New Vector Resonance as an Alternative to Higgs Boson

(Strong EWSB)

Ivan MeloUniversity of Zilina

Fyzika za Štandardným modelom klope na dvere Svit, 9.-16.9. 2007

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EWSB - one of Great Mysteries of Particle Physics

• SM ………………………. 1 Higgs

• Strong EWSB …….. no Higgs

• SUSY (MSSM) ..... 5 Higgs

• Large Extra Dimensions

• Little Higgs

Monotheists

Atheists

Polytheists

Problem !

New

Classical

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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

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SM

Strong EWSB

SUSY (MSSM)

Large Extra Dimensions

Little Higgs

= 0 → mH = 319 GeV

t1(2)

~

Λ is not 1019 GeV, Λ is as low as 103 GeV

H not elementary, it melts into techniquarks at ΛTC ≈ 1-3 TeV

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Fundamental energy scales

Greg Anderson, Northwestern University

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Every fundamental energy scale should have a dynamical origin

K. Lane

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Linear sigma model (model of nuclear forces)

SU(2)L x SU(2)R → SU(2)V

v = μ/√λ ≈ 90 MeV

U(σ,π)

σ = v + σ (spontaneous chiral symmetry breaking)

σ

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Standard model Higgs Lagrangian

SU(2)L x SU(2)R → SU(2)V

v = μ/√λ ≈ 246 GeV

U(σ,π)

σ

Higgs Lagrangian ≡ Linear sigma model

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SU(2)L x SU(2)R → SU(2)V (global)

SU(2)L x U(1)Y → U(1)Q (local)

mσ = μ2

mπ = 0

massless GB

Higgs mechanism: W,Z become massive by eating GB

EW pions Φ1,Φ2,χ become WL, ZL

Where are EW pions ???

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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 …

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Nonlinear σ model (QCD)

Effective Lagrangian valid until a few hundred MeV

v = 90 MeV

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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 !

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Nonlinear σ model (SM Higgs sector)

v = 246 GeV

Effective Lagrangian valid until 1-3 TeV

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

EWSBSU(2)L x SU(2)R → SU(2)V , vev ~ 246 GeV

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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

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Extended Technicolor (ETC)

ETC was introduced to give masses to fermions… but introduced also large FCNC and conflict with

precision EW measurements

Walking technicolor

ETC has also problem to explain large top mass (mt = 174 GeV)

Topcolor assisted technicolor

ETC

U D

ff

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WL WL → WL WL WL WL → t t t t → t t

L = i gπ Mρ /v (π- ∂μ π+ - π+ ∂μ π-) ρ0μ

+ gt t γμ t ρ0μ + gt t γμ γ5 t ρ0

μ

t t t

π = WL (Equivalence theorem)

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International Linear Collider: e+e- at 1 TeV

ee ―› νν WW ee ―› νν tt ee ―› ρtt ―› WW ttee ―› ρtt ―› tt tt

ee ―› WWee ―› tt

Large Hadron Collider: pp at 14 TeV

pp ―› jj WW pp ―› jj tt pp ―› ρtt ―› WW ttpp ―› ρtt ―› tt tt

pp ―› WWpp ―› tt

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Chiral effective LagrangianSU(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

Standard Model with Higgs replaced with ρ

BESS

Our model

gπ = Mρ /(2 v gv) gt = gv b2 /4 + … Mρ ≈ √a v gv /2 t

ωμ = [u+(∂μ + i g’/2 Yμτ3)u + u(∂μ+ i g Wμ . τ/2)u+]/2Aμ = [u+(∂μ + i g’/2 Yμτ3)u - u(∂μ+ i g Wμ . τ/2)u+]/2u = exp(i π . τ /2v)ψL = (tL,bL)

Pb = diag(p1,p2)

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Unitarity constraints

WL WL → WL WL , WL WL → t t, t t → t t

Low energy constraints

gπ ≤ 1.75 (Mρ= 700 GeV)gt ≤ 1.7 (Mρ= 700 GeV)

gv ≥ 10 → gπ ≤ 0.2 Mρ (TeV)|b2 – λ2| ≤ 0.04 → gt

≈ gv b2 / 4|b1 – λ1| ≤ 0.01 → b1 = 0

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Partial (Γ―›WW) andtotal width Γtot of ρ

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Subset of fusion diagrams + approximations (Pythia)

Full calculation of 66 diagrams at tree level (CompHEP)

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Pythia vs CompHEP

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

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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)

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

= gv

= gv

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e- e+ → t t

different from Higgs !

ρ (M= 700 GeV, b2=0.08, gv=20)

ρ

x+y=560 nmz=0.40 mmn=2x1010

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39/8 diagrams in the dominant gg channel

ttWW -

jjbjjbjjl lNo-resonancebackground

ρ

ρ

ρ

XttWW

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Cuts: 700-3Γρ < mWW < 700 +3Γρ (GeV) pT (t) > 100 GeV, |y(t)| < 2

σ(gg) = 10.2 fb ―› 1.0 fb

No resonance background: σ(gg) = 0.037 fb

MWW(GeV)

CompHEP results: pp → W W t t + X

ρ: Mρ=700 GeV, Γρ=4 GeV, b2=0.08, gv=10 39 diagrams 8 diagrams

gt1,2

= gv b2/4gπ=Mρ/2vgv

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l jjbjjbjj reconstruction (CompHEP, Pythia, Atlfast, Root)

One charged lepton channel:

jjbjjbjjlWbbWWWttWW l

Cuts: Tpelectron > 30 GeV

muon > 20 GeV

jets > 25 GeV

Reconstruction criterion

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2222

)()(

)()()(

2211

654321

tbWtbW

WjjWjjWjj

mmmm

mmmmmm

l

40% of events

mass of the W: 25Wm GeV

b-tagging efficiency 50%

of

Athena 9.0.3

33nu

mb

er o

f ev

ents

/17

GeV

GeV]mWW[

nu

mb

er o

f ev

ents

/17

GeV

GeV]mWW[

39 diagrams 8 diagrams

Lum=100/fb

12.2 events

Lum=100/fb

2.4 events

Distribution in invariant mass of WW pair (ρ →WW)

GeV]mWW[ GeV]mWW[

ρ: Mρ=700 GeV, Γρ=4 GeV, b2=0.08, gv=10

Pz(ν) chosen correctly in 61.5 % of events

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8 diagrams 39 diagramsn

um

ber

of

even

ts/0

.6 G

eV

nu

mb

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f ev

ents

/0.6

GeV

nu

mb

er o

f ev

ents

/2.5

GeV

nu

mb

er o

f ev

ents

/2.5

GeV

GeV]m jj[ GeV]m jj[

GeV]mWb[ GeV]mWb[

Mass of the W boson

Mass of the top quark

Lum=100/fbLum=100/fb

Lum=100/fbLum=100/fb

2.4 events

2.4 events 12.2 events

12.2 events

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GeV]mWW[

GeV]mWW[

nu

mb

er o

f ev

ents

/32

GeV

Lum = 100 fb-1

12.8 events

ρ: Mρ=1000 GeV Γρ=26 GeV

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versus

8 diagrams

ttttttWW

1. Can we improve WWtt reconstruction ?

2.

L = 100/fb2.4 events8 diagrams

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Conclusions

• New vector resonance as an alternative to Higgs Boson

• Modified BESS model motivated by technicolor

• Rich e+e- and pp phenomenology