The 4D Composite Higgs boson at the LHC and a LC · Yukawas in composite sector YT,YB 20 new fermionic resonances • 10 in the top sector • 10 in the bottom sector Model parameters

Outline 4DCHM Implementation LHC results LHC results LC results Conclusions Backup slides Backup slides

The 4D Composite Higgs bosonat 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


OutlinePreamble:

• 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 ∗, bb and τ+τ− (inorder of decreasing accuracy and/or significance) plus invisible

Motivation:

• Some inconsistency with the SM predictions existed (stillexists), particularly in the (most significant) γγ channel

• Either way, it is mandatory to explore BSM solutions

• Whereas the ‘fundamental Higgs’ hypothesis is beingquantitatively tested in several models, the ‘composite Higgs’one has only been marginally studied in comparison

• All (pseudo)scalar objects discovered in Nature have alwaysbeen fermion composites


Outline

Desclaimer:

• This talk is about a phenomenological analysis aimed atcapturing the essentials of CHMs, it is not about buildingthem and/or comparing their pros and cons

• It thus adopts a specific CHM realisation that it is entirelycalculable, the 4DCHM, apart from its UV structure

• For an analysis of the Higgs data, knowledge of the latter isnot strictly necessary

Content:

• The 4DCHM (touch and go)

• Implementation (trust me, it is damn complicated but it iscorrect)

• Results (not exciting as one might have hoped, yet not sofrustrating as in many other BSM scenarios)


4DCHM

Even with discovery of a Higgs particle, SM may not the end ofthe story (hierarchy and naturalness problems)

Two possible scenariosWeak 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 → HGeorgi and Kaplan, Phys.Lett. B136, 183 (1984)


4DCHMSimplest 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 mosteconomical:

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


4DCHM4DCHM of De Curtis, Redi, Tesi (arXiv:1110.1613): highlydeconstructed 4D version of general 5D theory

• Just two sites: Elementary and Composite sectors

• Mechanism of partial compositness (e.g. mixing betweenelementary and composite states - 3rd generation quarks, cfrγ − ρ mixing in QCD)

Effective 4D model, hence needs UV completion, (largely)irrelevant for Higgs sector

Minimal: single SO(5) multiplet of resonances from compositesector (only dof’s accessible at the LHC)

The 4DCHM represents the framework to study CHMs in acomplete and computable way

Generic features of all relevant CHMs are captured


4DCHMBosonic 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( iΠ2f ) 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.)


4DCHM

Bosonic sector mass spectrum

mγ = 0mW = 80GeVmZ = 91GeV

M∗ ' 3TeV

Bosonic sector mass spectrum

M2Z ≃ f 2

4g2∗ (s

2θ +

s2ψ2)ξ

M2Z1

= f 2g2∗

tan θ = sθ/cθ = g0/g∗tanψ = sψ/cψ =

√2g0Y /g∗

ξ = sin( v2f ) ≃

v2f

v = ⟨h⟩ = 246 GeV

Model parameters (gauge):

f ≃ 1 TeVand g∗ perturbative (≤ 4π)

M∗ = f g∗Gauge boson mass ≥ 1.5 TeV

from EWPTs


4DCHM

Fermionic sector

qelLΨT

telR

ΨBbelR∆bR

∆bL

∆tL

∆tR

ΨB

YB ,mYB

YT ,mYT

ΨT

Explicit breaking of SO(5) throughYukawas 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


4DCHM

Fermionic sector mass spectrum

Top and bottom sector (X = X/m∗)

mtop = 172GeV

m∗ ' 1TeV

Fermionic sector mass spectrum

m2b ∝ ξ

m2∗2∆2

bL∆2

bRY 2B

m2t ∝ ξ

m2∗2∆2

tL∆2

tRY 2T

m2T1

≃ 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


4DCHM

Recapping: Higgs sector at a glance

• Four PNGBs in the vector representation of SO(4) one ofwhich is composite Higgs boson

• Physical Higgs particle acquires mass through one-loopgenerated 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 withcomposite particles

2. 4DCHM gauge/fermion resonances couple to Higgs directly

• Zoo of new fermions and gauge bosons has potential to alterHiggs couplings via mixing and/or loops


4DCHM

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

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500 1000 1500 2000 250050

100

150

200

250

m f HGeVL

mH

HGeV

LMasses of lightest fermionic partners f as a function of Higgs masswith 165 GeV ≤ mt ≤ 175 GeV, for (left) f = 500 GeV and (right)f = 800 GeV. Fermionic parameters are varied between 0.5 and 3TeV. Gauge contribution corresponds to MZ ′,W ′ = 2.5 TeV. (From

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


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


Calculation

• More than 3000 Feynman rules ! A non-automated approachwould 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)


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

• Zbb and Ztt couplings

• Standalone Mathematica program performs scans on modelparameters

• Output can be read by LanHEP/CalcHEP to computephysical observables


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


LHC resultsLimits on heavy gauge bosons and fermions

Call these Z ′, W ′, t ′ and b′

• Bosons:

1. EWPTs (LEP, SLC & Tevatron) sets MZ ′,W ′ ≥ 1.5 TeV2. Z ′,W ′ have poor lepton rates, hence no stronger limits from

direct searches (Tevatron & LHC)

• Fermions:

1. Direct searches (LHC) more constraining, assume pairproduction (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 slightlylower


LHC results

Limits on mT1

200 300 400 500 600 700 80010-6

10-4

0.01

1

100

m T1HGeVL

ΣHp

p®

T1T

1LB

rHT

1®

WbL

2Hp

bL

200 300 400 500 600 700 80010-6

10-4

0.01

1

100

m T1HGeVL

ΣHp

p®

T1T

1LB

rHT

1®

ZtL

2Hp

bL

Black line is cross section assuming 100% BRs, red line is 95% CLobserved limit and purple circles are 4DCHM points for f = 1 TeV

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


LHC results

Limits on mB1

200 300 400 500 600 700 80010-8

10-6

10-4

0.01

1

100

m B1HGeVL

ΣHp

p®

B1B

1LB

rHB

1®

WtL

2Hp

bL

200 300 400 500 600 700 80010-8

10-6

10-4

0.01

1

100

m B1HGeVL

ΣHp

p®

B1B

1LB

rHB

1®

ZbL

2Hp

bL

Black line is cross section assuming 100% BRs, red line is 95% CLobserved limit and purple circles are 4DCHM points for f = 1 TeV

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


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, bb, WW , ZZ (neglect τ+τ−)

• Relevant hadro-production processes:

gg → H (gluon− gluon fusion) qq(′) → 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 )|SMΓtot(H)|SM

Γtot(H)|4DCHM

Y ′Y ′ = gg , VV


LHC resultsATLAS 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 Rparameters 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 = bbtake Y ′Y ′ = VV

• Use f = 1 TeV and g∗ = 2 for illustration, features generic to4DCHM


LHC results• Mixing effects only: ZZ ∗ → 4ℓ and WW ∗ → 2ℓ2νℓ(corrections to BRs different in 4DCHM)

• Both below 1 mostly, some points above, strong correlationsuggests common cause for effect

0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.040.85

0.90

0.95

1.00

1.05

RΓΓ

RV

V

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.


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 =

κ2Y ′κ2Yκ2H

Y ,Y ′ = b/τ/g/γ/V

κ2b/τ/g/γ/V =Γ(H → bb/τ+τ−/gg/γγ/VV )|4DCHM

Γ(H → bb/τ+τ−/gg/γγ/VV )|SM

κ2H =Γtot(H)|4DCHM

Γtot(H)|SM.


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 T1HTeVL

ΚH2

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 B1HTeVL

ΚH2

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

t ′ and b′ direct searches.


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 1.60.75

0.80

0.85

0.90

0.95

1.00

1.05

m T1HTeVL

Κg2

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.75

0.80

0.85

0.90

0.95

1.00

1.05

m B1HTeVL

Κg2

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



LHC results

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

• 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 T1HTeVL

ΚΓ2

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 B1HTeVL

ΚΓ2

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



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 1.60.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

m T1HTeVL

RΓΓ

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

m B1HTeVL

RΓΓ

Distributions of Rγγ versus (left) mT1 and (right) mB1 for f = 1TeV and g∗ = 2. Regions to left of vertical dashed-red lines

excluded by t ′ and b′ direct searches.


LHC results

• Compare all benchmarks to SM & data

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0R

H→ZZ

H→W+W −

H→γγ

H→bb

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 compliantwith t ′ and b′ direct searches.


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/d

of

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. Pointscompliant with t ′ and b′ direct searches.


LHC results

• Add mT1> 600 GeV (no limits on mB1

)

1.125

1.25

1.375

1.5

1.625

1.75

χ2/d

of

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. Pointscompliant with t ′ and b′ plus T1 direct searches.


LHC results

• After Moriond updates

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0µ

H→ZZ

H→W+W −

H→γγ

H→bb

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 benchmarksin (f , g∗). Line is SM. Points compliant with t ′ and b′ plus T1

direct searches.


LC resultsHiggs-strahlung (ZH)

• Production cross section affected by Z ′s: define R = σ4DCHMσSM

• 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

0 500 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

0 500 1000 1500

f=1000 GeV, gρ=2

ΓZ3 (GeV)

R

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


LC resultsHiggs-strahlung times BRs

• Take low energies, 250 and 500 GeV, and look at leadingζ = v2/f 2 corrections

• Couplings rescale simply:gSMHVV

g4DCHMHVV

=√1− ζ,

gSMHff

g4DCHMHff

= 1−2ζ√1−ζ

ΜVVΜΓΓ

Μbbgg

ΣHZHL

bbWW

ZZ

ΓΓ

gg

400 600 800 1000 1200 1400 16000.2

0.4

0.6

0.8

1.0

1.2

f HGeVL

Μ i

ILC 250 GeV ΣZHWW Bri

ΜVVΜΓΓ

Μbbgg

ΣHZHL

bbWW

ZZ

ΓΓ

gg

400 600 800 1000 1200 1400 16000.2

0.4

0.6

0.8

1.0

1.2

f HGeVLΜ i

ILC 500 GeV ΣZH WWBri

WW ,ZZ (red), γγ (black) and bb/gg (blue) signal strength asfunction 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.


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

µb

b

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

µg

g

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

µb

b

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

µg

g

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


LC resultsTop Yukawa coupling from e+e− → ttH

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

µb

b (

50

0 G

eV

)

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)

µb

b (

50

0 G

eV

)

Correlations among Rbbs with the inclusion of t ′ quarks (left) andwithout these (right), with f = 800 GeV, g∗ = 2.5 (green) and

f = 1000 GeV, g∗ = 2 (blue).


LC resultsHiggs self-coupling from Z (→ ℓ+ℓ−)HH(→ 4b) and ννHH(→ 4b)

• Rescaling is λ4DCHM = λSM1−2ζ√1−ζ

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

µν

νbbbb

Correlations among RZbbbb and Rνe νebbbb for two energy andluminosity stages, with f = 800 GeV, g∗ = 2.5 (green) and

f = 1000 GeV, g∗ = 2 (blue).


Conclusions• 4DCHM could provide explanation to LHC data pointing toHiggs discovery at 125–126 GeV (some better χ2’s than SM)

• Substantial parameter space scans show possible moderateenhancement in H → γγ, i.e., Rγγ ≈ 1.1

• Rγγ could grow to ≈ 1.3, if t ′ and b′ masses just below resultsof 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 andwanting light fermionic partners

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


Backup slides

• 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 23

)

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

• bR coupled to singlet in a 5−1/3 (ΨB)

• To generate b Yukawa it is necessary (by U(1)X symmetry) tocouple SM doublet to second doublet in 5−1/3 (ΨB) whichcontains

5−1/3 = (2, 2)−1/3⊕(1, 1)−1/3, (2, 2)−1/3 =

(B− 1

3T ′

B− 43

B ′

)


Backup slides

Lagrangian (gauge and fermions)

Lgauge =f 214Tr |DµΩ1|2 +

f 222(DµΦ2)(DµΦ2)

T

− 1

4ρAµνρ

Aµν − 1

4F Wµν F

Wµν

(↑ composite ↑ elementary kinetic terms)

Lfermions = Lelfermions + (∆tL q

elL Ω1ΨT +∆tR t

elRΩ1ΨT + h.c .)

+ ΨT (i DA −m∗)ΨT + ΨT (i D

A −m∗)ΨT

− (YT ΨT ,LΦT2 Φ2ΨT ,R +MYT

ΨT ,LΨT ,R + h.c .) + (T → B).

• Covariant derivatives

DµΩ1 = ∂µΩ1 − ig0WΩ1 + ig∗Ω1A, DµΦ2 = ∂µΦ2 − ig∗AΦ2

W [A] mediators of SU(2)L ⊗ U(1)Y [SO(5)⊗ U(1)X ]


Backup slides

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

Φ2 = ϕ0ΩT2 where ϕi0 = δi5.

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

• SM third generation quarks embedded in incompleterepresentation of SO(5)⊗ U(1)X to give correctY = T 3R + X under SU(2)L ⊗ U(1)Y

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

• YT ,B , MYT ,BYukawa parameters of composite sector

• m∗ mass parameter of fermionic resonances


Backup slides

Higgs interactionsIn unitary gauge link fields Ωn = 1+ i snh Π+ cn−1

h2Π2,

sn = sin(fh/f 2n ), cn = cos(fh/f 2n ), h =√haha,

2∑n=1

1

f 2n=

1

f 2

Identify Π =√2haT a GB matrix and T a’s SO(5)/SO(4) broken

generators (a = 1, 2, 3, 4)

Π =√2haT a = −i

(04 h

−hT 0

), hT = (h1, h2, h3, h4) .

Relate h to usual SM SU(2)L Higgs doublet

H =1√2

(−ih1 − h2−ih3 + h4

).


Backup slides

Use Ωn = 1+ δΩn to define Higgs interactions

Lgauge,H =− f 212g0g∗Tr

[W δΩ1A+ W AδΩT

1 + W δΩ1AδΩT1

]+

f 222g2∗

[ϕT0 δΩ

T2 AAϕ0 + ϕT0 AAδΩ2ϕ0 + ϕT0 δΩ

T2 AAδΩ2ϕ0

],

Lferm,H =∆tL qelL δΩ1ΨT +∆tR t

elR δΩ1ΨT

− YT ΨT ,L(ϕT0 ϕ0δΩ

T2 + δΩ2ϕ0ϕ

T0 + δΩ2ϕ

T0 ϕ0δΩ

T2 )ΨT ,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 gHViVjand gHfi fj

• Couplings to mass eigenstates obtained after diagonalization


Backup slidesSubtle loop cancellations/compensations

• Consider loop diagrams

H → γγ induced by fermionic loop

H → γγ induced by a charged vector loop


Backup slides

• 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 2.01.8

1.9

2.0

2.1

2.2

2.3

2.4

f HTeVL

g*

gH W W gH W WSM

-2.3

-2.25

-2.2

-2.15-2.1

1.0 1.5 2.01.8

1.9

2.0

2.1

2.2

2.3

2.4

f HTeVL

g*

gH W 2 W 2 gH W W

SM

1.151.175

1.2

1.225

1.25 1.275

1.3

1.3251.0 1.5 2.0

1.8

1.9

2.0

2.1

2.2

2.3

2.4

f HTeVL

g*

gH W 3 W 3 gH W W

SM

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


Backup slides

• 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 2.01.8

1.9

2.0

2.1

2.2

2.3

2.4

f HTeVL

g*

gH Z Z gH Z ZSM

-0.58

-0.56

-0.54

-0.52

-0.5

1.0 1.5 2.01.8

1.9

2.0

2.1

2.2

2.3

2.4

f HTeVL

g*

gH Z2 Z2 gH Z Z

SM

-1.75

-1.7

-1.65

-1.6

-1.55

1.0 1.5 2.01.8

1.9

2.0

2.1

2.2

2.3

2.4

f HTeVL

g*

gH Z3 Z3 gH Z Z

SM

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


Backup slides

• 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 T1HTeVL

g Ht

tg H

tt

SM

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

m B1HTeVL

g Hb

bg H

bb

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.


Backup slides

• 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 T1HTeVL

g HT

1T

1g H

tt

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 B1HTeVL

g HB

1B

1g H

bb

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.


Backup slides

• 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 T1HTeVL

g HT

2T

2g H

tt

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 T1HTeVL

g HT

3T

3g H

tt

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 T1HTeVL

g HT

4T

4g H

tt

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.


Backup slides

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

-0.2

-0.1

-0

0.1

0.2

0.3

0.4

0.5

0.6

400 600 800 1000 1200

H → gg

B’sT’s

mT1 [GeV]

A4D

CH

M /

AS

M

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

400 600 800 1000 1200

H → gg

Total

SM-like

Extra

mT1 [GeV]

A4D

CH

M /

AS

M

Loop contributions to H → gg in 4DCHM normalised to SM vsmT1 for f = 0.8 TeV and g∗ = 2.5.


Backup slides

• Loop compensations between SM-like and Extra quarks (γγ)

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

400 600 800 1000 1200

H → γγ

B’s

T’s

W’s

mT1 [GeV]

A4D

CH

M /

AS

M

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

400 600 800 1000 1200

H → γγ

Total

SM-like

Extra

mT1 [GeV]

A4D

CH

M /

AS

M

Loop contributions to H → γγ in 4DCHM normalised to SM vsmT1 for f = 0.8 TeV and g∗ = 2.5.


Backup slides

• Loop cancellations between Extra quarks

-0.2

-0.1

-0

0.1

0.2

0.3

0.4

0.5

0.6

400 600 800 1000 1200

H → gg

T1T2T3T4

mT1 [GeV]

A4D

CH

M /

AS

M

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

400 600 800 1000 1200

H → γγ

T1T2T3T4

mT1 [GeV]

A4D

CH

M /

AS

M

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


Backup slides

• Outlook:

1. ATLAS & CMS allow for κH ≥ 12. Need κH < 1 in 4DCHM (also useful for other BSMs, e.g.,

SUSY, 2HDMs - Higgs mixing)

γκ0 1 2

gκ

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0CMS Preliminary -1 12.2 fb≤ = 8 TeV, L s -1 5.1 fb≤ = 7 TeV, L s

BSMBR0.0 0.2 0.4 0.6 0.8 1.0

gκ

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0CMS 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.

Documents

The 4D Composite Higgs boson at the LHC and a LC · Yukawas in composite sector YT,YB 20 new fermionic resonances • 10 in the top sector • 10 in the bottom sector Model parameters