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
Monotheists
•
Strong EWSB …….. no Higgs
Atheists
•
SUSY (MSSM) ..... 5 Higgs
•
Large Extra Dimensions
•
Little Higgs
Classical
Polytheists
New
2
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
3
SM
= 0 → mH = 319 GeV
Strong EWSB H not elementary, it melts into techniquarks at ΛTC ≈ 1-3 TeV
~
t1(2)
SUSY (MSSM)
Large Extra Dimensions
Little Higgs
Λ is not 1019 GeV,
Λ is as low as 103 GeV
4
Fundamental energy scales
Greg Anderson, Northwestern University
5
Every fundamental energy scale should
have a dynamical origin
K. Lane
6
Linear sigma model (model of nuclear forces)
U(σ,π)
σ
v = μ/√λ ≈ 90 MeV
σ=v+σ
(spontaneous chiral symmetry breaking)
SU(2)L x SU(2)R → SU(2)V
7
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
8
Where are EW pions ???
mσ = μ2
mπ = 0
SU(2)L x SU(2)R → SU(2)V (global)
SU(2)L x U(1)Y → U(1)Q (local)
massless GB
Higgs mechanism: W,Z become
massive by eating GB
EW pions Φ1,Φ2,χ become WL, ZL
9
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 …
10
Nonlinear σ model (QCD)
v = 90 MeV
Effective Lagrangian valid until a few hundred MeV
11
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 !
12
Nonlinear σ model (SM Higgs sector)
v = 246 GeV
Effective Lagrangian valid until 1-3 TeV
13
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
14
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
15
Extended Technicolor (ETC)
ETC was introduced to give masses to fermions
… but introduced also large FCNC and conflict with
precision EW measurements
U
Walking technicolor
D
f
ETC
f
ETC has also problem to explain large top mass
(mt = 174 GeV)
Topcolor assisted technicolor
16
WL WL → WL WL
WL WL → t t
t
π = WL
tt→tt
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
17
International Linear Collider: e+e- at 1 TeV
ee ―› νν WW
ee ―› νν tt
ee ―› ρtt ―› WW tt
ee ―› ρtt ―› tt tt
ee ―› WW
ee ―› tt
Large Hadron Collider: pp at 14 TeV
pp ―› jj WW
pp ―› jj tt
pp ―› ρtt ―› WW tt
pp ―› ρtt ―› tt tt
pp ―› WW
pp ―› tt
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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)
BESS
μ
+
+
+
+ b1 ψL i γ (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 ψ L i γ μ u + A μ γ 5 u ψ L
Our model
+ λ2 ψR Pλ i γμ u Aμ γ5 u+ Pλ ψR
Standard Model with Higgs replaced with ρ
ωμ = [u+(∂μ + i g’/2 Yμτ3)u + u(∂μ+ i g Wμ . τ/2)u+]/2
gπ- u(∂=+ i M
v +g]/2v)
ρ /(2
Aμ = [u+(∂μ + i g’/2 Yμτ3)u
g
W
.
τ/2)u
μ
μ
t
g
= gv b2 /4 + …
u = exp(i π . τ /2v)
ψL = (tL,bL)
t
Pb = diag(p1,p2)
Mρ ≈ √a v gv /2
19
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)
20
Partial (Γ―›WW) and
total width Γtot of ρ
21
22
Subset of fusion diagrams +
approximations (Pythia)
Full calculation of 66 diagrams at tree level
(CompHEP)
23
Pythia vs CompHEP
ρ (M = 700 GeV, Γ = 12.5 GeV, gv = 20, b2 = 0.08)
Before cuts
√s (GeV)
Pythia (fb)
CompHEP (fb)
800
0.35
0.66
1000
0.95
1.16
1500
3.27
3.33
24
25
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)
26
27
R=
|N(ρ) – N(no res.)|
√N(ttγ+eett)+(N(no res.))
≈ S/√B > 5
= gv
= gv
28
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)
29
W W tt  X 39/8 diagrams in the dominant gg channel
ρ
No-resonance
background
W  W - tt
l l jjbjjb jj
ρ
ρ
30
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
σ(gg) = 10.2 fb ―› 1.0 fb
gt1,2 = gv b2/4
Cuts: 700-3Γρ < mWW < 700 +3Γρ (GeV)
pT (t) > 100 GeV,
|y(t)| < 2
No resonance background:
σ(gg) =
0.037 fb
31
l jjbjjbjj
reconstruction (CompHEP, Pythia, Atlfast, Root)
l
Athena 9.0.3
One charged lepton channel:
W W tt  W W bW  b W   l l jjbjjb jj 40% of events
Cuts:
pT
of
electron > 30 GeV
muon > 20 GeV
mass of the W:
jets > 25 GeV
b-tagging efficiency
mW  25 GeV
50%
Reconstruction criterion
 2  (m j j  mW ) 2  (m j
1 2
3 j4
 mW ) 2  (m j5 j6  mW ) 2 
(mW1b1  mt ) 2  (mW2b2  mt ) 2
32
Distribution in invariant mass of WW pair (ρ →WW)
ρ: Mρ=700 GeV,
Γρ=4 GeV,
b2=0.08, gv=10
m WW [GeV]
8 diagrams
39 diagrams
m WW [GeV]
Lum=100/fb
12.2 events
m WW [GeV]
number of events/17 GeV
number of events/17 GeV
Pz(ν) chosen correctly in 61.5 % of events
Lum=100/fb
2.4 events
m WW [GeV]
33
39 diagrams
8 diagrams
Lum=100/fb
2.4 events
number of events/0.6 GeV
number of events/0.6 GeV
Mass of the W boson
Lum=100/fb
2.4 events
number of events/2.5 GeV
number of events/2.5 GeV
m jj[GeV]
Mass of the top quark
Lum=100/fb
12.2 events
m jj[GeV]
Lum=100/fb
12.2 events
34
m Wb[GeV]
m Wb[GeV]
ρ: Mρ=1000 GeV
Γρ=26 GeV
number of events/32 GeV
m WW [GeV]
Lum = 100 fb-1
12.8 events
m WW [GeV]
35
1. Can we improve WWtt reconstruction ?
L = 100/fb
2.4 events
8 diagrams

2.

W W tt
versus
ttt t
8 diagrams
36
Conclusions
• New vector resonance as an alternative
to Higgs Boson
• Modified BESS model motivated by
technicolor
• Rich e+e- and pp phenomenology
37