Higgs bosons and Supersymmetry - Gladmiller/doc/ppcosmows.pdf · 2. Supersymmetry More motivations...
Transcript of Higgs bosons and Supersymmetry - Gladmiller/doc/ppcosmows.pdf · 2. Supersymmetry More motivations...
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:
• gauge symmetry ⇒ massless gauge bosons• SU(2)L forbids m(ψLψR + ψRψL) terms ⇒ massless fermions
D.J. Miller, Edinburgh, July 2, 2004 page 2 of 25
1. Electroweak Symmetry Breaking in the Standard Model
Higgs Mechanism
Introduce new SU(2) doublet scalar field (φ) with potential
V (φ) = λ|φ|4 − µ2|φ|2Minimum of the potential is not at zero
〈φ〉 = 1√2
(
0v
)
with v =
√
µ2
λ
Electroweak symmetry is broken
Interactions with scalar field provide:
• Gauge boson masses
MW =1
2gv MZ =
1
2
√
g2 + g′2v
• Fermion masses
Yf ψRψLφ −→ mf = Yfv/√
2
4 degrees of freedom., 3 become longitudinal components of W and Z,
one left over the Higgs boson
D.J. Miller, Edinburgh, July 2, 2004 page 3 of 25
1. Electroweak Symmetry Breaking in the Standard Model
The Higgs boson mass is not predicted in the SM
LEP limits (e+e− → ZH) ⇒ MH > 114.4 GeV at 95% C.L.
Electroweak Precision tests:
0
1
2
3
4
5
6
10020 400
mH [GeV]
∆χ2
Excluded Preliminary
∆αhad =∆α(5)
0.02761±0.000360.02747±0.00012incl. low Q2 data
Theory uncertainty
MH = 96+60−38 GeV MH < 219 GeV at 95% C.L.
D.J. Miller, Edinburgh, July 2, 2004 page 4 of 25
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
θαθβ = −θβθα
e.g. a chiral superfield (DαΨ = 0)
Ψ(x, θ, θ) = φ(x) + θψ(x) + θθF (x) [xµ = xµ + iθσµθ]
��
��
���
scalar
6
fermion@
@@
@@
@I
auxilliary field
Supersymmetry is just a rotation in the new enlarged space-time (x, θ, θ)
quarks, leptons ←→ squarks, sleptonsgauge bosons ←→ gauginosHiggs bosons ←→ higgsinos } neutralinos & charginos
“extra” particles are just different facets of the known SM particles
D.J. Miller, Edinburgh, July 2, 2004 page 14 of 25
2. Supersymmetry
The Hierarchy Problem Revisited
H
f
H
H H
f~
δM2H = +2
|λf |216π2Λ
2 + ... δM2H = −2
λf16π2Λ
2 + ...
Supersymmetry ⇒ |λf |2 = λf
quadratic divergence cancels (to all orders in perturbation theory)
⇒ Higgs mass stabilized!
D.J. Miller, Edinburgh, July 2, 2004 page 15 of 25
2. Supersymmetry
Supersymmetry breaking
Clearly supersymmetry is not a true symmetry of nature
— it must be broken
How supersymmetry is broken is not known but it might go something like this...
Hidden Sector Visible Sector
Exact Supersymmetry
E
Gauge theory becomesstrongly interactingCondensates form 〈FF 〉
-gravity
Gravitational interactions with hiddensector produce soft supersymmetry
breaking terms:M2
Λ
MPlanck
φ†φ
?
logarithmic running
Low energy softly broken supersymmetry
6
D.J. Miller, Edinburgh, July 2, 2004 page 16 of 25
2. Supersymmetry
More motivations for Supersymmetry
♦ Local supersymmetry Supergravity
♦ An essential ingredient of String Theory
Both of the above very exciting but only imply SuSy at some (high?) scaleThey are no motivation for low (TeV) scale SuSy
♦ Gauge coupling unification
If we want to unify the 3 forces atMGUT, need to unify their couplings
Supersymmetry more compatiblewith gauge unification
Desert between MEW ≈ 103 GeVand MGUT ≈ 1016 GeV
2 4 6 8 10 12 14 16 18Log10(Q/1 GeV)
0
10
20
30
40
50
60
α−1
α1−1
α2−1
α3−1
SM
SuSy
D.J. Miller, Edinburgh, July 2, 2004 page 17 of 25
2. Supersymmetry
♦ “Natural” mechanism of electroweak symmetry breaking
16π2 d
dtM2
Hu≈ 6h2
t (M2Hu
+M2Q3
+M3u3)− 6g22M
22 −
6
5g21M
21
[t = log QMGUT
]
large top mass pulls M2Hu< 0,
breaking Electroweak Symmetry
Explains why we have a“mexican hat” potential
[Still doesn’t explain whyMH(MGUT)�MGUT]
2
Hu
Hd
B~
L~
W~
g~qL~
tL~
tR~
qR~
4 6 8
Run
ning
Mas
s (G
eV)
M0
m1/2
10Log10Q (GeV)
12 14 165–97
8303A15
600
400
200
0
–200
µ + M0
22
D.J. Miller, Edinburgh, July 2, 2004 page 18 of 25
2. Supersymmetry
♦ Dark Matter
Supersymmetry allows lepton and baryon number violating interactions
⇒ Proton decay!
u
d
u
b~
-e
u
u
Bλ Lλ
Observation: life-time of the proton > 1032 years
D.J. Miller, Edinburgh, July 2, 2004 page 19 of 25
2. Supersymmetry
Introduce R-parity:
PR = (−1)3B−3L+2S
SM particle: PR = 1 SuSy partner: PR = −1
R-parity conservation ⇒
• Both B & L conserved ⇒ No proton decay
• The Lightest Supersymmetric Particle (LSP) is stable
Could the LSP be dark matter?
D.J. Miller, Edinburgh, July 2, 2004 page 20 of 25
2. Supersymmetry
Minimal Supersymmetric Standard Model (MSSM)
has minimum particle content for a supersymmetric model
Now have two Higgs doublets (analyticity and cancellation of anomalies)
Hd =
(
H0d
H−d
)
, Hu =
(
H+u
H0u
)
neutral components gain (real) vacuum expectation values
〈Hd〉 = 1√2
(
vd0
)
, 〈Hu〉 = 1√2
(
0vu
)
v2u + v2
d = v2 vu/vd ≡ tanβ
8 degrees of freedom: 3 eaten by W±, Z −→ 5 Higgs bosons left
2 scalar Higgs fields h, H1 pseudoscalar Higgs field A2 charged Higgs fields H±
D.J. Miller, Edinburgh, July 2, 2004 page 21 of 25
2. Supersymmetry
An example of MSSM Higgs boson masses
0 50 100 150 200 250 300 350 400 450 500MA
0
50
100
150
200
250
300
350
400
450
500
Hig
gs M
ass
[GeV
]
ScalarPseudoscalarCharged
MSUSY = 1 TeV
µ = 500 GeV
tanβ = 3
lightest Higgs mass . 135 GeV
D.J. Miller, Edinburgh, July 2, 2004 page 22 of 25
2. Supersymmetry
LHC Higgs coverage at ATLAS
ATLAS
LEP 2000
ATLAS
mA (GeV)
tan
β
1
2
3
4
56789
10
20
30
40
50
50 100 150 200 250 300 350 400 450 500
0h 0H A
0 +-H
0h 0H A
0 +-H
0h 0H A
00h H
+-
0h H+-
0h only
0 0Hh
ATLAS - 300 fbmaximal mixing
-1
LEP excluded
D.J. Miller, Edinburgh, July 2, 2004 page 23 of 25
2. Supersymmetry
Neutralinos & charginos
Supersymmetric partners to gauge bosons and Higgs bosons arefermions with the same quantum numbers ⇒ they mix
2 gauginos + 2 higgsinos −→ 4 neutralinos (χ0i , i = 1,4)
2 charged gauginos + 2 charged higgsinos −→ 4 charginos (χ±i , i = 1,2)
For many parameter choices, a neutralino is the “lightest supersymmetric particle”
R partity ⇒ LSP stable
Supersymmetry has very distinctive missing energy signatures
D.J. Miller, Edinburgh, July 2, 2004 page 24 of 25
3. Conclusions & Summary
3. Conclusions & Summary
♦ The Higgs mechanism breaks electroweak symmetry, providing massesfor the W & Z bosons and fermions
— it(or some altenative) will be discovered at the LHC
— Unlikely to be valid up to the GUT scale
— The SM Higgs mechanism needs extreme fine tuning(the hierarchy problem)
♦ Supersymmetry:
— extends space-time adding new fermionic coordinates
— cures the hierarchy problem in a very natural way
— explains the mexican hat
— provides a dark matter candidate – the neutralino
— contains multiple Higgs bosons
We should have some answers soon... (by 2010)
D.J. Miller, Edinburgh, July 2, 2004 page 25 of 25