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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
22
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
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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
er o
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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35
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