New Vector Resonance as an Alternative to Higgs Boson (Strong EWSB) Fyzika za Štandardným modelom klope na dvere Svit, 9.-16.9. 2007 New Vector Resonance as an Alternative to Higgs Boson (Strong EWSB) Ivan Melo University of Zilina

EWSB - one of Great Mysteries of Particle Physics Problem ! SM ………………………. 1 Higgs Strong EWSB …….. no Higgs SUSY (MSSM) ..... 5 Higgs Large Extra Dimensions Little Higgs Monotheists Atheists Polytheists Classical New

Naturalness problem (Fine-tuning, Gauge Hierarchy problem) ≈ - (200 GeV)2 for Λ = 103 GeV ≈ - (200 GeV)2 . 1032 for Λ = 1019 GeV mH ≈ 100 – 200 GeV ≈ - (200 GeV)2 . 1032 ≈ + (200 GeV)2 . 1032

SM Strong EWSB SUSY (MSSM) Large Extra Dimensions Little Higgs = 0 → mH = 319 GeV H not elementary, it melts into techniquarks at ΛTC ≈ 1-3 TeV ~ t1(2) Λ is not 1019 GeV, Λ is as low as 103 GeV

Fundamental energy scales Greg Anderson, Northwestern University

Every fundamental energy scale should have a dynamical origin K. Lane

Linear sigma model (model of nuclear forces) σ v = μ/√λ ≈ 90 MeV σ = v + σ (spontaneous chiral symmetry breaking) SU(2)L x SU(2)R → SU(2)V

Standard model Higgs Lagrangian U(σ,π) σ SU(2)L x SU(2)R → SU(2)V v = μ/√λ ≈ 246 GeV Higgs Lagrangian ≡ Linear sigma model

Where are EW pions ??? mσ = μ2 mπ = 0 EW pions Φ1,Φ2,χ become WL, ZL SU(2)L x SU(2)R → SU(2)V (global) massless GB SU(2)L x U(1)Y → U(1)Q (local) Higgs mechanism: W,Z become massive by eating GB EW pions Φ1,Φ2,χ become WL, ZL

Where is σ ? … the (linear) σ model, although it has some agreeable features, is quite artificial. A new particle is postulated, for which there is no experimental evidence … M. Gell-Mann, M. Levy, Nuovo Cimento 16 p.705 (1960) … and they decided to get rid of σ particle …

Nonlinear σ model (QCD) v = 90 MeV Effective Lagrangian valid until a few hundred MeV

Where is Higgs boson ? … Higgs Lagrangian, although it has some agreeable features, is quite artificial. A new particle is postulated, for which there is no experimental evidence … … so we get rid of the Higgs boson Higgs boson is not necessary, Higgs mechanism works even without Higgs !

Nonlinear σ model (SM Higgs sector) v = 246 GeV Effective Lagrangian valid until 1-3 TeV

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

Technicolor Technicolor of massless U and D techniquarks: SU(2)L x SU(2)R invariant As a result of dynamics, interactions of massless techniquarks, we get - SU(2)L x SU(2)R → SU(2)V - v = 246 GeV - EW pions = WL, ZL made of U,D techniquarks Best explanation of Naturalness & Hierarchy problems

Extended Technicolor (ETC) ETC was introduced to give masses to fermions … but introduced also large FCNC and conflict with precision EW measurements U D ETC Walking technicolor f f ETC has also problem to explain large top mass (mt = 174 GeV) Topcolor assisted technicolor

WL WL → WL WL WL WL → t t t t → t t (Equivalence theorem) L = i gπ Mρ /v (π- ∂μ π+ - π+ ∂μ π-) ρ0μ + gt t γμ t ρ0μ + gt t γμ γ5 t ρ0μ

International Linear Collider: e+e- at 1 TeV ee ―› ρtt ―› WW tt ee ―› ρtt ―› tt tt ee ―› WW ee ―› tt ee ―› νν WW ee ―› νν tt Large Hadron Collider: pp at 14 TeV pp ―› ρtt ―› WW tt pp ―› ρtt ―› tt tt pp ―› WW pp ―› tt pp ―› jj WW pp ―› jj tt

Chiral effective Lagrangian SU(2)L x SU(2)R global, SU(2)L x U(1)Y local L = Lkin + Lnon.lin. σ model - a v2 /4 Tr[(ωμ + i gv ρμ . τ/2 )2] + Lmass + LSM(W,Z) + b1 ψL i γμ (u+∂μ – u+ i gv ρμ . τ/2 + u+ i g’/6 Yμ) u ψL + b2 ψR Pb i γμ (u ∂μ – u i gv ρμ . τ/2 + u i g’/6 Yμ) u+ Pb ψR + λ1 ψL i γμ u+ Aμ γ5 u ψL + λ2 ψR Pλ i γμ u Aμ γ5 u+ Pλ ψR BESS Our model Standard Model with Higgs replaced with ρ ωμ = [u+(∂μ + i g’/2 Yμτ3)u + u(∂μ+ i g Wμ . τ/2)u+]/2 Aμ = [u+(∂μ + i g’/2 Yμτ3)u - u(∂μ+ i g Wμ . τ/2)u+]/2 u = exp(i π . τ /2v) ψL = (tL,bL) Pb = diag(p1,p2) gπ = Mρ /(2 v gv) gt = gv b2 /4 + … Mρ ≈ √a v gv /2 t

Unitarity constraints Low energy constraints gv ≥ 10 → gπ ≤ 0.2 Mρ (TeV) |b2 – λ2| ≤ 0.04 → gt ≈ gv b2 / 4 |b1 – λ1| ≤ 0.01 → b1 = 0 Unitarity constraints WL WL → WL WL , WL WL → t t, t t → t t gπ ≤ 1.75 (Mρ= 700 GeV) gt ≤ 1.7 (Mρ= 700 GeV)

Partial (Γ―›WW) and total width Γtot of ρ

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

Pythia vs CompHEP Before cuts √s (GeV) 800 1000 1500 ρ (M = 700 GeV, Γ = 12.5 GeV, gv = 20, b2 = 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

Backgrounds (Pythia) e+e- → e+e- tt e+e- → tt γ 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)

|N(ρ) – N(no res.)| √N(ttγ+eett)+(N(no res.)) R = ≈ S/√B > 5 = gv

e- e+ → t t ρ different from Higgs ! x+y=560 nm z=0.40 mm n=2x1010 ρ (M= 700 GeV, b2=0.08, gv=20)

39/8 diagrams in the dominant gg channel No-resonance background ρ ρ ρ

CompHEP results: pp → W W t t + X ρ: Mρ=700 GeV, Γρ=4 GeV, b2=0.08, gv=10 39 diagrams 8 diagrams MWW(GeV) gπ=Mρ/2vgv gt1,2 = gv b2/4 σ(gg) = 10.2 fb ―› 1.0 fb Cuts: 700-3Γρ < mWW < 700 +3Γρ (GeV) pT (t) > 100 GeV, |y(t)| < 2 No resonance background: σ(gg) = 0.037 fb

l jjbjjbjj reconstruction (CompHEP, Pythia, Atlfast, Root) Athena 9.0.3 One charged lepton channel: 40% of events electron > 30 GeV muon > 20 GeV Cuts: of mass of the W: GeV jets > 25 GeV b-tagging efficiency 50% Reconstruction criterion

Distribution in invariant mass of WW pair (ρ →WW) ρ: Mρ=700 GeV, Γρ=4 GeV, b2=0.08, gv=10 number of events/17 GeV 39 diagrams 8 diagrams Lum=100/fb 12.2 events 2.4 events Pz(ν) chosen correctly in 61.5 % of events number of events/17 GeV

8 diagrams 39 diagrams Mass of the W boson Mass of the top quark Lum=100/fb Lum=100/fb 12.2 events 2.4 events number of events/0.6 GeV number of events/0.6 GeV Mass of the top quark Lum=100/fb Lum=100/fb 2.4 events 12.2 events number of events/2.5 GeV number of events/2.5 GeV

ρ: Mρ=1000 GeV Γρ=26 GeV Lum = 100 fb-1 12.8 events number of events/32 GeV

1. Can we improve WWtt reconstruction ? L = 100/fb 2.4 events 8 diagrams 2. versus 8 diagrams

Conclusions New vector resonance as an alternative to Higgs Boson Modified BESS model motivated by technicolor Rich e+e- and pp phenomenology