Little Higgs Models Status and Concepts

Transcription

1 1/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Little Higgs Models Status and Concepts Jürgen Reuter DESY JRR/Shim, in preparation; JRR/Tonini/de Vries, JHEP 1402 (2014) 053; arxiv: ; JRR/Tonini, JHEP 1302 (2013) 077; Kilian/JRR/Rainwater PRD 74 (2006), ; PRD 71 (2005), ; Kilian/JRR PRD 70 (2004), Heräus Seminar "Understanding the LHC", Bad Honnef,

2 0 1/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Standard Model Triumph: 2012: Discovery of a Higgs boson Local p Observed p 0 Expected p 0 Observed p 0 Expected p 0 (category) (category) (inclusive) (inclusive) ATLAS Preliminary H γγ Data 2011, s = 7 TeV 1 Ldt = 4.8 fb Data 2012, s = 8 TeV 1 Ldt = 20.7 fb [GeV] m H 1 2σ 3σ 4σ 5σ 6σ 7σ [1/GeV] CMS Preliminary, s = 7-8 TeV, L = 24.3 fb eµ, eτ h, µτ h, τ h τ h H(125 GeV) ττ Data - Background Bkg. Uncertainty Events / 2 GeV Events Fitted bkg s = 7 TeV, Ldt = 4.8 fb 1 s = 8 TeV, Ldt = 20.7 fb Selected diphoton sample Data Sig+Bkg Fit (m =126.8 GeV) H Bkg (4th order polynomial) ATLAS H γγ Preliminary m γγ [GeV] ττ S/B Weighted dn/dm m ττ [GeV] H(125 GeV) ττ observed 400 Z ττ tt electroweak 200 QCD [GeV] m ττ

3 2/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Electroweak vacuum stability Recent analysis: Metastable vacuum with lifetime longer than the age of the universe Bezrukov et al., , Degrassi et al., arxiv: Top mass Mt in GeV Instability Meta stability Stability Non perturbativity Pole top mass Mt in GeV Instability ,2,3 Σ Meta stability Stability h h Hierarchy problem: why Higgs mass at electroweak scale? Fine-tuning of quadratic Higgs mass operator?

4 3/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Higgs as Pseudo-Goldstone boson Nambu-Goldstone Theorem: For each spontaneously broken global symmetry generator there is a massless boson in the spectrum. Old idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984 Light Higgs as (Pseudo)-Goldstone boson of a spontaneously broken global symmetry O(1 GeV) O(150 MeV) v Λ Analogous: QCD Scale Λ: chiral symmetry breaking, quarks, SUp3q c Scale v: pions, kaons,...

5 3/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Higgs as Pseudo-Goldstone boson Nambu-Goldstone Theorem: For each spontaneously broken global symmetry generator there is a massless boson in the spectrum. Old idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984 Light Higgs as (Pseudo)-Goldstone boson of a spontaneously broken global symmetry O(1 TeV) O(250 GeV) v Λ Scale Λ: global symmetry breaking, new particles, new (gauge) IA Scale v: Higgs, W {Z, l,... Without Fine-Tuning: experimentally excluded

6 4/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Collective symmetry breaking and 3-scale models Collective symmetry breaking: Arkani-Hamed/Cohen/Georgi/Nelson/..., different global symmetries; one of them unbroken ñ Higgs exact Goldstone boson Coleman-Weinberg: boson masses by radiative corrections, but: m H only at 2-loop level m H g 1 g 2 4π 4π Λ O(10 TeV) O(1 TeV) O(250 GeV) F v Λ Scale Λ: global SB, new IA Scale F : Pseudo-Goldstone bosons, new vectors/fermions Scale v: Higgs, W {Z, l,...

7 5/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Characteristics and Spectra O( 10 TeV) O(1 TeV) O(250 GeV) F v Λ Scale Λ: hidden sector, symmetry breaking Scale F : new particles Scale v: h, W {Z, l,... Terascale: new particles to stabilize the hierarchy SUSY H, A H ± q L t b2 2 q R b1 t 1 χ 0 4, χ± 2 M[TeV] 1.25 g χ Φ Φ ±± Φ ± Φ P Z γ Little Higgs W ± T U, C h τ 2 ν l τ 1 ll lr χ 0 2, χ± 1 t χ h η W ± Z t

8 6/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Generic properties of Little-Higgs models Extended global symmetry (extended scalar sector) Specific functional form of the potential Extended gauge symmetry: γ 1 A H, Z 1 Z H, W 1 W H New heavy fermions: T, but also U, C,... Product Group Models (e.g. Littlest Higgs) H H 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 Simple Group Models (e.g. Simplest Little Higgs) H 1 H 1 H 2 H 2 H 1 h H 2 G diag G

9 6/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Generic properties of Little-Higgs models Extended global symmetry (extended scalar sector) Specific functional form of the potential Extended gauge symmetry: γ 1 A H, Z 1 Z H, W 1 W H New heavy fermions: T, but also U, C,... Product Group Models (e.g. Littlest Higgs) Moose Models (e.g. Minimal Moose Model) H H /H 1 /H 2 /H 3 /H 4 /H 5 /Hn 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 /G 1 /G 2 /G 3 /G 4 /Gn

10 7/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Prime Example: Simple Group Model enlarged gauge group: SUp3q ˆ Up1q; globally Up3q Ñ Up2q Two nonlinear Φ representations L D µ Φ 1 2 ` D µ Φ 2 2 Φ 1{2 exp i f j 2{1 Θ f 1{2 0 0 f 1{2 Θ 1 a f 2 1 ` f2 2 η 0 0 η Coleman-Weinberg mechanism: Radiative generation of potential h T h η ` g2 ` Φ 16π 2 Λ2 1 2 ` Φ 2 2 g2 16π 2 f 2

11 7/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Prime Example: Simple Group Model enlarged gauge group: SUp3q ˆ Up1q; globally Up3q Ñ Up2q Two nonlinear Φ representations L D µ Φ 1 2 ` D µ Φ 2 2 Φ 1{2 exp i f j 2{1 Θ f 1{2 0 0 f 1{2 Θ 1 a f 2 1 ` f2 2 η 0 0 η Coleman-Weinberg mechanism: Radiative generation of potential h T h η ` g2 ` Φ 16π 2 Λ2 1 2 ` Φ 2 2 g2 16π 2 f 2 but: Φ : 1 Φ 1 Φ : 2 Φ 2 g4 16π 2 log ˆΛ2 µ 2 Φ : 1 Φ 2 2 ñ g4 16π 2 log ˆΛ2 µ 2 f 2 ph : hq

12 8/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Cancellations of Divergencies in Yukawa sector 9 ż λ t λ t ` λt λ T ` λ T {F d 4 k p2πq 4 1 k 2 pk 2 m 2 T q! λ 2 t pk 2 m 2 T q ` k 2 λ 2 T mt F λ T k 2 ) Little Higgs global symmetry imposes relation m T F λ2 t ` λ 2 T λ T ùñ Quadratic divergence cancels Collective Symm. breaking: λ t 9λ 1 λ 2, λ 1 0 Φ 2 Φ 2 or λ 2 0 ñ SUp3q Ñ Ψ Q Ψ Q λ2 1λ 2 2 ˆΛ2 rsup3qs 2 16π 2 log µ 2 Φ : 1 Φ 2 2 Φ 1 u c 1 u c 2 Φ 1

13 9/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, T parity & Dark Matter Cheng/Low, 2003; Hubisz/Meade, 2005; Wang/Yang/Zhu, 2013 T parity: T a Ñ T a, X a Ñ X a, automorphism of coset space analogous to R parity in SUSY, KK parity in extra dimensions Bounds on F MUCH relaxed, F TeV but: Pair production!, typical cascade decays Lightest T -odd particle (LTP) ñ Candidate for Cold Dark Matter Littlest Higgs: A 1 LTP W 1, Z GeV, Φ 1 TeV T, T TeV Annihilation: A 1 A 1 Ñ h Ñ W W, ZZ, hh Hubisz/Meade, M H (GeV) f M A H (GeV) /10/50/70/ f (GeV)

14 9/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, T parity & Dark Matter Cheng/Low, 2003; Hubisz/Meade, 2005; Wang/Yang/Zhu, 2013 T parity: T a Ñ T a, X a Ñ X a, automorphism of coset space analogous to R parity in SUSY, KK parity in extra dimensions Bounds on F MUCH relaxed, F TeV but: Pair production!, typical cascade decays Lightest T -odd particle (LTP) ñ Candidate for Cold Dark Matter Littlest Higgs: A 1 LTP W 1, Z GeV, Φ 1 TeV T, T TeV Annihilation: A 1 A 1 Ñ h Ñ W W, ZZ, hh Wang/Yang/Zhu, 2013 Relic density/si cross section M=M H -M AH (GeV) f (GeV) c h M AH (GeV)

15 9/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, T parity & Dark Matter Cheng/Low, 2003; Hubisz/Meade, 2005; Wang/Yang/Zhu, 2013 T parity: T a Ñ T a, X a Ñ X a, automorphism of coset space analogous to R parity in SUSY, KK parity in extra dimensions Bounds on F MUCH relaxed, F TeV but: Pair production!, typical cascade decays Lightest T -odd particle (LTP) ñ Candidate for Cold Dark Matter Littlest Higgs: A 1 LTP W 1, Z GeV, Φ 1 TeV T, T TeV Annihilation: A 1 A 1 Ñ h Ñ W W, ZZ, hh Wang/Yang/Zhu, 2013 σ SI ( cm 2 ) f (GeV) LHT-A best point XENON100(2012) XENON1T(2017) Relic density/si cross section 10-3 T parity Simplest LH: pseudoscalar η LTP M (GeV) A H Z 1 remains odd: good or bad (?) Martin, 2006; JRR/Tonini, 2014 T parity might be anomalous (???) Hill/Hill, 2007

16 10/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Constraints on Little Higgs Models How to constrain a generic model in HEP? direct searches of resonances electroweak precision tests flavour constraints nowadays: Higgs sector Higgs sector is the key to understand EW-scale physics (and beyond?)

17 11/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Statistical analysis We considered the three most popular Little Higgs models: Simplest Little Higgs (SLH) Schmaltz Littlest Higgs (L 2 H) Arkani-Hamed et al. Littlest Higgs with T-parity (LHT) Low et al. and realized a χ 2 analysis on their parameter spaces, taking into account the whole set of 7+8 TeV Higgs searches by ATLAS and CMS, and by fitting 21 different EW Precision Observables: χ 2 ÿ i `Oi O exp 2 i σi 2 where O i depends on the free parameters of the model considered.

18 12/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Data used: Higgs sector the Higgs results are expressed in terms of a signal strength modifier ř p ɛp i σ p µ i ř p ɛp i σsm p BR ph Ñ X i X i q BR ph Ñ X i X i q SM we included in our χ 2 analysis the best-fit values of µ i reported by the Collaborations for all the different 7+8 TeV channels i:

19 13/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Data used: EWPD every extension of SM has to satisfy at least the precision constraints of the electroweak sector: low-energy observables e.g. ν-scattering, parity violation observables... Z-pole observables e.g. m Z, Γ Z, Z-pole asymmetries...

20 14/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, LH Smoking guns Where do the LH corrections to the SM quantities come from? new decay channels of the Higgs, e.g. h Ñ A H A H in LHT modified Higgs couplings with SM fermions and vector bosons # e.g. 2 m2 W v y W h W `W, 1 SM y W 1 ` O `v 2 {f 2 LH interaction terms of Higgs with new fermions/vector bosons e.g. m T v y T h T T modified neutral- and charged-currents e.g. g ÿ c W f m T f, y T O `v 2 {f 2 SM fγ µ pg L ` δg L qp L ` pgr SM ` δg R qp R f Z µ

21 15/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Partial Higgs widths in LH 1-loop decays Γph Ñ ggq LH α2 sm 3 h 32π 3 v 2 ˇˇˇ Γph Ñ γγq LH ÿ f,col α 2 m 2 ÿ h ˇˇˇ 256π 3 v 2 f,ch 1 2 F 1 2 px f q y f ˇˇˇ2 4 2 F 1 px f q y 2 f ` ÿ F 1 px v q y v ` ÿ F 0 px s q y sˇˇˇ2 v,ch s,ch where x i 4m2 i, F m 2 i px i q are loop functions, y i the modified Yuk. coupl. h ñ tree-level decays narrow-width approximation: σ LH σ SM pgg Ñ hq Γph Ñ ggq LH Γph Ñ ggq SM where g hv V m2 V v Γph Ñ V V q LH Γph Ñ V V q SM ˆghV V g SM Γph Ñ f fq LH Γph Ñ f fq SM ˆghff g SM hff y V and g hff m f v y f hv V 2 2

22 16/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, SLH results JRR/Tonini, JHEP 1302 (2013) 077; JRR/Tonini/de Vries, JHEP 1402 (2014) 053 free parameters: f SSB scale, t β ratio of vevs of scalar fields φ 1, TeV, translates into lower bounds on new states masses, e.g. f 99% min m W 1 Á 1.35 TeV m T Á 2.81 TeV min. required fine tuning: 1%, defined as δµ2 µ 2 obs results mainly driven by EWPD χ 2 min {d.o.f χ 2 SM {d.o.f includes all run I data

23 17/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, L 2 H results JRR/Tonini, JHEP 1302 (2013) 077; JRR/Tonini/de Vries, JHEP 1402 (2014) 053 free parameters: f SSB scale, c mixing angle in gauge sector 3.20 TeV, translates into lower bounds on new states masses, e.g. f 99% min m W 1 Á 2.13 TeV m T Á 4.50 TeV min. required fine tuning: 0.1%, defined as δµ2 µ 2 obs results mainly driven by EWPD χ 2 min {d.o.f χ 2 SM {d.o.f includes data run I data Exclusion gets weaker by Higgs data (d.o.f.)!

24 17/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, L 2 H results JRR/Tonini, JHEP 1302 (2013) 077; JRR/Tonini/de Vries, JHEP 1402 (2014) 053 free parameters: f SSB scale, c mixing angle in gauge sector 3.20 TeV, translates into lower bounds on new states masses, e.g. f 99% min m W 1 Á 2.13 TeV m T Á 4.50 TeV min. required fine tuning: 0.1%, defined as δµ2 µ 2 obs results mainly driven by EWPD χ 2 min {d.o.f χ 2 SM {d.o.f includes data run I data Exclusion gets weaker by Higgs data (d.o.f.)!

25 18/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, LHT: Littlest Higgs with T parity Goldstone boson matrix: Σ e 2 i Π{f Π? 1 0 H? 2Φ H : 0 H t 2? 2Φ : H 0 Discrete T parity: ˆ? 2φ`` Φ9 φ` T : Π Ñ Ω Π Ω Ω diagp1, 1, 1, 1, 1q φ` φ 0 ` i φ P V CW λ φ 2f 2 Trpφ : φq ` iλ hφh f Hφ : : H t H φh µ 2 HH : ` λ h 4pHH : q 2` ` λ hφφh Hφ : φh : ` λ h 2 φ 2 HH: Trpφ : φq ` λ φ 2 φ 2 Trpφ : φqı 2 ` λφ 4 Trpφ : φφ : φq. λ φ 2 2pg 2 ` g 1 2 q ` 8λ 2 1 λ h λ φ 2 λ hφφh 4 3 λ φ 2 λ h 2 φ 2 16 λ2 1 λ φ pg2 ` g 1 2 q ` 16 3 λ2 1 Yukawa couplings k, R λ 1 {λ 2 L k kf Ψ2 ξψ c ` Ψ 1 xσyωξ : ΩΨ c m q ū 1 c u c m q d1 c d c m χ χ 1 c χ c + h.c. L t λ1f ` 2? 2 ɛ ijk ɛ xy Ψ1,t i Σ jx Σ ky ` ı Ψ2,t xσy i Σ1 jx Σ1 ky t 1 R λ 2f ` TL1 T R1 ` T L2 T R2

26 19/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, LHT results JRR/Tonini, JHEP 1302 (2013) 077; JRR/Tonini/de Vries, JHEP 1402 (2014) 053 free parameters: f SSB scale, R ratio of Yukawa couplings in top sector GeV, translates into lower bounds on new states masses, e.g. f 99% min m W 1 Á GeV m T Á GeV min. required fine tuning: 10%, defined as δµ2 µ 2 obs χ 2 min {d.o.f χ 2 SM {d.o.f results mainly driven by EWPD (see next slide) EWPT ñ f Á 405 GeV

27 20/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Higgs data vs. EWPD the shape of result driven by EW constraints (much smaller uncertainties) Higgs data only: for v{f Á 0.6 decay h Ñ A HA H open and dominant Higgs data only: subdominant dependence on R w.r.t. f is a consequence of the Collective Symmetry Breaking mechanism EWPT and Higgs data ñ f Á 694 GeV

28 21/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct searches: Drell-Yan and Vector-Like Quarks Reach in the gauge boson sector: depends on mixing angle

29 22/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct Searches: Focus on LHT Defining two benchmark scenarios: 1. heavy quarks

30 22/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct Searches: Focus on LHT Defining two benchmark scenarios: 2. heavy top/vectors

31 22/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct Searches: Focus on LHT Defining two benchmark scenarios: 1. k 1.5, 2. k 0.4

32 23/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Branching Ratios Decay patterns: Particle Decay BR k 1.0 BR k 0.4 l H ν H W ν H 62% 0% Z H l 31% 0% A H l 6% 100% W l 61% 0% H Z H ν 30% 0% A H ν 9% 100% T ` H W ` b 46% 45% Z t 22% 22% H t 21% 21% T H A H 11% 11% A H stable Z H A H H 100% 2% d H d 0% 41% u H u 0% 30% l 0% 14% H ν H ν 0% 14% Particle Decay BR k 1.0 BR k 0.4 d H W u 62% 0% H Z H d 30% 0% A H d 6% 100% u H W ` d 58% 0% H Z H u 30% 0% A H u 9% 100% T H A H t 100% 100% Z H t 0% 0% Φ 0{P A H H 100% 100% Φ A H W 100% 100% Φ A H pw q 2 100% 96% W H A H W 100% 2% u H d 0% 44% d H u 0% 27% l ν H 0% 16.5% ν H l 0% 16.5%

33 24/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Cross Sections (I) Heavy Quarks Heavy Top and Vectors

34 25/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Channels and signatures: Parameters final state leptons # jets {E T modes params 0 1 q H A H f, k 0 2 q H q H f, k 0 3 q H W H 0 4 q H q H W H W H W H Z H Z H Z H f, k f, k f, k f, k f, k 0 4 T `q f, k, R 0 5 q H W H 0 6 q H q H T T f, k f, k f, k, R final state leptons # jets {E T l 2 l 3 l 4 modes W H W H W H Z H q H q H q H W H T `q q H q H T T l`l 0 W H W H l`l 1 q H W H l`l 2 q H q H T T params f, k f, k f, k f, k f, k, R f, k f, k, R f, k f, k f, k f, k, R l l 2 q H q H f, k

35 26/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Channels and signatures (I) # l final state production σ 8 TeV ˆ Br pfbq σ 14 TeV ˆ Br pfbq # jets {E T modes k 1.0 k 0.4 k 1.0 k q H A H ˆ ˆ q H q H ˆ ˆ q H W H q H Z H q H q H ˆ ˆ10 3 W H W H 1.9 low 9.1 low W H Z H 4.8 low 23 low Z H Z H 0.56 low 3.0 low 0 4 T `q q H W H q H Z H q H q H ˆ ˆ ˆ10 3 T T

36 27/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Channels and signatures (II) # l final state production σ 8 TeV ˆ Br pfbq σ 14 TeV ˆ Br pfbq # jets {E T modes k 1.0 k 0.4 k 1.0 k 0.4 l 2 l 3 l 4 q H q H ˆ ˆ10 3 W H W H 0.77 low 3.9 low W H Z H 2.1 low 10 low T `q q H W H q H Z H q H q H ˆ ˆ10 3 T T l`l 0 W H W H 0.32 low 1.7 low l`l 1 q H W H l`l 2 q H q H T T l l 2 q H q H

37 28/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Recasting results 95% CL from Monojets + {E T from LHC8 JRR/Tonini/deVries, hard jet, {E T, no leptons, 2nd jet w. p T ą 30 GeV signal regions: ATLAS pp T, {E T q ą 120/220/350/500 GeV, CMS: {E T ą 250/300/350/400/450/500/550 GeV Dijet suppression: ATLAS φp {E T, j 2q ą 0.5, CMS φpj 1, j 2q ă 2.5 pp Ñ q H q H, pp Ñ q H A H

38 29/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Recasting results 95% CL from Jets + {E T from LHC8 ě 2 hard jets, {E T, no leptons signal regions: ATLAS {E T ą 200/300/350 GeV, CMS: JRR/Tonini/deVries,2013 pn j, N b q p2 3, 0q; p2 3, 1 2q; pě 4, 1 2q; pě 4, 0q; pě 4, ě 2q QCD suppression: ATLAS φp {E T, j 2q ą 0.5, {E T {m eff, CMS φpj 1, j 2q ă 2.5 pp Ñ q H q H Ñ pja H qpja H q

39 30/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Recasting results JRR/Tonini/deVries, % CL from Leptons + Jets + {E T from LHC8 single isolated lepton, ě 2 hard jets, {E T, signal regions: ATLAS {E T ą 200/300/350 GeV Cuts: {E T ą 250 GeV, m T pl, {E T q ą 250 GeV, {E T {m eff ą 0.2, m inc eff ą 800 GeV pp Ñ q H q H with q H Ñ W H q, Z H q, t H Ñ ta H, Z H Ñ HA H

40 31/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Combined analysis JRR/Tonini/deVries,2013 Operator bounds: O 4-f k2 ψ 128 π 2 f 2 L γ µ ψ L ψ1 L γ µψl 1 ` O ` g k Hubisz/Meade/Noble/Perelstein, 2005 Bound from combined analysis: f Á 638GeV

41 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Conclusions Little Higgs (composite) models are appealing solution of hierarchy problem, alternative to weakly coupled solutions like SUSY most of the parameter space of three popular Little Higgs models is still compatible at 99% CL with LHC run I+II data Electroweak precision data represent still the most severe constraints! Fine-tuning as a guideline to understand the naturalness of a model: Little Higgs models require a minimum level of 10% of fine tuning Limits on the LHT: 1. EWPO: f Á 405 GeV@95% CL

42 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Conclusions Little Higgs (composite) models are appealing solution of hierarchy problem, alternative to weakly coupled solutions like SUSY most of the parameter space of three popular Little Higgs models is still compatible at 99% CL with LHC run I+II data Electroweak precision data represent still the most severe constraints! Fine-tuning as a guideline to understand the naturalness of a model: Little Higgs models require a minimum level of 10% of fine tuning Limits on the LHT: 1. EWPO: f Á 405 GeV@95% CL 2. Higgs: f Á 607 GeV@95% CL

43 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Conclusions Little Higgs (composite) models are appealing solution of hierarchy problem, alternative to weakly coupled solutions like SUSY most of the parameter space of three popular Little Higgs models is still compatible at 99% CL with LHC run I+II data Electroweak precision data represent still the most severe constraints! Fine-tuning as a guideline to understand the naturalness of a model: Little Higgs models require a minimum level of 10% of fine tuning Limits on the LHT: 1. EWPO: f Á 405 GeV@95% CL 2. Higgs: f Á 607 GeV@95% CL 3. Higgs+EWPO: f Á 694 GeV@95% CL

44 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Conclusions Little Higgs (composite) models are appealing solution of hierarchy problem, alternative to weakly coupled solutions like SUSY most of the parameter space of three popular Little Higgs models is still compatible at 99% CL with LHC run I+II data Electroweak precision data represent still the most severe constraints! Fine-tuning as a guideline to understand the naturalness of a model: Little Higgs models require a minimum level of 10% of fine tuning Limits on the LHT: 1. EWPO: f Á 405 GeV@95% CL 2. Higgs: f Á 607 GeV@95% CL 3. Higgs+EWPO: f Á 694 GeV@95% CL 4. Direct searches: f Á 638 GeV@95% CL

45 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Conclusions Little Higgs (composite) models are appealing solution of hierarchy problem, alternative to weakly coupled solutions like SUSY most of the parameter space of three popular Little Higgs models is still compatible at 99% CL with LHC run I+II data Electroweak precision data represent still the most severe constraints! Fine-tuning as a guideline to understand the naturalness of a model: Little Higgs models require a minimum level of 10% of fine tuning Limits on the LHT: 1. EWPO: f Á 405 GeV@95% CL 2. Higgs: f Á 607 GeV@95% CL 3. Higgs+EWPO: f Á 694 GeV@95% CL 4. Direct searches: f Á 638 GeV@95% CL Omitted discussion of the 750 GeV impostor

46 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Conclusions Little Higgs (composite) models are appealing solution of hierarchy problem, alternative to weakly coupled solutions like SUSY most of the parameter space of three popular Little Higgs models is still compatible at 99% CL with LHC run I+II data Electroweak precision data represent still the most severe constraints! Fine-tuning as a guideline to understand the naturalness of a model: Little Higgs models require a minimum level of 10% of fine tuning Limits on the LHT: 1. EWPO: f Á 405 GeV@95% CL 2. Higgs: f Á 607 GeV@95% CL 3. Higgs+EWPO: f Á 694 GeV@95% CL 4. Direct searches: f Á 638 GeV@95% CL Omitted discussion of the 750 GeV impostor Eagerly awaiting the analysis of run II data

47 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Maybe the world is fine tuned...

48 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef,

49 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct Searches Heavy Quark States EW single dominates QCD pair production: Perelstein/Peskin/Pierce, 03

50 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct Searches Heavy Quark States EW single dominates QCD pair production: Perelstein/Peskin/Pierce, 03 Characteristic branching ratios : ΓpT Ñ thq «ΓpT Ñ tzq «1 2 ΓpT Ñ bw `q «M T λ 2 T 64π, Γ T GeV Proof of T as EW singlet; but: T Ñ Z 1 T, W 1 b, tη! AIM: Determination of M T, λ T, λ T 1 λ T 1 indirect (T T h impossible)

51 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, T Ñ Zt Ñ l`l lνb SN-ATLAS {E T ą 100 GeV, lll, p T ą 100{30 GeV, b, p T ą 30 GeV Bkgd.: W Z, ZZ, btz Observation for M T À 1.4 TeV -1 Events/40 GeV/300 fb ATLAS Invariant Mass (GeV)

52 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, T Ñ W b Ñ lνb SN-ATLAS {E T ą 100 GeV, l, p T ą 100 GeV, b, p T ą 200 GeV, max. jj, p T ą 30 GeV Bkgd.: t t, W b b, single t Observation for M T À 2.5 TeV -1 Events/40 GeV/300fb ATLAS Invariant Mass (GeV)

53 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, T Ñ th Ñ lνbbb SN-ATLAS l, p T ą 100 GeV, jjj, p T ą 130 GeV, at least 1 b-tag Bkgd.: t t, W b b, single t Events/30 GeV/300 fb ATLAS Observation for M T À 2.5 TeV Mass(jjjeν) (GeV)

54 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, T Ñ th Ñ lνbbb SN-ATLAS l, p T ą 100 GeV, jjj, p T ą 130 GeV, at least 1 b-tag Bkgd.: t t, W b b, single t Events/30 GeV/300 fb ATLAS Observation for M T À 2.5 TeV Mass(jjjeν) (GeV) Additional heavy quarks (Simple Group Models): U, C or D, S 05 Han et al., Large cross section: u or d PDF Huge final state l charge asymmetry Good mass reconstruction

55 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, T Ñ th Ñ lνbbb SN-ATLAS l, p T ą 100 GeV, jjj, p T ą 130 GeV, at least 1 b-tag Bkgd.: t t, W b b, single t Events/30 GeV/300 fb ATLAS Observation for M T À 2.5 TeV Mass(jjjeν) (GeV) Additional heavy quarks (Simple Group Models): U, C or D, S 05 Han et al., l + ν Large cross section: u or d PDF Huge final state l charge asymmetry q W + Q forward jet q Good mass reconstruction high p T jet

56 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, T Ñ th Ñ lνbbb SN-ATLAS l, p T ą 100 GeV, jjj, p T ą 130 GeV, at least 1 b-tag Bkgd.: t t, W b b, single t Events/30 GeV/300 fb ATLAS Observation for M T À 2.5 TeV Mass(jjjeν) (GeV) Additional heavy quarks (Simple Group Models): U, C or D, S 05 Han et al., Large cross section: u or d PDF Huge final state l charge asymmetry Good mass reconstruction

57 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct Searches Heavy Vectors Drell-Yan Production: Tevatron Limits GeV Dominant decays: Product group: Z 1 Ñ Zh, W W, W 1 Ñ W h, W Z Simple group: Z 1 Ñ qq, X Ñ ff

58 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct Searches Heavy Vectors Drell-Yan Production: Tevatron Limits GeV Dominant decays: Product group: Z 1 Ñ Zh, W W, W 1 Ñ W h, W Z Simple group: Z 1 Ñ qq, X Ñ ff

59 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct Searches Heavy Vectors Drell-Yan Production: Tevatron Limits GeV Dominant decays: Product group: Z 1 Ñ Zh, W W, W 1 Ñ W h, W Z Simple group: Z 1 Ñ qq, X Ñ ff Discovery channel: Z 1 Ñ ll, W 1 Ñ lν Γ Z GeV, Γ X GeV

60 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct Searches Heavy Vectors Drell-Yan Production: Tevatron Limits GeV Dominant decays: Product group: Z 1 Ñ Zh, W W, W 1 Ñ W h, W Z Simple group: Z 1 Ñ qq, X Ñ ff Discovery channel: Z 1 Ñ ll, W 1 Ñ lν Γ Z GeV, Γ X GeV Events/10 GeV/100 fb Z H cotθ=1.0 Z H cotθ=0.2 ATLAS Drell-Yan m ee (GeV) Events/20 GeV/100 fb ATLAS W H cotθ=0.2 W H cotθ=0.5 Drell-Yan top m T (GeV)

61 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Direct Searches Heavy Scalars Generally: Large model dependence no states complex singlet complex triplet Littlest Higgs, complex triplet: Φ 0, Φ P, Φ, Φ Cleanest channel: q q Ñ Φ``Φ Ñ llll: Killer: PS W W -Fusion: dd Ñ uuφ`` Ñ uuw `W ` 2 hard forward jets, hard close l`l` p T -unbalanced 0 Events/100 GeV/300 fb ATLAS m Φ = 1 TeV m T (GeV) Alternative: Model-Independent search in W W fusion: ILC: Beyer/Kilian/Krstonosic/Mönig/JRR/Schmidt/Schröder, 2006 LHC: Alboteanu/Kilian/JRR, 2008; Kilian/JRR/Sekulla, 2013

62 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Pseudo-Axions in Little Higgs Kilian/Rainwater/JRR, 2004, 2006; JRR, 2007 gauged Up1q group: Z 1 ÐÑ ungauged: η couples to fermions like a pseudoscalar m η À 400 GeV SM singlet, couplings to SM particles v{f suppressed η axion-like particle: BR [η] b b τ + τ c c gg γγ µ + µ Zh mη [GeV] Anomalous Up1q: ÝÑ 1 F α s 8π 2 ηf µν F ρσ ɛ µνρσ U p1q explicitly broken ñ Axion limits from astroparticle physics not applicable

63 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Classification of Axions in Little Higgs Models Number of Pseudo-Axions: n g l Mismatch between global (g) and local rank reduction (l) Product Group Models Arkani-Hamed,... Doubling of electroweak gauge group: SUp2q ˆ SUp2q Ñ SUp2qL, Up1q ˆ Up1q Ñ Up1q Y (latter not necessary) ñ l 1 Littlest Higgs, g: SUp5q Ñ SOp5q ñ n p4 2q 1 1 antisymmetric, g: Spp6q{SOp6q, n p3 2q 1 0 Simple Group Models Kaplan,Schmaltz,... Simple gauge group: SUpNq ˆ Up1q Ñ SUp2q ˆ Up1q ñ l N 2 Higgs is distributed over several global symmetry multiplets Simplest Little Higgs, g: rsup3qs 2 {rsup2qs 2 n g l Original Simple Group Model, g: rsup4qs 3 {rsup3q 3 ˆ SUp2qs, l: SUp4q Ñ SUp2q n g l Deconstructed Models Arkani-Hamed,... Minimal Moose: g rsup3qs 4 Ñ SUp3q, l rsup3q ˆ SUp2qs{SUp2q n g l site model: g rsup2qs 4 {rsup2qs 2, l rsup2qs 2 Ñ SUp2q, n 2 1 1

64 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, ZHη coupling as a discriminator Kilian/Rainwater/JRR, 2006 pseudo-axion: ξ exp riη{f s, Σ exp riπ{f s non-linear representation of the remaining Goldstone multiplet Π L kin. F 2 Tr pd µ pξσq : pd µ pξσqq... 2F pb µ ηq Im Tr pd µ Σq : Σ `Opη 2 q Use special structure of covariant derivatives: D µ Σ B µ Σ ` A a 1,µ `T a 1 Σ ` ΣpT a 1 q T ` A a 2,µ `T a 2 Σ ` ΣpT a 2 q T, Tr pd µ Σq : Σ W a µ Tr Σ : pt a 1 ` T a 2 qσ ` pt a 1 ` T a 2 q 0. Little Higgs mechanism cancels this coupling Simple Group Models: Φ expriσ{f s, ζ p0,... 0, F q T VEV directing in the N direction

65 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, L kin. F 2 D µ pζ : Φ : qd µ pφζq... ` i F pb µηqζ : `Φ : pd µ Φq pd µ Φ : qφ ζ ˆ 0 h Σ h :, V µ 0... ` if pb µ ηq `Φ : pd µ Φq pd µ Φ : qφ N,N. ˆWµ 0 ` heavy vector fields 0 0 V µ ` i F rσ, V µs 1 2F 2 rσ, rσ, V µss `... ˆWµ 0 ` i ˆ 0 Wµ h 0 0 F h : 1 ˆhh : W ` Whh : 0 W µ 0 2F 2 0 2h : `... Wh 1st term cancels by multiple Goldstone multiplets 2st term cancels by EW symmetry 3rd term pb µ ηqh : W µh vhz µb µ η.

66 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, More properties of Pseudo-Axions Take e.g. one specific model: Simplest Little Higgs Schmaltz, 2004 Simple Group Model, two Higgs-triplets with a tan β-like mixing angle 600 mη [GeV] mh [GeV] F2 = 2 TeV mh [GeV] tan β = tan β = tan β = F1 = 0.5 TeV µ [GeV] µ [GeV] tan β 1: heavy Higgs, (very) light pseudoscalar Heavy top decays: Kilian/Rainwater/JRR, µ [GeV]

67 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Discovery of Pseudo-axions Kilian/Rainwater/JRR, 2004, 2006 LHC: Gluon fusion, diphoton signal for m η Á 200 GeV, 7σ possible LHC: T Ñ tη ILC: e`e Ñ t tη

68 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Discovery of Pseudo-axions Kilian/Rainwater/JRR, 2004, 2006 LHC: Gluon fusion, diphoton signal for m η Á 200 GeV, 7σ possible LHC: T Ñ tη ILC: e`e Ñ t tη e e + t tb b #evt/2 GeV m η = 50 GeV 100 s = 800 GeV L = 1 ab 1 g ttη = M inv (b b) [GeV]

69 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Discovery of Pseudo-axions Kilian/Rainwater/JRR, 2004, 2006 LHC: Gluon fusion, diphoton signal for m η Á 200 GeV, 7σ possible LHC: T Ñ tη ILC: e`e Ñ t tη ZHη coupling forbidden in Product Group Models Discriminator of diff. model classes " * H Ñ Zη Ñ llbb gg Ñ η Ñ ZH Ñ llbb, llljj

70 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Discovery of Pseudo-axions Kilian/Rainwater/JRR, 2004, 2006 LHC: Gluon fusion, diphoton signal for m η Á 200 GeV, 7σ possible LHC: T Ñ tη ILC: e`e Ñ t tη ZHη coupling forbidden in Product Group Models Discriminator of diff. model classes " * H Ñ Zη Ñ llbb gg Ñ η Ñ ZH Ñ llbb, llljj

71 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Discovery of Pseudo-axions Kilian/Rainwater/JRR, 2004, 2006 LHC: Gluon fusion, diphoton signal for m η Á 200 GeV, 7σ possible LHC: T Ñ tη ILC: e`e Ñ t tη ZHη coupling forbidden in Product Group Models Discriminator of diff. model classes " * H Ñ Zη Ñ llbb gg Ñ η Ñ ZH Ñ llbb, llljj

72 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Discovery of Pseudo-axions Kilian/Rainwater/JRR, 2004, 2006 LHC: Gluon fusion, diphoton signal for m η Á 200 GeV, 7σ possible LHC: T Ñ tη ILC: e`e Ñ t tη ZHη coupling forbidden in Product Group Models Discriminator of diff. model classes " * H Ñ Zη Ñ llbb gg Ñ η Ñ ZH Ñ llbb, llljj

73 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, η pheno at ILC Kilian/Rainwater/JRR, 2006 If ZHη coupling present: Hη production in analogy to HA: 1.2 σ(e + e Z ηh) [fb] 1.2 σ(e + e Z /Z ηh) [fb] 1 µ = 150 GeV 1 µ = 150 GeV s [GeV] Light pseudoaxion, η Ñ bb, final state Hbb Intermediate range, η Ñ gg, final state Hjj η Ñ ZH: ZHH final state s [GeV] σ(e + e Hη Hb b) [fb] µ = 24 GeV 30 < Mbb < 70 GeV σ(e + e Hη Hjj) [fb] Mjj > 150 GeV σ(e + e η H ZHH) [fb] no Z no Z with Z 0.1 no Z with Z 0.5 with Z 0.2 SM s [GeV] SM s [GeV] SM s [GeV] More detailed insights from photon collider option

74 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, η pheno at ILC Kilian/Rainwater/JRR, 2006 If ZHη coupling present: Hη production in analogy to HA: 1.2 σ(e + e Z ηh) [fb] 1.2 σ(e + e Z /Z ηh) [fb] 1 µ = 150 GeV 1 µ = 150 GeV s [GeV] Light pseudoaxion, η Ñ bb, final state Hbb Intermediate range, η Ñ gg, final state Hjj η Ñ ZH: ZHH final state s [GeV] σ(e + e Hη Hb b) [fb] 0.3 σ(e + e Hη Hjj) [fb] 1.5 σ(e + e η H ZHH) [fb] µ = 97 GeV Mbb > 150 GeV no Z with Z Mjj > 150 GeV no Z with Z no Z with Z 0.2 SM s [GeV] SM s [GeV] SM s [GeV] More detailed insights from photon collider option

75 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Pseudo Axions at the Photon Collider Photon Collider as precision machine for Higgs physics (s channel resonance, anomaly coupling) Z L Z L S/B analogous to LC η in the µ model with (almost) identical parameters as A in MSSM ( ãñ Mühlleitner et al. (2001) )

76 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, 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 Z T Z T S/B analogous to LC η in the µ model with (almost) identical parameters as A in MSSM ( ãñ Mühlleitner et al. (2001) ) H (SM) H (with T) η [T] η [1 complete heavy gen.] η [3 gen. of heavy quarks] η [3 complete heavy gen.] m H, m η [GeV]

77 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, g bbη 0.4 g bbh m η Γ γγ rkevs 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 < M inv (b b) [GeV] 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 M inv (b b) [GeV]

78 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Simplest Little Higgs ( µ Model ) Schmaltz 04, Kilian/Rainwater/JRR 04 Field content (SUp3q c ˆ SUp3q w ˆ Up1q X quantum numbers) Φ 1,2 : p1, 1 3q 3 Ψ Q : p3, 3q 1 3 Ψ l : p1, 1 3q 3 d c : p 3, 1q 1 3 c u 1,2 : p 3, 2 1q 3 e c, n c : p1, 1q 1,0 Lagrangian L L kin. ` L Yuk. ` L pot. Ψ Q,L pu, d, Uq L, Ψ l pν, l, Nq 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., Hypercharge embedding L pot. µ 2 Φ 1 : Φ 2 ` h.c. (diagp1, 1, 2q{p2? 3q): Y X T 8 {? 3 D µ Φ pb µ 1 3 g XB X µ Φ ` igw w µ qφ

79 32/32 J. R. Reuter Little Higgs Models Heräus Seminar "Understanding the LHC", Bad Honnef, Constraints from Oblique Corrections: S, T, U Z L Z L ÝÑ Z L Z L T ρ M 2 ZZ Z Z T Z T ÝÑ Z T Z T S W 0 µνb µν, U W 0 µνw 0µν All low-energy effects order v 2 {F 2 (Wilson coefficients) S, T in the Littlest Higgs model, violation of Custodial SU(2): Csáki et al., 2002; Hewett et al., 2002; Han et al., 2003; Chen/Dawson, 2003; Kilian/JRR, 2003 S 8π c 2 pc 2 s 2 q g 2 `5 c1 2 pc 1 2 s ı 1 2 q v 2 g 1 2 F 2 Ñ 0 α T Ñ 5 4 v 2 F 2v2 λ 2 2φ 2 Mφ 4 Á v2 F 2 Constraints from contact IA: ( f p3q JJ, f p1q JJ ) 4.5 TeV À F {c2 10 TeV À F {c 1 2 Constraints evaded ðñ c, c 1! 1 B 1, Z 1, W 1 superheavy (OpΛq) decouple from fermions