The 4D Composite Higgs boson at the LHC and a LC Stefano Moretti - - PowerPoint PPT Presentation

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The 4D Composite Higgs boson at the LHC and a LC

Stefano Moretti (NExT Institute, Southampton & RAL)

With D. Barducci, A. Belyaev, M.S. Brown, S. De Curtis and G.M. Pruna Based on arXiv:1302.2371, arXiv:1306.6876 & arXiv:1304.4639

B’ham, 29 Feb 2014

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Outline

Preamble:

• A Higgs(-like) signal has been observed at the LHC

(supplemental earlier evidence from Tevatron as well)

• Both ATLAS and CMS confirm it, very SM-like
• Mass measurements around 125 GeV
• Candidate data samples: γγ, ZZ ∗, WW ∗, b¯

b and τ +τ − (in

• rder of decreasing accuracy and/or significance) plus invisible

Motivation:

• Some inconsistency with the SM predictions existed (still

exists), particularly in the (most significant) γγ channel

• Either way, it is mandatory to explore BSM solutions
• Whereas the ‘fundamental Higgs’ hypothesis is being

quantitatively tested in several models, the ‘composite Higgs’

• ne has only been marginally studied in comparison
• All (pseudo)scalar objects discovered in Nature have always

been fermion composites

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Outline

Desclaimer:

• This talk is about a phenomenological analysis aimed at

capturing the essentials of CHMs, it is not about building them and/or comparing their pros and cons

• It thus adopts a specific CHM realisation that it is entirely

calculable, the 4DCHM, apart from its UV structure

• For an analysis of the Higgs data, knowledge of the latter is

not strictly necessary Content:

• The 4DCHM (touch and go)
• Implementation (trust me, it is damn complicated but it is

correct)

• Results (not exciting as one might have hoped, yet not so

frustrating as in many other BSM scenarios)

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4DCHM

Even with discovery of a Higgs particle, SM may not the end of the story (hierarchy and naturalness problems) Two possible scenarios Weak coupling

• Supersymmetry

Strong coupling

• Technicolor
• Extra dimensions
• Composite Higgs

A possible Composite Higgs scenario

• Higgs doublet arise from a strong dynamics
• Higgs as a (Pseudo) Nambu-Goldstone Boson (PNGB)

Idea from the ’80s: spontaneous breaking of a symmetry G → H

Georgi and Kaplan, Phys.Lett. B136, 183 (1984)

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4DCHM

Simplest example was considered by Agashe, Contino and Pomarol

(arXiv:0412089)

• Symmetry pattern SO(5) → SO(4)

The coset SO(5)/SO(4) turn out to be one of the most economical: 4 Pseudo Nambu-Goldstone Bosons (PNGBs) (minimum number to be identified with the SM Higgs doublet) Potential generated by radiative corrections → light Higgs (a la Coleman, Weinberg ’73) Extra-particle content is present

• Spin 1 resonances
• Spin 1/2 resonances

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4DCHM

4DCHM of De Curtis, Redi, Tesi (arXiv:1110.1613): highly deconstructed 4D version of general 5D theory

• Just two sites: Elementary and Composite sectors
• Mechanism of partial compositness (e.g. mixing between

elementary and composite states - 3rd generation quarks, cfr γ − ρ mixing in QCD) Effective 4D model, hence needs UV completion, (largely) irrelevant for Higgs sector Minimal: single SO(5) multiplet of resonances from composite sector (only dof’s accessible at the LHC) The 4DCHM represents the framework to study CHMs in a complete and computable way Generic features of all relevant CHMs are captured

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4DCHM

Bosonic sector

Ω1

SU(2)L ⊗ U(1)Y SO(5) ⊗ U(1)X SO(5) ⊗ U(1)X SO(4) ⊗ U(1)X

g0, ˜ W g∗, ˜ A

Φ2 Elementary sector Composite Sector De Curtis, Redi, Tesi ’11

Ω1 = exp( iΠ

2f )

Π Goldstone Matrix f scale of the symmetry breaking (compositeness scale) Φ2 = Ω1ϕ0 ϕ0 = (0, 0, 0, 0, 1) = δi5 11 new gauge resonances 5 Neutral 6 Charged (c.c.)

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4DCHM

Bosonic sector mass spectrum

mγ = 0 mW = 80GeV mZ = 91GeV M∗ ≃ 3TeV

Bosonic sector mass spectrum

M2

Z ≃ f 2

4 g2

∗ (s2 θ +

s2

ψ

2 )ξ M2

Z1 = f 2g2 ∗

tan θ = sθ/cθ = g0/g∗ tan ψ = sψ/cψ = √ 2g0Y /g∗ ξ = sin( v

2f ) ≃ v 2f

v = ⟨h⟩ = 246 GeV Model parameters (gauge): f ≃ 1 TeV and g∗ perturbative (≤ 4π) M∗ = f g∗ Gauge boson mass ≥ 1.5 TeV from EWPTs

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4DCHM

Fermionic sector

qel

L

ΨT tel

R

Ψ ˜

B

bel

R

∆bR ∆bL ∆tL ∆tR ΨB YB, mYB YT , mYT Ψ ˜

T

Explicit breaking of SO(5) through Yukawas in composite sector YT, YB 20 new fermionic resonances

• 10 in the top sector
• 10 in the bottom sector

Model parameters (fermion sector) m∗ ∆tL, ∆tR, YT, mYT , ∆bL, ∆bR, YB, mYB

• Elementary(3rd) fermions mix with composites via link fields Ω1
• First two generation quarks and all leptons considered as in SM

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4DCHM

Fermionic sector mass spectrum Top and bottom sector ( ˜ X = X/m∗)

mtop = 172GeV m∗ ≃ 1TeV

Fermionic sector mass spectrum

m2

b ∝ ξ m2 ∗

2 ˜ ∆2

bL ˜

∆2

bR ˜

Y 2

B

m2

t ∝ ξ m2 ∗

2 ˜ ∆2

tL ˜

∆2

tR ˜

Y 2

T

m2

T1 ≃ m2 ∗

2 ( 2 + ˜ M2

YT − ˜

MYT √ 4 + ˜ M2

YT

) m2

B1 ≃ m2 ∗

2 ( 2 + ˜ M2

YB − ˜

MYB √ 4 + ˜ M2

YB

) Fermionic resonance mass ≃1 TeV

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4DCHM

Recapping: Higgs sector at a glance

• Four PNGBs in the vector representation of SO(4) one of

which is composite Higgs boson

• Physical Higgs particle acquires mass through one-loop

generated potential (Coleman-Weinberg)

• 4DCHM choice for fermionic sector gives finite potential, i.e.,

from location of minimum one extracts mH and ⟨h⟩

• Partial compositness:
• 1. SM gauge/fermion states couple to Higgs via mixing with

composite particles

• 2. 4DCHM gauge/fermion resonances couple to Higgs directly
• Zoo of new fermions and gauge bosons has potential to alter

Higgs couplings via mixing and/or loops

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4DCHM

• For natural choice of parameters, mH consistent with 125 GeV
• 500

1000 1500 2000 2500 50 100 150 200 250 300 mfGeV mHGeV

• 500

1000 1500 2000 2500 50 100 150 200 250 mfGeV mHGeV

Masses of lightest fermionic partners f as a function of Higgs mass with 165 GeV ≤ mt ≤ 175 GeV, for (left) f = 500 GeV and (right) f = 800 GeV. Fermionic parameters are varied between 0.5 and 3

• TeV. Gauge contribution corresponds to MZ ′,W ′ = 2.5 TeV. (From

De Curtis, Redi, Tesi (arXiv:1110.1613).)

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Particle spectrum

The particle spectrum of the 4DCHM is

• SM leptons: e, µ, τ, and νe, νµ, ντ
• SM quarks; u, d, c, s, t, b
• SM gauge bosons: γ, Z 0, W ±, g
• 5 extra neutral gauge bosons: Z ′

i=1,...,5

• 3 extra charged gauge bosons: W ′±

i=1,2,3

• 8 extra charged 2/3 fermions: t′

i=1,...,8

• 8 extra charged -1/3 fermions: b′

i=1,...,8

• 2 charged 5/3 fermions: T ′

i=1,2

• 2 charged -4/3 fermions: B′

i=1,2

• Higgs boson

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Calculation

• More than 3000 Feynman rules ! A non-automated approach

would have been impossible

• Implementation of the 4DCHM in numerical tools:
• LanHEP for automated generation of Feynman rules A.Semenov

(arXiv:1005.1909)

• CalcHEP for automated calculation of physical observables

(cross sections, widths...) Belyaev, Christensen and Pukhov

(arXiv:1207.6082)

• Uploaded onto HEPMDB: http://hepmdb.soton.ac.uk/

under 4DCHM(HAA+HGG)

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Experimental constraints

• Implemented outside LanHEP/CalcHEP tools:
• α, MZ and GF
• Top, bottom and Higgs masses (same for 4DCHM & SM)

165 GeV ≤ mt ≤ 175 GeV 2 GeV ≤ mb ≤ 6 GeV 124 GeV ≤ mH ≤ 126 GeV

• Zb¯

b and Zt¯ t couplings

• Standalone Mathematica program performs scans on model

parameters

• Output can be read by LanHEP/CalcHEP to compute

physical observables

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LHC results

Define benchmarks

• 4DCHM parameter scans with f and g∗ fixed to:

(a) f = 0.75 TeV and g∗ = 2 (b) f = 0.8 TeV and g∗ = 2.5 (c) f = 1 TeV and g∗ = 2 (d) f = 1 TeV and g∗ = 2.5 (e) f = 1.1 TeV and g∗ = 1.8 (f) f = 1.2 TeV and g∗ = 1.8

• All other parameters varied:

0.5 TeV ≤ m∗, ∆tL, ∆tR, YT, MYT , YB, MYB ≤ 5 TeV 0.05 TeV ≤ ∆bL , ∆bR ≤ 0.5 TeV

• Total number of random points for each (f , g∗): ≈ 15M.
• Survival rate of O(10−5), variations amongst (f , g∗)s ≤ 30%
• 4DCHM highly constrained, phenomenologically interesting

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LHC results

Limits on heavy gauge bosons and fermions Call these Z ′, W ′, t′ and b′

• Bosons:
• 1. EWPTs (LEP, SLC & Tevatron) sets MZ ′,W ′ ≥ 1.5 TeV
• 2. Z ′, W ′ have poor lepton rates, hence no stronger limits from

direct searches (Tevatron & LHC)

• Fermions:
• 1. Direct searches (LHC) more constraining, assume pair

production (7 TeV)

• 2. CMS with 5 fb−1, BR(t′ → W +b) = 100%

CMS with 1.14 fb−1, BR(t′ → Zt) = 100%

• 3. CMS with 4.9 fb−1, BR(b′ → W −t) = 100%

CMS with 4.9 fb−1, BR(b′ → Zb) = 100%

• 4. Limit on T1 and B1 about 400 GeV, but it could be slightly

lower

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LHC results

Limits on mT1

200 300 400 500 600 700 800 106 104 0.01 1 100 m T1GeV ΣppT1T1BrT1Wb2pb 200 300 400 500 600 700 800 106 104 0.01 1 100 m T1GeV ΣppT1T1BrT1Zt2pb

Black line is cross section assuming 100% BRs, red line is 95% CL

• bserved limit and purple circles are 4DCHM points for f = 1 TeV

and g∗ = 2. Dotted-red line corresponds to extrapolations of experimental results.

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LHC results

Limits on mB1

200 300 400 500 600 700 800 108 106 104 0.01 1 100 m B1GeV ΣppB1B1BrB1Wt2pb 200 300 400 500 600 700 800 108 106 104 0.01 1 100 m B1GeV ΣppB1B1BrB1Zb2pb

Black line is cross section assuming 100% BRs, red line is 95% CL

• bserved limit and purple circles are 4DCHM points for f = 1 TeV

and g∗ = 2. Dotted-red line corresponds to extrapolations of experimental results.

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LHC results

• Define R (µ) parameters, i.e., the observed events over SM:

RYY = σ(pp → HX)|4DCHM × BR(H → YY )|4DCHM σ(pp → HX)|SM × BR(H → YY )|SM YY = γγ, b¯ b, WW , ZZ (neglect τ +τ −)

• Relevant hadro-production processes:

gg → H (gluon − gluon fusion) q¯ q(′) → VH (Higgs − strahlung) V = W , Z

• Convenient to re-write (valid at LO and HO QCD)

RY ′Y ′

YY

= Γ(H → Y ′Y ′)|4DCHM × Γ(H → YY )|4DCHM Γ(H → Y ′Y ′)|SM × Γ(H → YY )|SM Γtot(H)|SM Γtot(H)|4DCHM Y ′Y ′ = gg, VV

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LHC results

ATLAS CMS Rγγ 1.8 ± 0.4 1.564+0.460

−0.419

RZZ 1.0 ± 0.4 0.807+0.349

−0.280

RWW 1.5 ± 0.6 0.699+0.245

−0.232

Rbb −0.4 ± 1.0 1.075+0.593

−0.566

Summary of pre-Moriond LHC measurements of some R parameters from latest ATLAS (ATLAS-CONF-2012-170) and CMS (CMS-PAS-HIG-12-045) data.

• For YY = γγ, WW , ZZ take Y ′Y ′ = gg while for YY = b¯

b take Y ′Y ′ = VV

• Use f = 1 TeV and g∗ = 2 for illustration, features generic to

4DCHM

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LHC results

• Mixing effects only: ZZ ∗ → 4ℓ and WW ∗ → 2ℓ2νℓ

(corrections to BRs different in 4DCHM)

• Both below 1 mostly, some points above, strong correlation

suggests common cause for effect

0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.04 0.85 0.90 0.95 1.00 1.05

RΓΓ R VV

Correlation between Rγγ and RVV , VV = WW (red) and ZZ (purple), for f = 1 TeV and g∗ = 2. All points compliant with direct searches for t′s and b′s.

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LHC results

• Introduce reduced couplings a la LHC HXSWG (A. Denner et al

(arXiv:1209.0040))

• We can cast Rs in terms of κ’s

RY ′Y ′

YY

= κ2

Y ′κ2 Y

κ2

H

Y , Y ′ = b/τ/g/γ/V κ2

b/τ/g/γ/V = Γ(H → b¯

b/τ +τ −/gg/γγ/VV )|4DCHM Γ(H → b¯ b/τ +τ −/gg/γγ/VV )|SM κ2

H = Γtot(H)|4DCHM

Γtot(H)|SM .

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LHC results

• κH smaller: b − b′ mixing, all Higgs rates rise

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.70 0.75 0.80 0.85 0.90

m T1TeV ΚH

2

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.70 0.75 0.80 0.85 0.90

m B1TeV ΚH

2

Distribution of κH versus (left) mT1 and (right) mB1 for f = 1 TeV and g∗ = 2. Regions to left of vertical dashed-red lines excluded by t′ and b′ direct searches.

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LHC results

• κg smaller: t − t′ mixing, t-loop dominant
• Subtle cancellations/compensations

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.75 0.80 0.85 0.90 0.95 1.00 1.05

m T1TeV Κg

2

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.75 0.80 0.85 0.90 0.95 1.00 1.05

m B1TeV Κg

2

Distribution of κg versus (left) mT1 and (right) mB1 for f = 1 TeV and g∗ = 2. Regions to left of vertical dashed-red lines excluded by t′ and b′ direct searches.

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LHC results

• κγ also smaller (less though): t − t′ mixing, t-loop

subdominant

• Again, subtle cancellations/compensations

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.956 0.958 0.960 0.962 0.964 0.966 0.968

m T1TeV ΚΓ

2

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.956 0.958 0.960 0.962 0.964 0.966 0.968

m B1TeV ΚΓ

2

Distribution of κγ versus (left) mT1 and (right) mB1 for f = 1 TeV and g∗ = 2. Regions to left of vertical dashed-red lines excluded by t′ and b′ direct searches.

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LHC results

• T1 and B1 masses play significant role, revisit Rγγ
• Leakage of points towars large Rγγ > 1 at small masses
• Asymptotic result for mT1,B1 → ∞ can be wrong by 10+%

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

m T1TeV RΓΓ

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

m B1TeV RΓΓ

Distributions of Rγγ versus (left) mT1 and (right) mB1 for f = 1 TeV and g∗ = 2. Regions to left of vertical dashed-red lines excluded by t′ and b′ direct searches.

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LHC results

• Compare all benchmarks to SM & data

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0 R H→ZZ H→W + W − H→γγ H→b¯ b

ATLAS CMS f =0.75 TeV, g ∗ =2.00 f =0.80 TeV, g ∗ =2.50 f =1.00 TeV, g ∗ =2.00 f =1.00 TeV, g ∗ =2.50 f =1.10 TeV, g ∗ =1.80 f =1.20 TeV, g ∗ =1.80

4DCHM against data for all (f , g∗) benchmarks. Points compliant with t′ and b′ direct searches.

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LHC results

• Perform χ2 fit and compare to SM, can be better

1.125 1.25 1.375 1.5 1.625 1.75

χ2 /dof

9.0 10.0 11.0 12.0 13.0 14.0

χ2

f =0.75 TeV, g ∗ =2.00 f =0.80 TeV, g ∗ =2.50 f =1.00 TeV, g ∗ =2.00 f =1.00 TeV, g ∗ =2.50 f =1.10 TeV, g ∗ =1.80 f =1.20 TeV, g ∗ =1.80 Standard Model

4DCHM χ2 fits for all benchmarks in (f , g∗). Line is SM. Points compliant with t′ and b′ direct searches.

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LHC results

• Add m ˜

T1 > 600 GeV (no limits on m˜ B1)

1.125 1.25 1.375 1.5 1.625 1.75

χ2 /dof

9.0 10.0 11.0 12.0 13.0 14.0

χ2

f =0.75 TeV, g ∗ =2.00 f =0.80 TeV, g ∗ =2.50 f =1.00 TeV, g ∗ =2.00 f =1.00 TeV, g ∗ =2.50 f =1.10 TeV, g ∗ =1.80 f =1.20 TeV, g ∗ =1.80 Standard Model

4DCHM χ2 fits for all benchmarks in (f , g∗). Line is SM. Points compliant with t′ and b′ plus ˜ T1 direct searches.

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LHC results

• After Moriond updates

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0 µ H→ZZ H→W + W − H→γγ H→b¯ b

ATLAS CMS f =0.75 TeV, f =0.80 TeV, f =1.00 TeV, f =1.10 TeV, f =1.20 TeV, 1.25 1.375 1.5 1.625 1.75 1.875

χ2 /dof

10.0 11.0 12.0 13.0 14.0 15.0

χ2 f =0.75 TeV, f =0.80 TeV, f =1.00 TeV, f =1.10 TeV, f =1.20 TeV, Standard Model

4DCHM against data (left) and χ2 fits (right) for all benchmarks in (f , g∗). Line is SM. Points compliant with t′ and b′ plus ˜ T1 direct searches.

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LC results

Higgs-strahlung (ZH)

• Production cross section affected by Z ′s: define R = σ4DCHM

σSM

• Visible at higher LC energies, needs Z ′s to be wide

0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 500 1000 1500 f=800 GeV, gρ=2.5 250 GeV 500 GeV 1000 GeV ΓZ3 (GeV) R 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 500 1000 1500 f=1000 GeV, gρ=2 ΓZ3 (GeV) R

Corrections induced by mixing plus Z3 exchange as a function of its width for benchmarks (b) (left) and (c) (right).

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LC results

Higgs-strahlung times BRs

• Take low energies, 250 and 500 GeV, and look at leading

ζ = v2/f 2 corrections

• Couplings rescale simply:

gSM

HVV

g4DCHM

HVV

= √1 − ζ,

gSM

Hff

g4DCHM

Hff

= 1−2ζ

√1−ζ

ΜVV ΜΓΓ Μbbgg ΣZH bb WW ZZ ΓΓ gg 400 600 800 1000 1200 1400 1600 0.2 0.4 0.6 0.8 1.0 1.2 f GeV Μi ILC 250 GeV ΣZHWW Bri ΜVV ΜΓΓ Μbbgg ΣZH bb WW ZZ ΓΓ gg 400 600 800 1000 1200 1400 1600 0.2 0.4 0.6 0.8 1.0 1.2 f GeV Μi ILC 500 GeV ΣZH WWBri

WW , ZZ (red), γγ (black) and b¯ b/gg (blue) signal strength as function of f . In green ratio of inclusive ZH cross sections. Horizontal for expected accuracies σ× BR for a 250 GeV and fb−1 (left) and 500 GeV and fb−1 (right) LC.

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LC results

• Can disentangle model via couplings (use proper benchmarks)

0.7 0.8 0.9 1 1.1 1.2 1.3 0.6 0.8 1 1.2 1.4 Higgs-strahlung (500 GeV) µWW µbb 0.7 0.8 0.9 1 1.1 1.2 1.3 0.6 0.8 1 1.2 1.4 Higgs-strahlung (500 GeV) µZZ µgg 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 0.8 0.9 1 1.1 1.2 VBF (1000 GeV) µWW µbb 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 0.8 0.9 1 1.1 1.2 VBF (1000 GeV) µZZ µgg

Correlations among Rs for HS (top) and VBF (bottom), with f = 800 GeV, g∗ = 2.5 (green) and f = 1000 GeV, g∗ = 2 (blue).

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LC results

Top Yukawa coupling from e+e− → t¯ tH

• Z ′s & t′s in propagators other than mixing effects
• Optimistic, good experimental accuracy: 35%(9%) at a 500

GeV and fb−1(1000 GeV and fb−1) LC.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1 1.5 2 2.5 3 3.5 σ(ttH) × BR(bb) µbb (1000 GeV) µbb (500 GeV) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1 1.5 2 2.5 3 3.5 σ(ttH) × BR(bb), no extra t’s µbb (1000 GeV) µbb (500 GeV)

Correlations among Rbbs with the inclusion of t′ quarks (left) and without these (right), with f = 800 GeV, g∗ = 2.5 (green) and f = 1000 GeV, g∗ = 2 (blue).

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LC results

Higgs self-coupling from Z(→ ℓ+ℓ−)HH(→ 4b) and ν¯ νHH(→ 4b)

• Rescaling is λ4DCHM = λSM

1−2ζ √1−ζ

• Difficult, poor experimental accuracy: 64%(38%) for

ZHH(ν¯ νHH) at a 500 GeV and fb−1(1000 GeV and fb−1) LC.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0.4 0.6 0.8 1 1.2 1.4 1.6 µZbbbb µννbbbb

Correlations among RZb¯

bb¯ b and Rνe ¯ νeb¯ bb¯ b for two energy and

luminosity stages, with f = 800 GeV, g∗ = 2.5 (green) and f = 1000 GeV, g∗ = 2 (blue).

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Conclusions

• 4DCHM could provide explanation to LHC data pointing to

Higgs discovery at 125–126 GeV (some better χ2’s than SM)

• Substantial parameter space scans show possible moderate

enhancement in H → γγ, i.e., Rγγ ≈ 1.1

• Rγγ could grow to ≈ 1.3, if t′ and b′ masses just below results
• f our extrapolations
• 4DCHM main effect is reduction of Hbb (b-b′ mixing),

smaller Γtot(H)

• Competing effects from Hgg also smaller, Hγγ almost stable
• Relevant by-product: approximations assuming t′ and b′

masses infinite cannot be accurate

• Composite Higgs solution to LHC data seemingly possible and

wanting light fermionic partners

• Revisit t′, b′ searches in 4DCHM dependent way (in progress)
• Future LC ideal to test modified hb¯

b, hW +W −, hZZ etc.

• LC can also probe altered top Yukawa and possibly λ
• LC sensitive to virtual t′, Z ′ (W ′ less) in Higgs processes

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• SM left doublet can be embedded in (2, 2)2/3 ∈ ΨT as,

52/3 = (2, 2)2/3 ⊕ (1, 1)2/3, (2, 2)2/3 = ( T T 5

3

B T 2

3

)

• tR coupled to singlet in different 52/3 representation, Ψ

T

• bR coupled to singlet in a 5−1/3 (Ψ

B)

• To generate b Yukawa it is necessary (by U(1)X symmetry) to

couple SM doublet to second doublet in 5−1/3 (ΨB) which contains 5−1/3 = (2, 2)−1/3⊕(1, 1)−1/3, (2, 2)−1/3 = ( B− 1

3

T ′ B− 4

3

B′ )

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Lagrangian (gauge and fermions) Lgauge = f 2

1

4 Tr|DµΩ1|2 + f 2

2

2 (DµΦ2)(DµΦ2)T − 1 4ρ

˜ A µνρ ˜ Aµν − 1

4F

˜ W µν F ˜ W µν

(↑ composite ↑ elementary kinetic terms) Lfermions = Lel

fermions + (∆tL¯

qel

L Ω1ΨT + ∆tR¯

tel

R Ω1Ψ ˜ T + h.c.)

+ ¯ ΨT(i ˆ D

˜ A − m∗)ΨT + ¯

Ψ ˜

T(i ˆ

D

˜ A − m∗)Ψ ˜ T

− (YT ¯ ΨT,LΦT

2 Φ2Ψ ˜ T,R + MYT ¯

ΨT,LΨ ˜

T,R + h.c.) + (T → B).

• Covariant derivatives

DµΩ1 = ∂µΩ1 − ig0 ˜ W Ω1 + ig∗Ω1˜ A, DµΦ2 = ∂µΦ2 − ig∗˜ AΦ2 ˜ W [˜ A] mediators of SU(2)L ⊗ U(1)Y [SO(5) ⊗ U(1)X]

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• SO(5) ⊗ U(1)X → SO(4) ⊗ U(1)X from SO(5) vector

Φ2 = ϕ0ΩT

2

where ϕi

0 = δi5.

• ΨT,B and ˜

ΨT,B fundamental representations of SO(5) [embedding composite fermions]

• SM third generation quarks embedded in incomplete

representation of SO(5) ⊗ U(1)X to give correct Y = T 3R + X under SU(2)L ⊗ U(1)Y

• ∆t,b/L,R mixing parameters between elementary and

composite sectors

• YT,B, MYT,B Yukawa parameters of composite sector
• m∗ mass parameter of fermionic resonances

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Higgs interactions In unitary gauge link fields Ωn = 1 + i sn

h Π + cn−1 h2 Π2,

sn = sin(fh/f 2

n ),

cn = cos(fh/f 2

n ),

h = √ hˆ

ahˆ a, 2

∑

n=1

1 f 2

n

= 1 f 2 Identify Π = √ 2hˆ

aT ˆ a GB matrix and T ˆ a’s SO(5)/SO(4) broken

generators (ˆ a = 1, 2, 3, 4) Π = √ 2hˆ

aT ˆ a = −i

( 04 h −hT ) , hT = (h1, h2, h3, h4) . Relate h to usual SM SU(2)L Higgs doublet H = 1 √ 2 ( −ih1 − h2 −ih3 + h4 ) .

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Use Ωn = 1 + δΩn to define Higgs interactions Lgauge,H = − f 2

1

2 g0g∗Tr [ ˜ W δΩ1˜ A + ˜ W ˜ AδΩT

1 + ˜

W δΩ1˜ AδΩT

1

] + f 2

2

2 g2

∗

[ ϕT

0 δΩT 2 ˜

A˜ Aϕ0 + ϕT

0 ˜

A˜ AδΩ2ϕ0 + ϕT

0 δΩT 2 ˜

A˜ AδΩ2ϕ0 ] , Lferm,H =∆tL¯ qel

L δΩ1ΨT + ∆tR¯

tel

R δΩ1Ψ ˜ T

− YT ¯ ΨT,L(ϕT

0 ϕ0δΩT 2 + δΩ2ϕ0ϕT 0 + δΩ2ϕT 0 ϕ0δΩT 2 )Ψ ˜ T,R

+ (T → B) + h.c.

• In unitary gauge h1, h2, h3 eaten by W ±, Z and h4 is H
• Expand δΩ1,2 to first order in H to extract gHViVj and gHfi¯

fj

• Couplings to mass eigenstates obtained after diagonalization

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Subtle loop cancellations/compensations

• Consider loop diagrams

H → γγ induced by fermionic loop H → γγ induced by a charged vector loop

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• Consider HViVi charged couplings (SM-like and Extra)

0.955 0.96 0.965 0.97 0.975 0.98 0.985 0.99 1.0 1.5 2.0 1.8 1.9 2.0 2.1 2.2 2.3 2.4

fTeV g gH W W gH W W

SM

2.3 2.25 2.2 2.15 2.1 1.0 1.5 2.0 1.8 1.9 2.0 2.1 2.2 2.3 2.4

fTeV g gH W 2 W 2 gH W W

SM

1.15 1.175 1.2 1.225 1.25 1.275 1.3 1.325 1.0 1.5 2.0 1.8 1.9 2.0 2.1 2.2 2.3 2.4

fTeV g gH W 3 W 3 gH W W

SM

Couplings of Higgs boson in 4DCHM to charged gauge bosons (W left, W2 middle, W3 right) normalised to SM values.

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• Consider HViVi neutral couplings (SM-like and Extra)

0.96 0.965 0.97 0.975 0.98 0.985 0.99 0.995 1.0 1.5 2.0 1.8 1.9 2.0 2.1 2.2 2.3 2.4

fTeV g gH Z Z gH Z Z

SM

0.58 0.56 0.54 0.52 0.5 1.0 1.5 2.0 1.8 1.9 2.0 2.1 2.2 2.3 2.4

fTeV g gH Z2 Z2 gH Z Z

SM

1.75 1.7 1.65 1.6 1.55 1.0 1.5 2.0 1.8 1.9 2.0 2.1 2.2 2.3 2.4

fTeV g gH Z3 Z3 gH Z Z

SM

Couplings of Higgs boson in 4DCHM to neutral gauge bosons (Z left, Z2 middle, Z3 right) normalised to SM values.

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• Consider Hfi¯

fi couplings (SM-like)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.75 0.80 0.85 0.90 0.95

m T1TeV gH t t gH t t

SM

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95

m B1TeV gH b b gH b b

SM

Couplings of Higgs boson in 4DCHM to top (left) and bottom (right) quarks normalised to SM values vs mT1 and mB1 for f = 0.8 TeV and g∗ = 2.5.

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• Consider Hfi¯

fi couplings (extra light)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.4 0.2 0.0 0.2 0.4

m T1TeV gH T1 T1 gH t t

SM

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.5 1.0 0.5 0.0 0.5 1.0 1.5

m B1TeV gH B1 B1 gH b b

SM

Couplings of Higgs boson in 4DCHM to lightest heavy top (left) and bottom (right) quarks normalised to SM values vs mT1 and mB1 for f = 0.8 TeV and g∗ = 2.5.

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• Consider Hfi¯

fi couplings (extra heavy)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.0 0.5 0.0 0.5 1.0

m T1TeV gH T2 T2 gH t t

SM

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.0 0.5 0.0 0.5 1.0

m T1TeV gH T3 T3 gH t t

SM

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.0 0.5 0.0 0.5 1.0

m T1TeV gH T4 T4 gH t t

SM

Couplings of Higgs boson in 4DCHM to second (left), third (middle) and fourth (right) lightest heavy top quarks normalised to SM values vs mT1 and mB1 for f = 0.8 TeV and g∗ = 2.5.

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• Loop compensations between SM-like and Extra quarks (gg)
• 0.2
• 0.1

0.1 0.2 0.3 0.4 0.5 0.6 400 600 800 1000 1200 H → gg B’s T’s mT1 [GeV] A4DCHM / ASM

• 0.2

0.2 0.4 0.6 0.8 1 1.2 400 600 800 1000 1200 H → gg Total SM-like Extra mT1 [GeV] A4DCHM / ASM

Loop contributions to H → gg in 4DCHM normalised to SM vs mT1 for f = 0.8 TeV and g∗ = 2.5.

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• Loop compensations between SM-like and Extra quarks (γγ)
• 0.14
• 0.12
• 0.1
• 0.08
• 0.06
• 0.04
• 0.02

0.02 0.04 400 600 800 1000 1200 H → γγ B’s T’s W’s mT1 [GeV] A4DCHM / ASM

• 0.2

0.2 0.4 0.6 0.8 1 1.2 400 600 800 1000 1200 H → γγ Total SM-like Extra mT1 [GeV] A4DCHM / ASM

Loop contributions to H → γγ in 4DCHM normalised to SM vs mT1 for f = 0.8 TeV and g∗ = 2.5.

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• Loop cancellations between Extra quarks
• 0.2
• 0.1

0.1 0.2 0.3 0.4 0.5 0.6 400 600 800 1000 1200 H → gg T1 T2 T3 T4 mT1 [GeV] A4DCHM / ASM

• 0.14
• 0.12
• 0.1
• 0.08
• 0.06
• 0.04
• 0.02

0.02 0.04 400 600 800 1000 1200 H → γγ T1 T2 T3 T4 mT1 [GeV] A4DCHM / ASM

Loop contributions to H → gg (left) and γγ (right) in 4DCHM normalised to SM amplitude vs mT1 for f = 0.8 TeV and g∗ = 2.5.

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• Outlook:
• 1. ATLAS & CMS allow for κH ≥ 1
• 2. Need κH < 1 in 4DCHM (also useful for other BSMs, e.g.,

SUSY, 2HDMs - Higgs mixing)

γ

κ

1 2

g

κ

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

CMS Preliminary

• 1

12.2 fb ≤ = 8 TeV, L s

• 1

5.1 fb ≤ = 7 TeV, L s

BSM

BR

0.0 0.2 0.4 0.6 0.8 1.0

g

κ

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

CMS Preliminary

• 1

12.2 fb ≤ = 8 TeV, L s

• 1

5.1 fb ≤ = 7 TeV, L s

CMS fits to κg and κγ for (left) κH = 1 and (right) κH > 1.