Higgs bosons and Supersymmetry 1. The Higgs mechanism in the Standard Model — The story so far — The SM Higgs boson at the LHC — Problems with the SM Higgs boson 2. Supersymmetry — Surpassing Poincar´ e — Supersymmetry motivations — The MSSM 3. Conclusions & Summary D.J. Miller, Edinburgh, July 2, 2004 page 1 of 25
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Higgs bosons and Supersymmetry
1. The Higgs mechanism in the Standard Model— The story so far— The SM Higgs boson at the LHC— Problems with the SM Higgs boson
2. Supersymmetry— Surpassing Poincare— Supersymmetry motivations— The MSSM
3. Conclusions & Summary
D.J. Miller, Edinburgh, July 2, 2004 page 1 of 25
1. Electroweak Symmetry Breaking in the Standard Model
1. Electroweak Symmetry Breaking in the Standard Model
Observation:
• Weak nuclear force mediated by W± and Z bosons
MW = 80.423± 0.039GeV MZ = 91.1876± 0.0021GeV
• W couples only to left–handed fermions
• Fermions have non-zero masses
Theory:
We would like to describe electroweak physics by an SU(2)L⊗U(1)Y gauge theory.
Chiral theory ⇒ { Left–handed fermions are SU(2) doubletsright–handed fermions are SU(2) singlets
There are two problems with this, both concerning mass:
1. Electroweak Symmetry Breaking in the Standard Model
Sensitivity |∂Otheo/∂logMH|/σmeas
Winter 2004
ΓZΓZ
σhadσ0
RlR0
AfbA0,l
Al(Pτ)Al(Pτ)
RbR0
RcR0
AfbA0,b
AfbA0,c
AbAb
AcAc
Al(SLD)Al(SLD)
sin2θeffsin2θlept(Qfb)
mWmW
ΓWΓW
QW(Cs)QW(Cs)
sin2θ−−(e−e−)sin2θMS
sin2θW(νN)sin2θW(νN)
gL(νN)g2
gR(νN)g2
0
24
0 1 2 3 4 5
MH [GeV]
Summer 2003
ΓZ [GeV]ΓZ [GeV]σhad [nb]σ0
RlR0
AfbA0,l
Al(Pτ)Al(Pτ)
RbR0
RcR0
AfbA0,b
AfbA0,c
AbAb
AcAc
Al(SLD)Al(SLD)
sin2θeffsin2θlept(Qfb)
mW [GeV]mW
ΓW [GeV]ΓW
sin2θW(νN)sin2θW(νN)
QW(Cs)QW(Cs)
0
21
10 102
103
logarithmic sensitivity to MH [c.f. top mass]
Not clear how to combine different measurements
&%'$
NuTeV
D.J. Miller, Edinburgh, July 2, 2004 page 5 of 25
1. Electroweak Symmetry Breaking in the Standard Model
• The Large Hadron Collider (LHC) will switch on in 2007
main goal: discover the mechanism of Electroweak Symmetry Breaking
Guaranteed to see something
WW scattering at LHC will violate unitarity without Higgs boson(or something else)
H
+W
-W
+W
-W
⇒M2H .
8π√
25GF
. (780 GeV)2
D.J. Miller, Edinburgh, July 2, 2004 page 6 of 25
1. Electroweak Symmetry Breaking in the Standard Model
SM Higgs production at the LHC
σ(pp→H+X) [pb]√s = 14 TeV
Mt = 175 GeV
CTEQ4Mgg→H
qq→Hqqqq_’→HW
qq_→HZ
gg,qq_→Htt
_
gg,qq_→Hbb
_
MH [GeV]0 200 400 600 800 1000
10-4
10-3
10-2
10-1
1
10
10 2
0 100 200 300 400 500 600 700 800 900 1000
Main production channel is gg → H�
��
��
��
��+
�� ���
��
D.J. Miller, Edinburgh, July 2, 2004 page 7 of 25
1. Electroweak Symmetry Breaking in the Standard Model
SM Higgs branching ratios
D.J. Miller, Edinburgh, July 2, 2004 page 8 of 25
1. Electroweak Symmetry Breaking in the Standard Model
1
10
10 2
102
103
mH (GeV)
Sig
nal s
igni
fican
ce H → γ γ + WH, ttH (H → γ γ ) ttH (H → bb) H → ZZ(*) → 4 l
H → ZZ → llνν H → WW → lνjj
H → WW(*) → lνlν WH → WWW(*)
Total significance
5 σ
∫ L dt = 100 fb-1
(no K-factors)
ATLAS
D.J. Miller, Edinburgh, July 2, 2004 page 9 of 25
1. Electroweak Symmetry Breaking in the Standard Model
Is the Standard Model valid to all energies?
V (φ) = λ(φ†φ)2 − µ2(φ†φ) MH =√
2λ(v2)v
Coupling λ runs with energy, t ≡ logQ2/v2:
dλdt
= 316π2(4λ
2 + λm2t v
2 −m4t v
4/4)
• Triviality upper bound on MH
Large λ: λ(Q2) ≈ λ(v2)/(1− 3λ(v2)4π2 logQ2/v2) <∞
−→M2H ≤ 8π2v2/3 log Q2
v2
[this triviality problem is endemic to scalar theories]
• Vacuum stability lower bound on MH
Small λ: large mt pulls λ(Q2) < 0
−→ electroweak vacuum unstable
D.J. Miller, Edinburgh, July 2, 2004 page 10 of 25
1. Electroweak Symmetry Breaking in the Standard Model
If no new physics up to MGUT ≈ 1016 GeV
⇒MH ≈ 130–170 GeV
Fits well with Electroweak precision tests...
D.J. Miller, Edinburgh, July 2, 2004 page 11 of 25
1. Electroweak Symmetry Breaking in the Standard Model
The Hierarchy Problem
The Standard Model (SM) has a fundamental flaw:
The parameters of the model must be fine tuned
The Higgs mass gains corrections from fermion loops
H
f
H
Quadratic divergence:
δM2H = −2
|λf |216π2Λ
2 + ...
Λ ∼ Scale of new physics ∼ 1016 GeV (?)
⇒ δM2H ∼ 1030 GeV !
must arrange for parameters to cancel to one part in 1026
Is this a hint that new physics will be seen at the LHC?
D.J. Miller, Edinburgh, July 2, 2004 page 12 of 25
2. Supersymmetry
2. Supersymmetry
The new physics most favoured by theorists is Supersymmetry
— a symmetry between particles with different spins
Coleman-Mandula theorem:
Most general symmetries of the S matrix are• boosts, rotations and translations of the Poincare group• symmetries of compact Lie groups (e.g. U(1), SU(2), E6...)
But they didn’t consider groups with anti-commuting generators
Supersymmetry enlarges the Poincare group by introducing new fermioniccoordinates of space-time, θ, θ [anticommuting Weyl spinors]
fields φ(x)−→promoted
superfields Ψ(x, θ, θ)
D.J. Miller, Edinburgh, July 2, 2004 page 13 of 25
2. Supersymmetry
Expand superfields in powers of θ and θ:
Since θ only has two components, terms like θθθ must vanish