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

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

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

4. 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

5. Fundamental energy scales
Greg Anderson, Northwestern University

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

7. 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

8. 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

9. 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

10. 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 …

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

12. 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 !

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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

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

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

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

24. 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)
Pythia (fb)
CompHEP (fb)

26. Backgrounds (Pythia) e+e- → e+e- tt e+e- → tt γ
σ(0.8 TeV) = fb → 0.13 fb (0.20 fb)
σ(1.0 TeV) = fb → fb (0.16 fb)

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

29. 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)

30. 39/8 diagrams in the dominant gg channel
No-resonance
background ρ ρ ρ

31. 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) = fb ―› fb
Cuts: Γρ < mWW < Γρ (GeV)
pT (t) > 100 GeV, |y(t)| < 2
No resonance background: σ(gg) = fb

32. 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

33. 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

34. 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

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

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

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