1. Strong EWSB in Top Quark Production at ILC Ivan Melo M. Gintner, I. Melo, B. Trpišová (University of Žilina) Praha, Mar 30, 2006

2. Motivation for new vector (ρ) resonances: Strong EW Symmetry Breaking (SEWSB) Vector resonance model ρ signal at future e + e - colliders e + e - → νν tt e + e - → t t Beamstrahlung Outline

3. EWSB: SU(2) L x U(1) Y → U(1) Q Weakly interacting models: - SUSY - Little Higgs Strongly interacting models: - Technicolor

4. Summary of the DCR Physics Group Strongly interacting Higgs sector: a priority !!!! - Summarize/update the scenario with resonances - See for new studies with the chiral approach

5. Chiral SB in QCD SU(2) L x SU(2) R → SU(2) V, vev ~ 90 MeV EWSB SU(2) L x SU(2) R → SU(2) V, vev ~ 246 GeV

6. W L W L → W L W L W L W L → t t t t → t t L = i g π M ρ /v (π - ∂ μ π + - π + ∂ μ π - ) ρ 0 μ + g t t γ μ t ρ 0 μ + g t t γ μ γ 5 t ρ 0 μ ttt π = W L

7. International Linear Collider: e+e- at 1 TeV ee ―› νν WWee ―› νν tt ee ―› ρ tt ―› WW tt ee ―› ρ tt ―› tt tt ee ―› WW ee ―› tt Large Hadron Collider: pp at 14 TeV pp ―› jj WWpp ―› jj tt pp ―› ρ tt ―› WW tt pp ―› ρ tt ―› tt tt pp ―› WW pp ―› tt

8. Chiral effective Lagrangian SU(2) L x SU(2) R global, SU(2) L x U(1) Y local L = L kin + L non.lin. σ model - a v 2 /4 Tr[(ω μ + i g v ρ μ. τ/2 ) 2 ] + L mass + L SM (W,Z) + b 1 ψ L i γ μ (u + ∂ μ – u + i g v ρ μ. τ/2 + u + i g’/6 Y μ ) u ψ L + b 2 ψ R P b i γ μ (u ∂ μ – u i g v ρ μ. τ/2 + u i g’/6 Y μ ) u + P b ψ R + λ 1 ψ L i γ μ u + A μ γ 5 u ψ L + λ 2 ψ R P λ i γ μ u A μ γ 5 u + P λ ψ R Standard Model with Higgs replaced with ρ BESS Our model g π = M ρ /(2 v g v ) g t = g v b 2 /4 + … M ρ ≈ √a v g v /2 t ω μ = [u + (∂ μ + i g’/2 Y μ τ 3 )u + u(∂ μ + i g W μ. τ/2)u + ]/2 A μ = [u + (∂ μ + i g’/2 Y μ τ 3 )u - u(∂ μ + i g W μ. τ/2)u + ]/2 u = exp( i π. τ /2v) ψ L = (t L,b L ) P b = diag(p 1,p 2 )

9. Unitarity constraints W L W L → W L W L, W L W L → t t, t t → t t Low energy constraints g π ≤ 1.75 (M ρ = 700 GeV) g t ≤ 1.7 (M ρ = 700 GeV) g v ≥ 10 → g π ≤ 0.2 M ρ (TeV) |b 2 – λ 2 | ≤ 0.04 → g t ≈ g v b 2 / 4 |b 1 – λ 1 | ≤ 0.01 → b 1 = 0

10. Partial (Γ―›WW) and total width Γ tot of ρ

12. Subset of fusion diagrams + approximations (Pythia) Full calculation of 66 diagrams at tree level (CompHEP)

13. Pythia vs CompHEP ρ (M = 700 GeV, Γ = 12.5 GeV, g’’ = 20, b 2 = 0.08) Before cuts √s (GeV) 800 1000 1500 Pythia (fb) 0.35 0.95 3.27 CompHEP (fb) 0.66 1.16 3.33

15. Backgrounds (Pythia) e + e - → tt γ e + e - → e + e - tt σ(0.8 TeV) = 300.3 + 1.3 fb → 0.13 fb (0.20 fb ) σ(1.0 TeV) = 204.9 + 2.4 fb → 0.035 fb (0.16 fb)

17. R = |N(ρ) – N(no res.)| √(N(no res.)) ≈ S/√B > 5

18. e - e + → t t different from Higgs ! ρ (M= 700 GeV, b 2 =0.08, g’’=20) ρ x+y=560 nm z=0.40 mm n=2x10 10

19. Beamstrahlung Bunch parameters at IP: TESLA (500 GeV): N = 2 x 10 10 σ x = 554 nm σ y = 5 nm σ z = 0.3 mm δ BS = 0.02 – 0.2 L = N 2 H d f/ 4πσ x σ y SLC (SLAC): N = 5 x 10 10 σ x = 1500 nm σ y = 1500 nm σ z = 1.05 mm δ BS = 0.00045 pinch effect

20. e- e+ bunch b E(b)= Ne/(2π ε 0 L R 2 ) b R = 2 σ x = 2 σ y L is bunch length x yz y(z) = b 0 cos[(√3D y /2) 1/2 z/L] D y = 2N r e σ z /[γσ y (σ x +σ y )] Pinch effect Disruption

21. p e- r s F= eE(b) r= p/eE(b) P W = 2ke 2 γ 4 /(3r 2 ), v→c=1 ΔE = P W Δt = P W Δz δ BS = ∫ ΔE /E = 4N 2 γ r e 3 /[3 √3 σ z (σ x +σ y ) 2 ] = 2 – 20 % z L = N 2 H d f/ 4πσ x σ y D y = 2N r e σ z /[γσ y (σ x +σ y )]

22. Conclusions strong ρ-resonance model (modified BESS) e + e - → ννtt R ≤ 26 at CM energy = 1 TeV, L = 200 fb -1 e + e - → tt L scan = 1 fb -1