goldstone-Bosons and Little Higgs Higgs as Pseudo-Goldstone Boson Nambu-Goldstone Bosons The Little Higgs mechanism Examples of Models Phenomenology For example: Littlest Higgs Neutrino masses Effective Field Theories Electroweak Precision Observables Direct Searches Reconstruction of Little Higgs Models Pseudo Axions in LHM T parity and Dark Matter Conclusions

The Higgs Mechanism in the Standard Model Electroweak Theory: SU(2) U(1) gauge theory Q L U = exp[igθ a τ a /2], V = exp[ig θ Y Y/2] ( ) u UQ L, f R f R, W µ UW µ U + i d g ( µu)u L

The Higgs Mechanism in the Standard Model Electroweak Theory: SU(2) U(1) gauge theory Q L U = exp[igθ a τ a /2], V = exp[ig θ Y Y/2] ( ) u UQ L, f R f R, W µ UW µ U + i d g ( µu)u L Problem: Mass terms for W, Z and fermions not gauge invariant Solution: Introduction of a field which absorbs the mismatch of transformation laws: Higgs field Spontaneous symmetry breaking: Higgs gets a Vacuum Expectation value (VEV): ( ) 0 V(Φ) = µ 2 Φ Φ + λ(φ Φ) 2, Φ exp[iπ/v] v + H D µ Φ 2 1 2 M 2 W W 2 a, Y d Q L Φd R m d d L d R

Hierarchy Problem M h [GeV] 750 500 250 Λ[GeV] 10 3 10 6 10 9 10 12 10 15 10 18

Hierarchy Problem 750 500 250 M h [GeV] 10 3 10 6 10 9 10 12 10 15 10 18 Λ[GeV] Motivation: Hierarchy Problem Effective theories below a scale Λ

Hierarchy Problem 750 500 250 M h [GeV] 10 3 10 6 10 9 10 12 10 15 10 18 Λ[GeV] Motivation: Hierarchy Problem Effective theories below a scale Λ Loop integration cut off at order Λ: Λ 2

Hierarchy Problem 750 500 250 M h [GeV] 10 3 10 6 10 9 10 12 10 15 10 18 Λ[GeV] Motivation: Hierarchy Problem Effective theories below a scale Λ Loop integration cut off at order Λ: Λ 2 Problem: Naturally, m h O(Λ 2 ): m 2 h = m 2 0 + Λ 2 (loop factors) Light Higgs favoured by EW precision observables (m h < 0.5 TeV) m h Λ Fine-Tuning!? Solution: Mechanism for eliminating loop contributions

Higgs as Pseudo-Goldstone Boson Invent (approximate) symmetry to protect particle mass Traditional (SUSY): Spin-Statistics = Loops of bosons and fermions

Higgs as Pseudo-Goldstone Boson Invent (approximate) symmetry to protect particle mass Traditional (SUSY): Spin-Statistics = Loops of bosons and fermions Little Higgs: Gauge group structure/global Symmetries = Loops of particles of like statistics Old Idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984 Light Higgs as Pseudo-Goldstone boson spontaneously broken (approximate) global symmetry; non-linear sigma model w/o Fine-Tuning: v Λ/4π

The Nambu-Goldstone-Theorem Nambu-Goldstone Theorem: For each spontaneously broken global symmetry generator there is a massless boson in the spectrum.

The Nambu-Goldstone-Theorem Nambu-Goldstone Theorem: For each spontaneously broken global symmetry generator there is a massless boson in the spectrum. π i iθ a T a ikπ k V π i T a ijπ j = 0 Nonlinear Realization (Example SU(3) SU(2)): V(Φ) = ( f 2 (Φ Φ) ) [ ( 2 i Φ = exp f 2 V π i π j Tjkf a k + V f π j Tji a = 0 v }{{}}{{} =(m 2 ) ij =0 0 π π π 0 )] ( ) 0 e iπ Φ 0 f + σ

Construction of a Little Higgs model π h??

Construction of a Little Higgs model π h?? Let s try!

Construction of a Little Higgs model π h?? Let s try! Lagrangian has translational symmetry: π π + a (exact) Goldstones have only derivative interactions

Construction of a Little Higgs model π h?? Let s try! Lagrangian has translational symmetry: π π + a (exact) Goldstones have only derivative interactions Gauge and Yukawa interactions? Expanding the kinetic term: f 2 Φ 2 = h 2 + 1 f 2 (h h) h 2 +... h Theory becomes stronlgy interacting at Λ = 4πf. h 1 f 2 Λ 2 16π Bad news Easy attempts: no potential or quadratic divergences again Collective Symmetry breaking: Two ways of model building: 1. simple Higgs representation, doubled gauge group 2. simple gauge group, doubled Higgs representation

Prime Example: Simple Group Model enlarged gauge group: SU(3) U(1); globally U(3) U(2) Two nonlinear Φ representations L = D µ Φ 1 2 + D µ Φ 2 2 [ Φ 1/2 = exp ±i f ] 2/1 Θ f 1/2 0 0 f 1/2 Θ = 1 f 2 1 + f2 2 η 0 0 η h T h η Coleman-Weinberg mechanism: Radiative generation of potential + = g2 ( 16π 2 Λ2 Φ 1 2 + Φ 2 2) g2 16π 2 f 2

Yukawa interactions and heavy Top Simplest Little Higgs ( µ Model ) Schmaltz (2004), Kilian/Rainwater/JR (2004) Field content (SU(3) c SU(3) w U(1) X quantum numbers) Φ 1,2 : (1, 3) 1 3 Ψ Q : (3, 3) 1 3 Ψ l : (1, 3) 1 3 d c : ( 3, 1) 1 3 c u 1,2 : ( 3, 1) 2 3 e c, n c : (1, 1) 1,0 Lagrangian L = L kin. + L Yuk. + L pot. Ψ Q,L = (u, d, U) L, Ψ l = (ν, l, N) L : L Yuk. = λ u 1u 1,R Φ 1 Ψ T,L λ u 2u 2,R Φ 2 Ψ T,L λd Λ ɛijk d b RΦ i 1Φ j 2 Ψk T,L λ n n 1,R Φ 1 Ψ Q,L λe Λ ɛijk e R Φ i 1Φ j 2 Ψk Q,L + h.c.,

Cancellations of Divergencies in Yukawa sector λ t λ t + λt λ T + λ T /f

Cancellations of Divergencies in Yukawa sector + + λ t λ t λt λ T λ T /f d 4 k 1 { (2π) 4 k 2 (k 2 m 2 T ) λ 2 t (k 2 m 2 T ) + k 2 λ 2 T m T F λ T k 2}

Cancellations of Divergencies in Yukawa sector + + λ t λ t λt λ T λ T /f d 4 k 1 { (2π) 4 k 2 (k 2 m 2 T ) λ 2 t (k 2 m 2 T ) + k 2 λ 2 T m T F λ T k 2} Little Higgs global symmetry imposes relation m T F = λ2 t + λ 2 T λ T = Quadratic divergence cancels Collective Symm. breaking: λ t λ 1 λ 2, λ 1 = 0 Φ 1 Φ 2 or λ 2 = 0 SU(3) Ψ Q Ψ Q λ2 1λ 2 2 [SU(3)] 2 16π 2 log Φ 1 Φ 1 u c 1 u c 2 ( Λ 2 µ 2 ) Φ 1 Φ 2 2

Scales and Masses µ O(10 TeV) O(1 TeV) O(250 GeV) F v Λ Scale Λ: global SB, new dynamics, UV embedding Scale F : Pseudo-Goldstone bosons, new vector bosons and fermions Scale v: Higgs, W ±, Z, l ±,... Boson masses radiative (Coleman-Weinberg), but: Higgs protected by symmetries against quadratic corrections @ 1-loop level

Scales and Masses µ O(10 TeV) O(1 TeV) O(250 GeV) F v Λ Scale Λ: global SB, new dynamics, UV embedding Scale F : Pseudo-Goldstone bosons, new vector bosons and fermions Scale v: Higgs, W ±, Z, l ±,... H H 0 Boson masses radiative (Coleman-Weinberg), but: Higgs protected by symmetries against quadratic corrections @ 1-loop level G 1 G 1 [H G 2 G 1 1, H 2 ] 0 g 1 0 g 2 0 /H 1 H /H 2 H M H g 1 g 2 Λ/16π 2

Generic properties Extended scalar (Higgs-) sector Extended global symmetry

Generic properties Extended scalar (Higgs-) sector Extended global symmetry Specific form of the potential: V(h, Φ) = C 1 F 2 Φ + i 2 F h h + C 2 F 2 Φ i 2 F h h h massless @ 1-loop level, h = v, M h v, M Φ F, i Φ v 2 /F h and Φ mix Extended Gauge Sector : B, Z, W ± (Hypercharge singlets & triplets)

Little Higgs Models Plethora of Little Higgs Models in 3 categories: Moose Models Orig. Moose (Arkani-Hamed/Cohen/Georgi, 0105239) Simple Moose (Arkani-Hamed/Cohen/Katz/Nelson/Gregoire/Wacker, 0206020) Linear Moose (Casalbuoni/De Curtis/Dominici, 0405188) Simple (Goldstone) Representation Models Littlest Higgs (Arkani-Hamed/Cohen/Katz/Nelson, 0206021) Antisymmetric Little Higgs (Low/Skiba/Smith, 0207243) Custodial SU(2) Little Higgs (Chang/Wacker, 0303001) Littlest Custodial Higgs (Chang, 0306034) Little SUSY (Birkedal/Chacko/Gaillard, 0404197) Simple (Gauge) Group Models Orig. Simple Group Model (Kaplan/Schmaltz, 0302049) Holographic Little Higgs (Contino/Nomura/Pomarol, 0306259) Simplest Little Higgs (Schmaltz, 0407143) Simplest Little SUSY (Roy/Schmaltz, 0509357) Simplest T parity (Kilian/Rainwater/JR/Schmaltz,...)

Varieties of Particle spectra H = SU(5) [SU(2) U(1)]2, G = SO(5) SU(2) U(1) Arkani-Hamed/Cohen/Katz/Nelson, 2002 m Φ Φ ± Φ ±± Z W ± T Φ P B h W ± Z t

Varieties of Particle spectra H = SU(5) [SU(2) U(1)]2, G = SO(5) SU(2) U(1) Arkani-Hamed/Cohen/Katz/Nelson, 2002 H = SO(6) [SU(2) U(1)]2, G = Sp (6) SU(2) U(1) Low/Skiba/Smith, 2002 m Φ Φ ± Φ ±± Z W ± T m Φ Φ P Z B W ± T h Φ P B W ± H = [SU(3)]2 SU(3) U(1), G = [SU(2)] 2 SU(2) U(1) Schmaltz, 2004 [SU(4)] 4 [SU(3)] 4 Z t m = H ± h A H Z X 0 /Y 0 W ± Z t ± W T U, C Kaplan/Schmaltz, 2003 2HDM, h 1/2, Φ 1,2,3, Φ P 1,2,3, Z 1,...,8, W ± 1,2, q, l h η W ± Z t

The Littlest Higgs Model Setup Symmetry breaking: SU(5) SO(5) (global) [SU(2) U(1)] 2 SU(2) L U(1) Y (local) 1 heavy triplet X µ, 1 heavy singlet Y µ

The Littlest Higgs Model Setup Symmetry breaking: SU(5) SO(5) (global) [SU(2) U(1)] 2 SU(2) L U(1) Y (local) The unbroken Lagrangian: L = L (3) 0 + L (1) 0 + L G 0. 1 heavy triplet X µ, 1 heavy singlet Y µ L (3) 0 = 1 2g1 2 Tr A 1µν A µν 1 1 2g2 2 Tr A 2µν A µν 2 2 tr A µ 1 J (3) µ L (1) 0 = 1 2g 2 1 Gauge group generators: T1 a = 1 τ a 0, T2 a = 1 0 2 2 0 Tr B 1µν B µν 1 1 2g 2 2 Tr B 2µν B µν 2 B µ 1 J (1) µ. 0 τ a, Y 1 = 1 10 diag(3, 3, 2, 2, 2) Y 2 = 1 10 diag(2, 2, 2, 3, 3)

L G 0 = F 2 ( 8 Tr(D µξ)(d µ Ξ), Ξ = exp 2i ) 0 0 1 F Π Ξ 0, Ξ 0 = 0 1 0 1 0 0 Π = 1 0 h φ ( ) h 0 h T 2 Φ ++ Φ +, φ = 2 φ h Φ +. Φ 0 + iφ 1 0

L G 0 = F 2 ( 8 Tr(D µξ)(d µ Ξ), Ξ = exp 2i ) 0 0 1 F Π Ξ 0, Ξ 0 = 0 1 0 1 0 0 Π = 1 0 h φ ( ) h 0 h T 2 Φ ++ Φ +, φ = 2 φ h Φ +. Φ 0 + iφ 1 0 Covariant derivative: D µ Ξ = µ Ξ + i k=1,2 [ ] (A µ k Ξ + Ξ(A µ k ) T ) + (B µ k Ξ + Ξ(B µ k ) T )

L G 0 = F 2 ( 8 Tr(D µξ)(d µ Ξ), Ξ = exp 2i ) 0 0 1 F Π Ξ 0, Ξ 0 = 0 1 0 1 0 0 Π = 1 0 h φ ( ) h 0 h T 2 Φ ++ Φ +, φ = 2 φ h Φ +. Φ 0 + iφ 1 0 Covariant derivative: D µ Ξ = µ Ξ + i k=1,2 [ ] (A µ k Ξ + Ξ(A µ k ) T ) + (B µ k Ξ + Ξ(B µ k ) T ) Chiral fields: Q R : b R, t R, T R, and Q L : q L = ( tl b L ), T L, L t = Q Qi /DQ + L Y λ 2 F ( T L T R + h.c.).

Neutrino masses Kilian/JR, 2003; del Aguila et al., 2004; Han/Logan/Wang, 2005 Naturalness does not require cancellation mechanism for light fermions Lepton-number violating interactions can generate neutrino masses (due to presence of triplet scalars) Lagrangian invariant under full gauge symmetry L N = g N F ( L c ) T ΞL with L = (iτ 2 l L, 0, 0) T EWSB: Generation of neutrino masses m ν g N v 2 /F

Heavy Vector Fields Mixing of the gauge fields: A µ 1 = W µ + g X c 2 X µ, B µ 1 = B µ + g Y c 2 Y µ, A µ 2 = W µ g X s 2 X µ, B µ 2 = B µ g Y s 2 Y µ,

Heavy Vector Fields Mixing of the gauge fields: A µ 1 = W µ + g X c 2 X µ, B µ 1 = B µ + g Y c 2 Y µ, A µ 2 = W µ g X s 2 X µ, B µ 2 = B µ g Y s 2 Y µ, Expand the Goldstone Lagrangian L G 0 = MX 2 c 2 s 2 tr X X + g X tr[x V (3) ] + 1 2 2 M Y 2 c 2 s 2 Y Y + g Y Y V (1) 4 + 1 2 tr(d µφ) (D µ φ) + (D µ h) (D µ h) 1 [ 6F 2 tr V (3) V (3)] +...,

Effective Field Theories How to clearly separate effects of heavy degrees of freedom?

Effective Field Theories How to clearly separate effects of heavy degrees of freedom? Toy model: Two interacting scalar fields ϕ, Φ [ ( ) ] 1 Z[j, J] = D[Φ] D[ϕ] exp i dx 2 ( ϕ)2 1 2 Φ( +M 2 )Φ λϕ 2 Φ...+JΦ+jϕ Low-energy effective theory integrating out heavy degrees of freedom (DOF) in path integrals, set up Power Counting Completing the square: Φ = Φ + λ ( ) 1 M 2 1 + 2 M 2 ϕ 2 1 2 ( Φ)2 1 2 M 2 Φ 2 λϕ 2 Φ = 1 ) 1 2 Φ (M 2 + 2 )Φ + (1 λ2 2M 2 ϕ2 + 2 M 2 ϕ 2.

Integrating out Integrating out the X and Y vector fields L (1) + L (3) = L EW g,gf + f (3) JJ tr[j (3) J (3) ] + f (3) V J tr[v (3) J (3) ] + f (1) V V tr[v (3) V (3) ] + f (1) JJ J (1) J (1) + f (1) V J V (1) J (1) + f (1) V V V (1) V (1) In the Littlest Higgs e.g. f (3) V V = 1 (1 6F 2 + 32 ) (c2 s 2 ) 2 Coleman-Weinberg potential of the scalar fields @ 1-loop: L CW 0 = 1 2 M 2 φ tr[φφ ] + µ 2 (h h) λ 4 (h h) 2 λ 2φ i ( h φh h T φ h ) λ 2φφ tr[(φφ )(hh )] λ 4φ i(h h) ( h φh h T φ h ) λ 6 (h h) 3 Sensitive to UV completion, dimensionless parameters k and k. EWSB Constraints on k, k

Integrate out the heavy scalar (Power counting!) φ = φ 2iλ 2φ M 2 φ ( 1 + D2 M 2 φ ) 1 + 2λ ( 2φφ Mφ 2 hh 1 + λ ) 4φ h h hh T λ 2φ Higgs mass up to order v 4 /F 2 m 2 H = 2λeff 4 v2! = 2v 2 e 2 s + e2 k 2 w c2 c 2 w c 2 e 2 s 2 w s2 + e2 c 2 w s 2! e 2 s 2 w s2 c + e 2 2 c 2 w s 2 c 2 k + λ2 t c 2 k t! k + λ2 t c 2 k t (Remember µ 2 = m 2 H /2) EWSB λ eff 4 > 0 λ2 2φ M 4 φ < 1 8F 2

Equations of Motion (EOM) Couplings V J induce after SSB anom. couplings of W, Z to fermions Applying EOM eliminates corrections from field redefinitions

Equations of Motion (EOM) Couplings V J induce after SSB anom. couplings of W, Z to fermions Applying EOM eliminates corrections from field redefinitions Custodial-SU(2) Conserving Terms 0 = tr[v (3) δl µ ] = tr[v (3) V (3) ] 2 δw µ g 2 tr[v (3) µd ν W µν ] 2 tr[v (3) J (3) ] L (3) = L EW g,gf + f (3) JJ O(3) JJ + f V W O V W + f (3) V V O(3) V V O V W = tr V (3) µνw µν, O (3) JJ = tr J (3) J (3), O (3) V V = tr V (3) V (3)

Effective Dim. 6 Operators O (I) JJ = 1 F 2 tr[j (I) J (I) ] O h,1 = 1 F 2 ( (Dh) h ) (h (D h ) ) v2 2 Dh 2 O hh = 1 F 2 (h h v 2 /2) (Dh) (Dh) O h,3 = 1 F 2 1 3 (h h v 2 /2) 3

O W W = 1 F 2 1 2 (h h v 2 /2) tr W µν W µν O B = 1 F 2 i 2 (D µh) (D ν h)b µν O BB = 1 F 2 1 4 (h h v 2 /2)B µν B µν O V q = 1 qh( /Dh)q F 2

Oblique Corrections: S, T, U All low-energy effects order v 2 /F 2 Low-energy observables parameterized by S, T, 2 parameters for contact interactions (no U here) O V W, O V B Change in gauge couplings g and g g = e s w [ 1 + M 2 W (f V W + 2f V B ) ] g = e c w [ 1 + [M 2 Z M 2 W ](f V W + 2f V B ) ] S parameter (O V W, O V B ) SU(2) c -violating sector (O h,1 ) S = 8πv 2 (f V W + 2f V B ) α T = M 2 W /M 2 W = 2v 2 f (1) V V 2v2 λ 2 2φ M 4 φ

Shift in physical vector masses: ( ) 2 ( ) 2 ev ev MW 2 = (1 + x) MZ 2 = (1 + y) 2s w 2s w c w x = α ( S/(4s 2 w) + T ) y = α S/(4s 2 wc 2 w)

Shift in physical vector masses: ( ) 2 ( ) 2 ev ev MW 2 = (1 + x) MZ 2 = (1 + y) 2s w 2s w c w x = α ( S/(4s 2 w) + T ) y = α S/(4s 2 wc 2 w) Very low energies Fermi theory Four-Fermion Interactions 2 GF = 1 v2 (1 + z) with z = α T v2 4 f (3) JJ. G F -M Z -α scheme (muon decay, LEP I, Bhabha), define the parameters ˆv 0 and ŝ 0 by s 2 w = ŝ 2 0 ˆv 0 = ( 2 G F ) 1/2 and M Z = eˆv 0 = 2ŝ 0 ĉ 0 ( ) ( ) 1 + ĉ2 0 ĉ 2 0 (y + z) c 2 ŝ2 w = ĉ 2 0 1 ŝ2 0 0 ĉ 2 0 (y + z) ŝ2 0

Constraints on LHM Constraints from contact IA: ( f (3) JJ, f (1) JJ ) c2 F /4.5 TeV c 2 F /10 TeV Constraints evaded c, c 1 B, Z, W, ± superheavy (O(Λ)) decouple from fermions

Constraints on LHM Constraints from contact IA: ( f (3) JJ, f (1) JJ ) c2 F /4.5 TeV c 2 F /10 TeV Constraints evaded c, c 1 B, Z, W, ± superheavy (O(Λ)) decouple from fermions S, T in the Littlest Higgs model, violation of Custodial SU(2): Csáki et al., 2002; Hewett et al., 2002; Han et al., 2003; Kilian/JR, 2003 Mixing of (Z, B, Z ) and (W ±, W ± ) S [ 8π = c 2 (c 2 s 2 ) g +5 c 2 (c 2 s 2 ) 2 ] v 2 g 2 F 2 0 α T 5 4 v 2 F 2v2 λ 2 2φ 2 Mφ 4 v2 F 2

EW Precision Observables T 0.6 LHM F = 3.5 TeV Higgs mass variable (Coleman-Weinberg, UV completion) 0.4 0.2 0 0.2 m H = 700 GeV 400 GeV 250 GeV 120 GeV SM 0.4 0.2 0 0.2 LHM F = 4.5 TeV S S = 1 12π ln m2 H m 2 0 T = 3 16πc 2 ln m2 H w m 2 0 Peskin/Takeuchi, 1992; Hagiwara et al., 1992 Making the Higgs heavier reduces amount of fine-tuning

Direct Searches Heavy Gauge Bosons: Detection: Resonance in e + e f f, Drell-Yan Tevatron: M B 650 GeV

Direct Searches Heavy Gauge Bosons: Detection: Resonance in e + e f f, Drell-Yan Tevatron: M B 650 GeV 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Branching ratios Z BR(Z ->ll) BR(Z ->qq) BR(Z ->WW,Zh) 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Total width Z, fixed M Z : Γ Z = g2 ( cot 2 2φ + 24 tan 2 φ ) M Z 96π Determination of F, c, s O(10 2 ) lepton events @ LHC w. 300 fb 1

Heavy Scalars: Φ P : e + e, q q Φ P h, Φ P hz L Φ ± : e + e, q q Φ + W L, Φ± W LZ L Φ ±± : e e ννφ, Φ ±± W L W L Φ 0 : e + e, q q Z LΦ, Φ Z LZ L, hh, not W + W

Heavy Scalars: Φ P : e + e, q q Φ P h, Φ P hz L Φ ± : e + e, q q Φ + W L, Φ± W LZ L Φ ±± : e e ννφ, Φ ±± W L W L Φ 0 : e + e, q q Z LΦ, Φ Z LZ L, hh, not W + W Heavy Quarks: T production @ LHC: bq T q Decay T W + L b, th, tz Perelstein/Peskin/Pierce, 2003 Total cross section BRs (limit g 0): Γ T = m T λ 2 T /(16π) Γ(T th) Γ(T tz) 1 2 Γ(T bw + ) m T λ 2 T 64π Determination of m T, λ T

Reconstruction of LHM Kilian/JR, 2003; Han et al., 2005 How to unravel the structure of LHM @ colliders? Symmetry structure Quadr. Div. Cancell. Nonlinear Goldstone boson structure

Reconstruction of LHM Kilian/JR, 2003; Han et al., 2005 How to unravel the structure of LHM @ colliders? Symmetry structure Quadr. Div. Cancell. Nonlinear Goldstone boson structure SIGNALS: Anom. Triple Gauge Couplings: W W Z, W W γ Anom. Higgs Coupl.: H(H)W W, H(H)ZZ Anom. Top Couplings: ttz, tbw Direct Search (LHC) M V, F, c, c Vectors: ILC: Contact Terms e + e l + l, [ν νγ] M B 10[5] TeV Higgsstr., WW fusion: HZff, HW ff angular distr./energy dependence f (1/3) V J Check from TGC (ILC: per mil precision), GigaZ f (3) JJ Combining Determination of all coefficients in the gauge sector

Scalars: Affected by scalars and vectors T, f (1) V V, B known (λ 2φ /M 2 φ) 2 Higgsstr., W W fusion Higgs coupl., f (3) V V Higgs BRs f (1) V V, f (3) V V ; (take care of t) Goldstone contr. Evidence for nonlinear nature f (3) V V HH production f h,3 (difficult!) LHC ILC 1-2 % accuracy @ Higgs measurements Reconstruction of scalar sector up to F 2 TeV Direct production @ LHC Top: t t production f V q, v t, a t; accuracy 1-2 % tbw from t decays, single t production g tth/g bbh anom. Yukawa coupl. f hq, nonlin. structure w. 2.5% accuracy

Pseudo Axions in LHM Kilian/Rainwater/JR, 2004 broken diagonal generator: η in QCD; couples to fermions as a pseudoscalar, behaves as a axion analogous particles: techni-axion, topcolor-axion, (N)MSSM-axion QCD-(PQ) axion: α s L Ax. = 1 Λ 8π A 2 g ηg Gµν µν, Gµν = 1 2 ɛµνρσ G ρσ Anomalous U(1) η : explicit symmetry breaking m η and g ηγγ independent axion bounds not applicable no new hierarchy problem m η v 250 GeV η EW singlet, couplings an to SM particles v/f suppressed

Example: Simple Group Model Scalar Potential: µφ 1 Φ 2 + h.c. + Coleman-Weinberg pot.: m η = κ µ 2 µ m 2 H = 2(δm 2 + m 2 η)

Example: Simple Group Model Scalar Potential: µφ 1 Φ 2 + h.c. + Coleman-Weinberg pot.: m η = κ µ 2 µ m 2 H = 2(δm 2 + m 2 η) 1 b b BR [η] new Higgs decays (H Zη, H ηη) 0.1 τ + τ BR(H ηη) < 10 4 [ 5 10% OSG] 0.01 0.001 10 4 c c gg γγ µ + µ Zh 50 100 150 200 250 300 m η [GeV] m H [GeV] m η [GeV] BR(Zη) 341 223 0.1 % 375 193 0.5 % 400 167 0.8 % 422 137 1.0 % 444 96 1.2 % 464 14 1.4 %

Pseudo Axions at LHC and ILC LHC: Gluon Fusion (axial U(1) η anomaly), Peak in diphoton spectrum

Pseudo Axions at LHC and ILC LHC: Gluon Fusion (axial U(1) η anomaly), Peak in diphoton spectrum ILC: associated production 1 0.1 σ tot [fb] e + e t tη s = 1 TeV Problem: Cross section vs. bkgd. 10 4 1000 e e + t tb b #evt/2 GeV s = 800 GeV L = 1 ab 1 g ttη = 0.2 0.01 g ttη = 0.1 0.2 0.5 100 10 m η = 50 GeV 100 150 0.001 0 100 200 300 400 500 m η [GeV] 0 50 100 150 M inv (b b) [GeV] Possibility: Z Hη (analogous to A in 2HDM) Kilian/JR/Rainwater (in prep.)

Pseudo Axions at the Photon Collider Photon Collider as precision machine for Higgs physics (s channel resonance, anomaly coupling) S/B analogous to LC η in the µ model with (almost) identical parameters as A in MSSM ( Mühlleitner et al. (2001) )

Pseudo Axions at the Photon Collider Photon Collider as precision machine for Higgs physics (s channel resonance, anomaly coupling) 10 1 σ eff (γγ η, H) [pb] 0.1 S/B analogous to LC η in the µ model with (almost) identical parameters as A in MSSM ( Mühlleitner et al. (2001) ) 0.01 0.001 H (SM) H (with T) η [T] η [1 complete heavy gen.] η [3 gen. of heavy quarks] η [3 complete heavy gen.] 100 200 300 400 500 600 700 m H, m η [GeV]

g bbη = 0.4 g bbh m η 100 130 200 285 Γ γγ [kev] 0.15 0.27 1.1 3.6 1400 1200 1000 800 600 400 γγ (H, η) b b #evt/2 GeV m η = 100 GeV see = 200 GeV Lee = 400 fb 1 cos(θ) T < 0.76 p z / s ee < 0.1 200 130 0 80 100 120 140 160 M inv (b b) [GeV] 10 4 1000 100 10 γγ (H, η) b b #evt/2 GeV see = 500 GeV Lee = 1 ab 1 cos(θ) T < 0.76 p z / s ee < 0.04 m η = 200 GeV 285 100 200 300 400 M inv (b b) [GeV]

T parity and Dark Matter Cheng/Low, 2003; Hubisz/Meade, 2005 T parity: T a T a, X a X a, automorphism of coset space analogous to R parity in SUSY, KK parity Bounds on f relaxed, but: pair production! Lightest T -odd particle (LTP) Candidate for Cold Dark Matter Littlest Higgs: A LTP W, Z 650 GeV Φ 1 TeV T, T 0.7-1 TeV Annihilation: A A h W W, ZZ, hh 500 400 M H (GeV) 300 200 f M A (GeV) H 108 144 180 216 252 288 0/10/50/70/100 100 600 800 1000 1200 1400 1600 1800 2000 f (GeV)

Conclusions Little Higgs elegant alternative to SUSY structure stabilizes EW scale Gauge/Global Symmetry Generics: new heavy gauge bosons, scalars, quarks Little Higgs in accord w EW precision observ. w/o Fine Tuning (M H!) New developments: Pseudo-Axions, T -parity, LH Dark Matter UV embedding, GUT, Flavor? Clear experimental signatures: direct search [Gauge & Top sector, LHC (ILC)] precision observables [Gauge, Scalar, Top sector ILC (LHC)] Strategy for Reconstruction by Complementarity of ILC & LHC