Implications of Vector Boson Scattering Unitarity in Composite Higgs - - PowerPoint PPT Presentation

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models

Diogo Buarque Franzosi

In collaboration with Piero Ferrarese

Open Questions in Particle Physics and Cosmology April 4, 2017 - Goettingen

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.1/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion

1 Introduction: New Strong Dynamics 2 Fundamental Minimal Composite Higgs Model 3 Unitarity: Strong Vector Boson Scattering in CH 4 Experimental signatures 5 Conclusion

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.2/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics

The Standard Model

1606.02266

• Last successful prediction of the SM:

Discovered Higgs boson h very SM-like

• Nevertheless SM suffers from several

inconsistencies: naturalness/hierarchy, DM, neutrino masses, triviality, inflation, baryogenesis, ...

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.3/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics

The Standard Model

1606.02266

• Last successful prediction of the SM:

Discovered Higgs boson h very SM-like

• Nevertheless SM suffers from several

inconsistencies: naturalness/hierarchy, DM, neutrino masses, triviality, inflation, baryogenesis, ...

• Implies new physics!

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.3/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics

New Strong Dynamics

• Technicolor (Weinberg 76, Susskind 79) is a gauge theory that

is strongly coupled at ∼ 1 TeV and breaks Chiral symmetry through a condensate of techni-quarks - as in QCD

• The techni-quarks carry electroweak charge, thus EW

Symmetry breaking is embedded in chiral SB

• Pros: naturalness, assymptonic freedom (or safety), DM

candidates (techni-baryon number), unification (?), inflation, ...

• Issues: large S-parameter, large Higgs mass, non SM Higgs

couplings, fermion masses vs FCNC, ...

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.4/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics

Is it dead?!

Issues: fermion masses vs FCNC, large S-parameter, large Higgs mass, non SM Higgs couplings?

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.5/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics

Is it dead?!

Issues: fermion masses vs FCNC, large S-parameter, large Higgs mass, non SM Higgs couplings? The answer is NO!! A large number of theories unexplored

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.5/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics

Fermion masses

• Larger scale Λ > ΛTC generates low energy 4-fermion

interactions, schematically: α

¯ QQ ¯ QQ Λ2

+ β

¯ QQ ¯ ψψ Λ2

+ κ QQQψ

Λ2

+ h.c. + γ

¯ ψψ ¯ ψψ Λ2

ETC PC FCNC

• Extended Technicolor (ETC) (Dimopoulos, Susskind 79,

Eichten, Lane 80)

• Partial Compositeness (PC) Kaplan 91 - improved hierarchy

and FCNC constraints

• Light weak doublet scalar fundamental (e.g. Supersymmetric

TC) or of composite nature...

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.6/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics

Walking Technicolor

• Realistic TC theories are quasi-conformal, since

quasi-conformality suppress undesirable flavour changing neutral current and can reduce contribution to the S-parameter - Walking Technicolor (WTC)

• ¯

QQ condensate enhanced. ¯ QQETC ∼ ln

• ΛETC

ΛTC

γ ¯ QQTC ∼

• ΛETC

ΛTC

γ(α∗) ¯ QQTC

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.7/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics

4 light + 8 heavy techni-quarks in SU(3) (Brower, Hasenfratz,

Rebbi, Weinberg, Witzel 16)

• ensure chiral SB in the IR
• walking is tunable by mh

(heavy quark mass)

• it is nevertheless hard to get

large enough anomalous dimensions, e.g. Ratazzi,

Rychkov, Tonni, Vichi 10 for ETC and Pica, Sannino et al. 16 for PC

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.8/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics

Light scalar: Higgs boson mass

• Techni-dilaton. In Walking dynamics it is expected a

component of the Higgs to be a pseudo-Goldstone boson from the breaking of scale invariance.

• Top-quark correction,

M2

H = (MTC H )2 + 3(4πκFπ)2/(16π2v2)[−4r2 t m2 t + ...]+non

• pert. Foadi, Frandsen, Sannino 12’
• Pseudo-Goldstone boson (“Composite Higgs”), - Higgs is the

pseudo-GB of the breaking of a global symmetry Georgi, Kaplan

84’

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.9/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion New Strong Dynamics

Higgs couplings

• techni-dilaton component couples like SM Higgs (if Fσ ∼ v).
• CH component couples like SM-Higgs → ghWW = gSM

hWW cos θ

• Techni-σ component unknown, but gσππ in QCD is

mysteriously described by linear sigma model

(Belyaev, Brown, Foadi, Frandsen, Sannino 13’) Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.10/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Fundamental Minimal Composite Higgs Model

Fundamental Minimal Composite Higgs Model

• Possible SB patterns from fundamental fermions:

SU(N) × SU(N) → SU(N), SU(2N) → SO(2N) or Sp(2N)

Peskin 80, Preskill 80

• the so-called minimal CH model is based on the coset

SO(5)/SO(4) - can be achieved via 4-fermion operators

Gersdorff, Ponton, Rosenfeld 15

• Minimal custodial scenario SU(4)/Sp(4) Galloway et al 10’,

Cacciapaglia, Sannino 14’

• UV completion example: 2 Dirac flavours fundamental of

SU(2) gauge theory

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.11/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Fundamental Minimal Composite Higgs Model

• Vacuum misaligned with vacuum that breaks EW symmetry:

Σ0 = cos θΣB + sin θΣH

• The 5 (pseudo-)NGB field is parametrized by the exponential

map U = exp

• i

√ 2 f

5

• a=1

πaY a

• CCWZ Lowest order NGB Lagrangian

L = 1 2f 2xµxµ − V

• Dynamical generation of EW scale v = f sin θ

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.12/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Fundamental Minimal Composite Higgs Model

Scalar Sector

• Scalar sector: 5 GB (3 eaten+ h, η) + 1 σ mixing w/ h (Arbey

et al. 15’)

Lσ = 1 2κ(σ)f 2xµxµ + 1 2∂µσ∂µσ − 1 2M2

σσ2 − V

κ(σ) = 1 + κ′σ + · · ·

• Modification in the Higgs coupling, ghVV /gSM

hVV ∼ cos θ.

EWPO, sin θ 0.2

• On the other hand, minimization of potential, e.g.

cos θ → 2Cm/(y′

tCt) top-loop and techni-quark mass.

Indicates not so small angles - different origin Cx ∼ 1

• η phenomenology hard, σ ∼fb
• First principle lattice calculation Mσ = 4.7(2.6)/ sin θ TeV

(Arthur, Drach, Hietanen, Pica, Sannino, 16’)

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.13/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Fundamental Minimal Composite Higgs Model

Spin-1 sector

• Local Hidden Symmetry construction(DBF, Cacciapaglia, Cai,

Deandrea, Frandsen 16’)→ LO parameters: ˜

g, r, MV , MA

• First principle lattice calculation, MV = 3.2(5)/ sin θ TeV,

MA = 3.6(9)/ sin θ TeV (Arthur et al. 16’) Fµ = Vµ + Aµ =

10

• a=1

Va

µVa + 5

• a=1

Aa

µYa.

SU(2)V SU(2)L× SU(2)R TC CH V v 0,±

µ

3 (3,1)⊕(1,3) − → ρ µ − → ρ µ s0,±

µ

3 − → a µ ˜ s0,±

µ

3 (2,2) ˜ v 0

µ

1 A a0,±

µ

3 (2,2) − → a µ x0

µ

1 ˜ x0

µ

1 (1,1)

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.14/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity

Longitudinal VBS Unitarity

• Lattice provides good estimate of heavy vector mass; however

it poorly provide scalar mass and other quantities of effective Lagrangian

• Analiticity and unitarity of n-point functions can lead to

further information on the spectra of strong dynamics, e.g. dispersion relations and Weinberg sum rules

• Unitarity of Vector Boson Scattering is a powerful tool.

A(s) ∼ s f 2

• What can it say about the spectra and couplings of CH

models, Mσ, κ′ (scalar), ˜ g and r?

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.15/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity

Amplitudes

• The SU(4) breaking terms are low energy effects and can be

neglected

• The 2 → 2 NGB scattering can thus be decomposed in

(similarly to isospin in pion scattering) Bijnens, Lu 11’: 5×5→ 1⊕10⊕14 (C = I, S, MS channels)

• and further in partial waves,

A(s, t) = 32π

∞

• J=0

aJ(s)(2J + 1)PJ(cos θ)

• Elastic unitarity condition ImaCJ(s) = |aCJ(s)|2
• Fixed order amplitudes are not unitary, but obey perturbative

unitarity relations, e.g. Ima(1)

CJ (s) = |a(0) CJ (s)|2

• |aCJ(s)| > 1 indicates lost of perturbativity and unitarity

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.16/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity

LO amplitudes (leading spin)

a(0)

I0 (s) =

s 16πf 2 , a(0)

S1 (s) =

s 192πf 2 , a(0)

MS0(s) =

−s 64πf 2 Unitarity violation at √s 4√πf

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.17/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity

NLO amplitudes

• Higher-order corrections important for perturbative analysis
• Loop diagrams renormalized by higher dimensional operators (MS)

L6 = L0xµxνxµxν+L1xµxµxνxν+L2xµxνxµxν+L3xµxµxνxν . a(1)

I0 (s)

= s2 32πf 4

• 1

16π2 29 12 + 46 18 log s µ2

• + 2πi
• + 2

3

• LI(µ)
• a(1)

S1 (s)

= s2 32πf 4

• 1

16π2

• − 35

432 + 1 12 log s µ2

• + 1

72πi

• + 2

3

• LS(µ)
• a(1)

MS0(s)

= s2 32πf 4

• 1

16π2 83 144 − 4 9 log s µ2

• + 1

8πi

• + 2

3

• LMS(µ)
• LMS(µ) = 2

7

• LI(µ) + 10

LS(µ)

• Implications of Vector Boson Scattering Unitarity in Composite Higgs Models

Diogo Buarque Franzosi - p.18/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity

4 6 8 10 12

• 0.4
• 0.2

0.0 0.2 0.4

s [TeV] LI(8TeV)

sin θ = 0.2

• NLO can only worsen

unitarity violation

• LO unitarity violation has

physical relevance → strong VBS effects must appear before that scale

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.19/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity

Inverse Amplitude Method

• Unitarization models give a phenomenological description of

scattering amplitudes much beyond the scale of unitarity violation

• They typically saturate unitarity, which is a feature expected

in strong dynamics

• IAM method has been successfully used to describe pion-pion

and pion-kaon scattering up to 1.2 GeV Dobado 92. aIAM

CJ (s) =

a(0)

CJ (s)

1 − a(1)

CJ (s)

a(0)

CJ (s) Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.20/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity

From the denominator of IAM a mass and running width can be extracted M2

I

= 2f 2

1 16π2

29

12

• + 2

3

LI(MI) , ΓI = M3

I

16πf 2 M2

S

= (f 2/6)

1 16π2

• − 35

432

• + 2

3

LS(MS) , ΓS = M3

S

192πf 2 M2

MS

= −(f 2/2)

1 16π2

83

144

• + 2

3

LMS(MMS) , ΓMS = M3

MS

64f 2 For µ = √s, aIAM

CJ (s) = −

ΓC/MC s − M2

I + i ΓC MC s + 32πs ΓC MC kC log

√s

M

• kC = −43

96π2 , 1 64π2 , −1 12π2 and (C, J) = (I, 0), (S, 1), (MS, 0).

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.21/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity

• Spin-1: lattice inspired MS = 3.2(5)/ sin θ TeV

→ LS(MV ) = 2.225 × 10−3

• Spin-0: MI = υI/ sin θ TeV

→ LI(MI) = −0.0229556 + 0.181548/υ2

I

LO NLO IAM sinθ=0.2 sinθ=0.15 5 10 15 20 25 30 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

s [TeV] |aS(J=1)|

LO NLO IAM a=1 a=0.15 a=0.2 2 4 6 8 10 12 14 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

s [TeV] |aI(J=0)|

• Spin-0 MS: υMS 10 appear at higher scales, as well as

higher spin resonances

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.22/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity

Vector contribution

LO NLO IAM LO+v aV =0.8 aV =1 aV =1.2 5 10 15 20 25 30 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

s [TeV] |aS(J=1)|

πaπbVc

µ :

igV Y aY bV c(pa − pb)Ξabc, gV = −MV 2f aV = −M2

V (1 − r 2)

√ 2˜ gf 2 av

I0(s)

= −g 2

V

8π

• (2 + 3 s

M2

V

) − 2(M2

V

s + 2) log(1 + s M2

V

)

• av

S1(s)

= g 2

V

32π

• s

3(s − M2

V ) −

s 2M2

V

− (M2

V

s + 2)

• 2 − (2M2

V

s + 1) log(1 + s M2

V

)

• aV ∼ 1

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.23/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Longitudinal Vector Boson Scattering Unitarity

Scalar singlet contribution

σπaπb : −2i gσ f pa · pb, gσ = κ′/2 A(s, t, u) = −g2

σ

s f 2 s s − M2

σ

LO a=0.5 a=1 a=1.5 2 4 6 8 10 0.0 0.5 1.0 1.5 2.0

s [TeV] |aI(J=0)|

IAM gσ=0.63 gσ=0.8 gσ=0.4 3 4 5 6 7 8 0.0 0.5 1.0 1.5 2.0

s [TeV] |aI(J=0)|

solid: IAM, dashed: fixed width, dotted: running width

gσ 0.63, Mσ TeV / sin θ

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.24/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Experimental Signatures

Experimental Signatures

• Vector production, aV ∼ 1

Vectors mix with EW gauge bosons ∼ g/ g → DY and VBF production, diboson and di-fermion decay.

• Strong VBS:
• non-resonant LET, sin θ ≤ 0.2. Conservative scenario.
• Scalar singlet, gσ ∼ 0.63. Assume small mixing,

α ∼ 2m2

h/m2 σ → VBF production and diboson decay dominate

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.25/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Experimental Signatures

Vector phenomenology

• Due to high masses vectors have to be probed by 100 TeV

collider

• Including DY and VBF production
• Limits from Thamm, Torre, Wulzer 15

3 4 5 6 7 8 9 10

˜ g

0.6 0.8 1.0 1.2 1.4

r

aV = − 1 aV = 1

σV0 × BR 95%CL exclusions @ 100 TeV - θ = 0.15 ll - L = 1ab −1 WZ - L = 1ab −1 ll - L = 10ab −1 WZ - L = 10ab −1

3 4 5 6 7 8 9 10

˜ g

0.6 0.8 1.0 1.2 1.4

r

aV = − 1 aV = 1

σV0 × BR 95%CL exclusions @ 100 TeV - θ = 0.2 ll - L = 1ab −1 WZ - L = 1ab −1 ll - L = 10ab −1 WZ - L = 10ab −1

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.26/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Experimental Signatures

Strong VBS in pp → jjZZ → jj4ℓ

• LVBS embeded in more complicated 2 → 6

processes

• Sherpa simulation CH+σ, background SM

ZZ+jets (EW+QCD)

• Rivet analysis: 2 anti-kT jets, 4 isolated leptons

+ cuts to enhance VBS topology cut 100 TeV 14 TeV 2 jets |η| > 3.5 , η1 · η2 < 0 |ηj| > 3. , ηj1 · ηj2 < 0 ZZ invariant mass mZZ > 3TeV mZZ > 3TeV di-jet invariant mass mjj > 1 TeV mjj > 1 TeV Zs centrality |ηZi | < 2. |ηZi | < 2. Zs momentum pT,Zi > 1 TeV pT,Zi > 0.5 TeV

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.27/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Experimental Signatures

Non-resonant excess at 100 TeV

• Simple counting statistical analysis: P(k; λ, ǫ) =

1 2ǫ

1+ǫ

1−ǫ dx e−xλ (xλ)k k!

• LHC will be able to measure Higgs coupling hZZ with precision 5% (3%

in a optimistic scenario) Mariotti, Passarino 16 → sin θ ∼ 0.31 (sin θ ∼ 0.24), so it will never probe the motivated region.

ZZjj QCD+EW LET sin θ = 0.1 LET sin θ = 0.15 LET sin θ = 0.2 10−16 10−15 10−14 10−13 10−12 10−11 10−10 pp → ZZjj @ 100 TeV dσ/dM [pb/GeV] 5000 10000 15000 20000 25000 1 2 3 4 5 6 7 8 M(ZZ) [GeV] S/B

5 10 15 20 25 L - ab−1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 P(BSM@95%CL)

CHLET scenario @ 100 TeV

sinθ = 0. 2 sinθ = 0. 15 sinθ = 0. 1

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.28/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Experimental Signatures

Heavy scalar at 100 TeV

ZZjj QCD+EW LET+σ sin θ = 0.1- a = 0.6 , gσ = 0.63 LET+σ sin θ = 0.15 - a = 0.9 , gσ = 0.63 LET+σ sin θ = 0.2 - a = 1.2 , gσ = 0.63 LET+σ sin θ = 0.1 - a = 0.8 , gσ = 0.8 10−16 10−15 10−14 10−13 10−12 10−11 10−10 pp → ZZjj @ 100 TeV dσ/dM [pb/GeV] 5000 10000 15000 20000 25000 1 2 3 4 5 6 7 8 M(ZZ) [GeV] S/B

5 10 15 20 25 L - ab−1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 P(BSM@95%CL)

CHLET+σ scenario @ 100 TeV

sinθ = 0. 2 - a = 1. 2gσ = 0. 63 sinθ = 0. 15 - a = 0. 9gσ = 0. 63 sinθ = 0. 1 - a = 0. 6gσ = 0. 63 sinθ = 0. 1 - a = 0. 8gσ = 0. 8

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.29/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion Experimental Signatures

Heavy scalar at LHC

ZZjj QCD+EW LET sin θ = 0.2 LET+σ sin θ = 0.2 10−19 10−18 10−17 10−16 10−15 10−14 10−13 pp → ZZjj @ 14 TeV dσ/dM [pb/GeV] 3000 4000 5000 6000 7000 8000 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 M(ZZ) [GeV] S/B

• This optimistic scenario has

too low cross section

• May have non-negligible

mixing and gluon fusion can help production

• Other VBS channels

important

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.30/34

New Strong Dynamics FMCHM VBS Unitarity Signatures Conclusion

Summary and conclusion

• CH models are promising alternatives to the SM
• Unitarity constraints the effect of strong dynamics to specific

scales

• Dynamically inspired unitarization models provide a way to

assess effective parameters. We found: aV ∼ 1, gσ ∼ 0.63 and Mσ 1 TeV / sin θ

• The effect on realistic observables can be categorized in

strong VBS and resonance production

• A 100 TeV collider is motivated due to high scale;
• More optimisitc scenario may be observed at LHC - other

channels necessary

• VBS will be able to probe θ angle more than hZZ coupling at

the LHC

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.31/34

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.32/34

Effective description

• Parametrization of vacuum

Σ0 = cos θ (iσ2) sin θ (1) − sin θ (1) − cos θ (iσ2)

• .
• EW embeding

Si = 1

2

σi

• ,

Y = S6 = 1

2

−σT

3

• Unbroken V a and spontaneously broken Y a generators

V a · Σ0 + Σ0 · V aT = 0 , Y a · Σ0 − Σ0 · Y aT = 0

• The (pseudo-)NGB field is parametrized by the exponential

map U = exp

• i

√ 2 f

5

a=1 πaY a

• CCWZ construction: ωµ = U†DµU xµ = 2YaωµY a

sµ = 2VaωµV a

• L4 = 1

2f 2xµxµ

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.33/34

π+π−v0 : igV (p− − p+) π±π0v∓ : igV (p± − p0) (1) The Higgs couples to the s0,± triplet, π±hs∓ : gV (p± − ph) π0hs0 : gV (p0 − ph) (2) and η to ˜ s0,± according to, π±η˜ s∓ : ∓igV (p± − pη) π0η˜ s0 : igV (p0 − pη) (3) (we have used a redefinition ˜ s0 → −i˜ s0 w.r.t. Ref.[?]) and hη˜ v0 : −gV (ph − pη) . (4)

Implications of Vector Boson Scattering Unitarity in Composite Higgs Models Diogo Buarque Franzosi - p.34/34