3. What is a “New Physics Scenario”?
“New Physics”:
A structural change to the Standard Model Lagrangian
“Scenario”:
“A sequence of events especially when imagined”
5. Why New Physics?
Four Paradigms
Experiment doesn’t match theoretical predictions
Best motivation
6. Why New Physics?
Four Paradigms
Experiment doesn’t match theoretical predictions
Best motivation
Parameters are “Unnatural”
Well defined and have good theoretical motivation
7. Why New Physics?
Four Paradigms
Experiment doesn’t match theoretical predictions
Best motivation
Parameters are “Unnatural”
Well defined and have good theoretical motivation
Reduce/Explain the multitude of parameters
Typically has limited success, frequently untestable
8. Why New Physics?
Four Paradigms
Experiment doesn’t match theoretical predictions
Best motivation
Parameters are “Unnatural”
Well defined and have good theoretical motivation
Reduce/Explain the multitude of parameters
Typically has limited success, frequently untestable
To know what is possible
Let’s us know what we can look for in experiments
Limited only by creativity and taste
9. The Plan
Beyond the SM Physics is 30+ years old
There is no one leading candidate for new physics
New physics models draw upon all corners of the SM
In 2 hours there will be a sketch some principles
used in a half dozen paradigms
that created hundreds of models
and spawned thousands of papers
10. Outline
The Standard Model
Motivation for Physics Beyond the SM
Organizing Principles for New Physics
New Physics Scenarios
Supersymmetry
Extra Dimensions
Strong Dynamics
11. Standard Model: a story of economy
symmetry unification→
15 Particles, 12 Force carriers
↔ 2700 ¯ψV ψ Couplings
12. Standard Model: a story of economy
νe
L eL eR uL uR dRdLuLuL uRuR dL dL dR dR
symmetry unification→
15 Particles, 12 Force carriers
↔ 2700 ¯ψV ψ Couplings
13. Standard Model: a story of economy
νe
L eL eR uL uR dRdLuLuL uRuR dL dL dR dR
e q u d
5 Particles 3 Couplings
symmetry unification→
15 Particles, 12 Force carriers
↔ 2700 ¯ψV ψ Couplings
14. Standard Model: a story of economy
νe
L eL eR uL uR dRdLuLuL uRuR dL dL dR dR
e q u d
5 Particles 3 Couplings
symmetry unification→
4 forces, 20 particles, 20 parameters
x 3
Mystery of Generations:
15 Particles, 12 Force carriers
↔ 2700 ¯ψV ψ Couplings
16. The Standard Model
... where we stand today
LSM = LGauge + LFermion + LHiggs + LYukawa
LGauge = −
1
4
Bµν
2
−
1
4
Wa
µν
2
−
1
4
GA
µν
2
17. The Standard Model
... where we stand today
LSM = LGauge + LFermion + LHiggs + LYukawa
LGauge = −
1
4
Bµν
2
−
1
4
Wa
µν
2
−
1
4
GA
µν
2
LFermion = ¯QiiD Qi + ¯Uc
i iD Uc
i + ¯Dc
i iD Dc
i + ¯LiiD Li + ¯Ec
i iD Ec
i
18. The Standard Model
... where we stand today
LSM = LGauge + LFermion + LHiggs + LYukawa
LGauge = −
1
4
Bµν
2
−
1
4
Wa
µν
2
−
1
4
GA
µν
2
LFermion = ¯QiiD Qi + ¯Uc
i iD Uc
i + ¯Dc
i iD Dc
i + ¯LiiD Li + ¯Ec
i iD Ec
i
LHiggs = |DµH|2
− λ(|H|2
− v2
/2)2
19. The Standard Model
... where we stand today
LSM = LGauge + LFermion + LHiggs + LYukawa
LGauge = −
1
4
Bµν
2
−
1
4
Wa
µν
2
−
1
4
GA
µν
2
LFermion = ¯QiiD Qi + ¯Uc
i iD Uc
i + ¯Dc
i iD Dc
i + ¯LiiD Li + ¯Ec
i iD Ec
i
LHiggs = |DµH|2
− λ(|H|2
− v2
/2)2
LYuk = yij
u QiUc
j H + yij
d QiDc
jH∗
+ yij
e LiEc
j H∗
21. Motivations for Physics Beyond the Standard Model
The Hierarchy Problem
Dark Matter
Exploration
22. The Hierarchy Problem
The SM suffers from a stability crisis
−µ2
−
3y2
t Λ2
t
16π2
+
3
4 g2
Λ2
W
16π2
+
1
4 g 2
Λ2
B
16π2
+
λΛ2
H
16π2
Higgs vev determined by effective mass, not bare mass
Many contributions that must add up to -(100 GeV)2
=
23. A recasting of the problem:
Why is gravity so weak?
GN
GF
= 10−32
Explain how to make GF large (i.e. v small)
Explain why GN is so small (i.e. MPl large)
24. 1998: Large Extra Dimensions
(Arkani-Hamed, Dimopoulos, Dvali)
High scale is a “mirage”
Gravity is strong at the weak scale
Need to explain how gravity is weakened
MPlanckMWeak
α
2001: Universal Extra Dimensions
(Appelquist, Cheng, Dobrescu)
25. 1978: Technicolor
(Weinberg, Susskind)
1999: Warped Gravity
(Randall, Sundrum)
2001: Little Higgs
(Arkani-Hamed, Cohen, Georgi)
The Higgs is composite
h
Resolve substructure at small distances
αM2
Composite
Why hadrons are lighter than Planck Scale
28. A New Symmetry
Scalar
Fermion
φ
ψ Supersymmetry
φ → ψ
Scalar Mass related to Fermion Mass
φ
Scalar
Scalar
φ
Shift Symmetry
φ → φ +
Scalar Mass forbidden
µ2
= 0 not specialUV dynamics at
29. A New Symmetry
Scalar
Fermion
φ
ψ Supersymmetry
φ → ψ
Scalar Mass related to Fermion Mass
φ
Scalar
Scalar
φ
Shift Symmetry
φ → φ +
Scalar Mass forbidden
1981: Supersymmetric Standard Model
(Dimopoulos, Georgi)
2001: Little Higgs
(Arkani-Hamed, Cohen, Georgi)
1974: Higgs as Goldstone Boson
(Georgi, Pais)
µ2
= 0 not specialUV dynamics at
30. Dark Matter
85% of the mass of the Universe is not described by the SM
There must be physics beyond the Standard Model
Cold dark matter
Electrically & Color Neutral
Cold/Slow
Relatively small self interactions
Interacts very little with SM particles
No SM particle fits the bill
31. The WIMP Miracle
DM was in equilibrium with SM in the Early Universe
1 3 10 30 100 300 1000
−20
−15
−10
−5
0
logY(x)/Y(x=0)
x ≡ m/T
σAnnv
Increasing
32. The WIMP Miracle
DM was in equilibrium with SM in the Early Universe
T mDM
1 3 10 30 100 300 1000
−20
−15
−10
−5
0
logY(x)/Y(x=0)
x ≡ m/T
σAnnv
Increasing
33. The WIMP Miracle
DM was in equilibrium with SM in the Early Universe
T mDM
T ∼ mDM
Reverse process energetically disfavored
1 3 10 30 100 300 1000
−20
−15
−10
−5
0
logY(x)/Y(x=0)
x ≡ m/T
σAnnv
Increasing
34. The WIMP Miracle
DM was in equilibrium with SM in the Early Universe
T mDM
T ∼ mDM
Reverse process energetically disfavored
1 3 10 30 100 300 1000
−20
−15
−10
−5
0
logY(x)/Y(x=0)
x ≡ m/T
σAnnv
Increasing
35. The WIMP Miracle
DM was in equilibrium with SM in the Early Universe
T mDM
T mDM
DM too dilute to find each other
T ∼ mDM
Reverse process energetically disfavored
1 3 10 30 100 300 1000
−20
−15
−10
−5
0
logY(x)/Y(x=0)
x ≡ m/T
σAnnv
Increasing
36. The WIMP Miracle
DM was in equilibrium with SM in the Early Universe
T mDM
T mDM
DM too dilute to find each other
T ∼ mDM
Reverse process energetically disfavored
Relic density is “frozen in”
1 3 10 30 100 300 1000
−20
−15
−10
−5
0
logY(x)/Y(x=0)
x ≡ m/T
σAnnv
Increasing
44. Chirality
A symmetry acting a fermions that forbids masses
Ψ =
f
¯fc M ¯ΨΨ = M(ffc
+ ¯f ¯fc
)
f → eiα
f fc
→ eiαc
fc
Can do independent phase rotations
45. Chirality
A symmetry acting a fermions that forbids masses
Ψ =
f
¯fc M ¯ΨΨ = M(ffc
+ ¯f ¯fc
)
α = −αc
Vector symmetry
Allows mass
Jµ
V = ¯Ψγµ
Ψ
f → eiα
f fc
→ eiαc
fc
Can do independent phase rotations
46. Chirality
A symmetry acting a fermions that forbids masses
Ψ =
f
¯fc M ¯ΨΨ = M(ffc
+ ¯f ¯fc
)
α = −αc
Vector symmetry
Allows mass
Jµ
V = ¯Ψγµ
Ψ
α = αc
Axial symmetry
Forbids mass
Jµ
A = ¯Ψγ5γµ
Ψ
f → eiα
f fc
→ eiαc
fc
Can do independent phase rotations
47. The Standard Model is a Gauged Chiral Theory
All masses are forbidden by a gauge symmetry
15 different bilinears all forbidden
QUc
∼ (1, 2)− 1
2 QEc
∼ (3, 2)7
6
Dc
Ec
∼ (¯3, 1)4
3
Uc
L ∼ (¯3, 2)− 5
3
Ec
Ec
∼ (1, 1)+2
LL ∼ (1, 1)−1
QQ ∼ (¯3, 3)1
3
Dc
Dc
∼ (3, 1)2
3
Dc
L ∼ (3, 2)− 1
6
etc...
The Standard Model force carriers forbid fermion masses
48. Electroweak Symmetry Breaking
Breaking of Chiral Symmetry
SU(2)L × U(1)Y → U(1)EMH ∼
0
v
V (H) = λ|H|4
− µ2
|H|2
LYuk = yij
u QiUc
j H + yij
d QiDc
jH∗
+ yij
e LiEc
j H∗
Q =
U
D L =
ν
E
LYuk = mij
u UiUc
j + mij
d DiDc
j + mij
e EiEc
j
Fermions pick up Dirac Masses
49. Effective Field Theory
Take a theory with light and heavy particles
LFull = Llight(ψ) + Lheavy(Ψ, ψ)
If we only can ask questions in the range
√
s Λcut off
<
∼ MΨ
Λcut off
√
s
mψ
MΨ
50. Effective Field Theory
Take a theory with light and heavy particles
LFull = Llight(ψ) + Lheavy(Ψ, ψ)
If we only can ask questions in the range
√
s Λcut off
<
∼ MΨ
Λcut off
√
s
mψ
MΨ
with n > 0
Dynamics of light fields described by
Lfull(ψ) = Llight(ψ) + δL(ψ) δL ∼ O(ψ)/Λn
cut off
Only contribute as δσ ∼
√
s
Λcut off
n
known as “irrelevant operators”
Nonrenomalizable
51. We have only tested the SM to certain precision
How do we know that there aren’t those effects?
We know the SM isn’t the final theory of nature
We should view any theory we test as
an “Effective Theory” that describes the dynamics
Shouldn’t be constrained by renormalizability
One way of looking for new physics is by
looking for these nonrenormalizable operators
60. Flavor Symmetries
Symmetries that interchange fermions
Turn off all the interactions of the SM = Free Theory
L = ¯ψi
i∂ ψi ψi → Uj
i ψj U(N) symmetry
61. Flavor Symmetries
Symmetries that interchange fermions
Turn off all the interactions of the SM = Free Theory
Q, Uc
, Dc
, L, Ec
= 15 Fermions/Generation
45 Total fermions that look the same in the free theory
global symmetry⇒ U(45)
L = ¯ψi
i∂ ψi ψi → Uj
i ψj U(N) symmetry
62. Flavor Symmetries
Symmetries that interchange fermions
Turn off all the interactions of the SM = Free Theory
Q, Uc
, Dc
, L, Ec
= 15 Fermions/Generation
45 Total fermions that look the same in the free theory
global symmetry⇒ U(45)
Gauge interactions destroy most of this symmetry
U(3)5
= U(3)Q × U(3)Uc × U(3)Dc × U(3)L × U(3)Ec
Yukawa couplings break the rest...
but they are the only source of U(3)5 breaking
L = ¯ψi
i∂ ψi ψi → Uj
i ψj U(N) symmetry
63. Prevents Flavor Changing Neutral Currents
Imagine two scalars with two sources of flavor breaking
LYuk = yij
Hψiψc
j + κij
φψiψc
j
H = v + h mij
= yij
v
64. Prevents Flavor Changing Neutral Currents
Imagine two scalars with two sources of flavor breaking
LYuk = yij
Hψiψc
j + κij
φψiψc
j
H = v + h mij
= yij
v
Can diagonalize mass matrix with unitary transformations
ψi → Uj
i ψj ψc
i → V j
i ψc
j mij
→ (UT
mV )ij
= Miδij
LYuk → Miδij
ψiψc
j (1 + h/v) + (UT
κV )ij
φψiψj
65. Prevents Flavor Changing Neutral Currents
Imagine two scalars with two sources of flavor breaking
LYuk = yij
Hψiψc
j + κij
φψiψc
j
H = v + h mij
= yij
v
Higgs doesn’t change flavor, but other scalar field is a disaster
K0
¯K0
d s
¯s¯d
φ
κ ∝ yUnless
mφ
κ
>
∼ 100 TeVor
Can diagonalize mass matrix with unitary transformations
ψi → Uj
i ψj ψc
i → V j
i ψc
j mij
→ (UT
mV )ij
= Miδij
LYuk → Miδij
ψiψc
j (1 + h/v) + (UT
κV )ij
φψiψj
66. Anomaly Cancellation
Quantum violation of current conservation
∂µ
Ja
µ ∝ Tr Ta
Tb
Tc
(Fb ˜Fc
)
Ta
Tb
Tc
ψ
An anomaly leads to a mass for a gauge boson
m2
=
g2
16π2
3
Λ2
73. νe
L eL eR uL uR dRdLuLuL uRuR dL dL dR dR
Grand Unification
e q u d SU(3) × SU(2) × U(1)
Gauge coupling unification indicates forces arise from single entity
74. νe
L eL eR uL uR dRdLuLuL uRuR dL dL dR dR
Grand Unification
e q u d
¯5 10 SU(5)
SU(3) × SU(2) × U(1)
Gauge coupling unification indicates forces arise from single entity
75. νe
L eL eR uL uR dRdLuLuL uRuR dL dL dR dR
Grand Unification
e q u d
¯5 10 SU(5)
νe
R
Ψ SO(10)
SU(3) × SU(2) × U(1)
Gauge coupling unification indicates forces arise from single entity
76. Standard Model Summary
The Standard Model is chiral gauge theory
It is an effective field theory
It is anomaly free & anomaly cancellation
restricts new charged particles
Making sure that there is no new sources
of flavor violation ensures that new theories are
not horribly excluded
SM Fermions fit into GUT multiplets,
but gauge coupling unification doesn’t quite work
81. SUSY Breaking
SUSY is not an exact symmetry
We don’t know how SUSY is broken, but
SUSY breaking effects can be parameterized in the Lagrangian
Lsoft = Lm2
0
+ Lm 1
2
+ LA + LB
82. SUSY Breaking
SUSY is not an exact symmetry
We don’t know how SUSY is broken, but
SUSY breaking effects can be parameterized in the Lagrangian
Lsoft = Lm2
0
+ Lm 1
2
+ LA + LB
Lm2
0
= m2
ψ
i
j
˜ψ†
i
˜ψj
+m2
Hu
|Hu|2
+ m2
Hd
|Hd|2
ψ ∈ Q, Uc
, Dc
, L, Ec
83. SUSY Breaking
SUSY is not an exact symmetry
We don’t know how SUSY is broken, but
SUSY breaking effects can be parameterized in the Lagrangian
Lsoft = Lm2
0
+ Lm 1
2
+ LA + LB
Lm 1
2
= m1
˜B ˜B + m2
˜W ˜W + m3˜g˜g
Lm2
0
= m2
ψ
i
j
˜ψ†
i
˜ψj
+m2
Hu
|Hu|2
+ m2
Hd
|Hd|2
ψ ∈ Q, Uc
, Dc
, L, Ec
84. SUSY Breaking
SUSY is not an exact symmetry
We don’t know how SUSY is broken, but
SUSY breaking effects can be parameterized in the Lagrangian
Lsoft = Lm2
0
+ Lm 1
2
+ LA + LB
Lm 1
2
= m1
˜B ˜B + m2
˜W ˜W + m3˜g˜g
LA = aij
u
˜Qi
˜Uc
j Hu + aij
d
˜Qi
˜Dc
jHd + aij
e
˜Li
˜Ec
j Hd
Lm2
0
= m2
ψ
i
j
˜ψ†
i
˜ψj
+m2
Hu
|Hu|2
+ m2
Hd
|Hd|2
ψ ∈ Q, Uc
, Dc
, L, Ec
85. SUSY Breaking
SUSY is not an exact symmetry
We don’t know how SUSY is broken, but
SUSY breaking effects can be parameterized in the Lagrangian
Lsoft = Lm2
0
+ Lm 1
2
+ LA + LB
Lm 1
2
= m1
˜B ˜B + m2
˜W ˜W + m3˜g˜g
LA = aij
u
˜Qi
˜Uc
j Hu + aij
d
˜Qi
˜Dc
jHd + aij
e
˜Li
˜Ec
j Hd
LB = Bµ HuHd
Lm2
0
= m2
ψ
i
j
˜ψ†
i
˜ψj
+m2
Hu
|Hu|2
+ m2
Hd
|Hd|2
ψ ∈ Q, Uc
, Dc
, L, Ec
86. Problem with Parameterized SUSY Breaking
There are over 100 parameters once
Supersymmetry no longer constrains interactions
Most of these are new flavor violation parameters
or CP violating phases
Horribly excluded
Susy breaking is not generic!
m2i
j
˜Q†
i
˜Qj ˜Qi → ˜Uj
i
˜Qj
gs ˜g ˜Q†
i Qi
→ gs ˜g ˜Q†
i ( ˜U†
U)i
jQj
87. Soft Susy Breaking
i.e. Super-GIM mechanism
Universality of soft terms
d
¯d ¯s
s
˜g ˜g
˜d, ˜s,˜b
˜d, ˜s,˜b
K0
K
0
88. Soft Susy Breaking
i.e. Super-GIM mechanism
Universality of soft terms
d
¯d ¯s
s
˜g ˜g
˜d, ˜s,˜b
˜d, ˜s,˜b
K0
K
0
Need to be Flavor Universal Couplings
A ∝ 11
m2
0 ∝ 11Scalar Masses
Trilinear A-Terms
Approximate degeneracy of scalars
89. Proton Stability
New particles new ways to mediate proton decay
Dangerous couplings
Proton
Pion
u u
u
d
˜d
¯u
e+
LRPV = λBUc
Dc ˜Dc + λLQL ˜Dc
Supersymmetric couplings that violate SM symmetries
A new symmetry forbids these couplings: (−1)3B+L+2s
90. Proton Stability
New particles new ways to mediate proton decay
Lightest Supersymmetric Particle is stable
Dangerous couplings
Proton
Pion
u u
u
d
˜d
¯u
e+
LRPV = λBUc
Dc ˜Dc + λLQL ˜Dc
Supersymmetric couplings that violate SM symmetries
A new symmetry forbids these couplings: (−1)3B+L+2s
91. Proton Stability
New particles new ways to mediate proton decay
Lightest Supersymmetric Particle is stable
Dangerous couplings
Must be neutral and colorless -- Dark Matter
Proton
Pion
u u
u
d
˜d
¯u
e+
LRPV = λBUc
Dc ˜Dc + λLQL ˜Dc
Supersymmetric couplings that violate SM symmetries
A new symmetry forbids these couplings: (−1)3B+L+2s
92. Mediation of Susy Breaking
MSSM
Primoridal
Susy BreakingMediation
Susy breaking doesn’t occur inside the MSSM
Felt through interactions of intermediate particles
Studied to reduce the number of parameters
Gauge Mediation
Universal “Gravity” Mediation
Anomaly Mediation
Usually only 4 or 5 parameters...
but for phenomenology, these are too restrictive
93. The Phenomenological MSSM
The set of parameters that are:
Not strongly constrained
Easily visible at colliders
First 2 generation sfermions are degenerate
3rd generation sfermions in independent
Gaugino masses are free
Independent A-terms proportional to Yukawas
Higgs Masses are Free
5
5
3
3
4
20 Total Parameters
94. Charginos & Neutralinos
The Higgsinos, Winos and Binos
˜Hu ∼ 21
2
→ 0, +1 ˜Hd ∼ 2− 1
2
→ 0, −1 ˜W ∼ 30 → 0, +1, −1 ˜B ∼ 10 → 0
After EWSB:
2 Charge +1 Dirac Fermions
4 Charge 0 Majorana Fermions
L = µ ˜Hu
˜Hd + m2
˜W ˜W + m1
˜B ˜B
+(H†
u
˜Hu + H†
d
˜Hd)(g ˜W + g ˜B)
All mix together, but typically mixture is small
Tend find charginos next to their neutralino brethren
Neutralinos are good DM candidates
97. Collider signatures
9 RESULTS AND LIMITS 13
)2
Chargino Mass (GeV/c
100 110 120 130 140 150 160 170
3l)(pb)!
±
1
"#0
2
"~BR($%
0
0.2
0.4
0.6
0.8
1
1.2
-1
CDF Run II Preliminary, 3.2 fb
)2
Chargino Mass (GeV/c
LEP 2 direct
limit
BR$NLO
%Theory
%1±Expected Limit
%2±Expected Limit
95% CL Upper Limit: expected
Observed Limit
) > 0µ=0, (
0
=3, A&=60, tan
0
mSugra M
q
¯q
˜χ0
˜χ0
χ0
2
χ+
1
˜
˜ν
ν
Trileptons+MET: If sleptons are availableNeutralinos
Charginos
Sleptons
Mass
3Leptons+MET
98. Collider signatures
Trileptons+MET
Without sleptons in the decay chain
Neutralinos
Charginos
Sleptons
Mass
q
¯q
˜χ0
˜χ0
χ0
2
χ+
1 ν
W+
Z0
30% leptonic Br of W, 10% leptonic Br of Z
3% Total Branching Rate
99. ]2
[GeV/cg~M]2
[GeV/cq~M
q~= Mg~M 2
= 460 GeV/cq~M
300 400 500
-2
10
300 400 500
-2
10
200 300 400 500200 300 400 500
FIG. 2: Observed (solid lines) and expected (dashed lines)
95% C.L. upper limits on the inclusive squark and gluino
production cross sections as a function of Mq
(left) and
Mg
(right) in different regions of the squark-gluino mass
plane, compared to NLO mSUGRA predictions (dashed-
dotted lines). The shaded bands denote the total uncertainty
on the theory.
0 100 200 300 400 500 600
0
100
200
300
400
500
600
no mSUGRA
solution
LEP
UA1
UA2
g~
=
M
q~
M
0 100 200 300 400 500 600
0
100
200
300
400
500
600
observed limit 95% C.L.
expected limit
FNAL Run I
)
-1
<0 (L=2.0fbµ=5,!=0, tan0A
]
2
[GeV/cg
~M
]
2
[GeV/cq
~M
6
[4] H
[5] C
a
t
p
i
d
p
f
[6] D
0
[7] D
(
[8] T
[9] T
0
[10] M
(
[11] J
(
[12] M
(
[13] A
N
[14] F
(
[15] B
[16] B
Collider signatures
Gluino Pairs: 4j +MET Squark Pairs: 2j +MET Squark-Gluino Pairs: 3j +MET
q
¯q
˜g
˜g
q
q
¯q
¯q
˜χ0
˜χ0
˜q
˜q
q
q
¯q ¯q
˜χ0
˜χ0
˜q
˜q
q
qq ˜g
¯q
g
˜χ0
˜χ0
˜q
˜q
˜q
mSUGRA Search
m3 : m2 : m1 = 6 : 2 : 1
101. The Higgs Mass Problem
VHiggs = λ|H|4
+ µ2
|H|2
m2
h0 = 2λv2
= −2µ2
102. The Higgs Mass Problem
VHiggs = λ|H|4
+ µ2
|H|2
m2
h0 = 2λv2
= −2µ2
mh0 ≤ MZ0λsusy =
1
8
g2
+ g 2
cos2
2β
Need a susy copy of quartic coupling, only gauge coupling works in MSSM
103. The Higgs Mass Problem
m2
h0 = 2λv2
= −2µ2
H
t
˜t
H
δλ =
3y4
top
8π2
log
mstop
mtop
mh0 ≤ MZ0λsusy =
1
8
g2
+ g 2
cos2
2β
Need a susy copy of quartic coupling, only gauge coupling works in MSSM
104. The Higgs Mass Problem
δµ2
= −
3y2
top
8π2
m2
stop
H t ˜t
H
m2
h0 = 2λv2
= −2µ2
H
t
˜t
H
δλ =
3y4
top
8π2
log
mstop
mtop
mh0 ≤ MZ0λsusy =
1
8
g2
+ g 2
cos2
2β
Need a susy copy of quartic coupling, only gauge coupling works in MSSM
105. The Higgs Mass Problem
δµ2
= −
3y2
top
8π2
m2
stop
H t ˜t
H
Higgs mass gain is only log
Fine tuning loss is quadratic
Difficult to make the Higgs heavier than 125 GeV in MSSM
FT ∼
m2
h0
δµ2
m2
h0 = 2λv2
= −2µ2
H
t
˜t
H
δλ =
3y4
top
8π2
log
mstop
mtop
mh0 ≤ MZ0λsusy =
1
8
g2
+ g 2
cos2
2β
Need a susy copy of quartic coupling, only gauge coupling works in MSSM
106. Susy is the leading candidate for BSM Physics
Dark Matter candidate
Gauge Coupling Unification
Compelling structure
Become the standard lamppost
Basic Susy Signatures away from mSUGRA
are still being explored
A lot of the qualitative signatures of Susy
appear in other models
108. Kaluza-Klein Modes
The general method to analyze higher dimensional theories
S = d4
x dy |∂M φ(x, y)|2
− M2
|φ(x, y)|2
y
xµ
109. Kaluza-Klein Modes
The general method to analyze higher dimensional theories
S = d4
x dy |∂M φ(x, y)|2
− M2
|φ(x, y)|2
y
xµ
(∂µ∂µ
− ∂2
5 + M2
)φ(x, y) = 0
Equations of Motion
110. Kaluza-Klein Modes
The general method to analyze higher dimensional theories
S = d4
x dy |∂M φ(x, y)|2
− M2
|φ(x, y)|2
y
xµ
(∂µ∂µ
− ∂2
5 + M2
)φ(x, y) = 0
Equations of Motion
φ(x, y) =
n
φn(x)fn(y)
∂µ∂µ
+ M2
+
2πn
R
2
φn(x) = 0
One 5D field = tower of 4D fields
fn(y) =
e2πiny/R
√
2πR
112. Large Extra Dimensions
Gravity
SM
Integrate out extra dimension
S4+n = d4
x dn
y
√
g M2+n
∗ R4+n + δn
(y)LSM
S4 eff = d4
x
√
g M4+n
∗ Ln
R4 + LSM
M2
Pl = M2+n
∗ Ln
Identify new Planck Mass
113. Large Extra Dimensions
Gravity
SM
Integrate out extra dimension
S4+n = d4
x dn
y
√
g M2+n
∗ R4+n + δn
(y)LSM
S4 eff = d4
x
√
g M4+n
∗ Ln
R4 + LSM
M2
Pl = M2+n
∗ Ln
Identify new Planck Mass
n L
1 1010 km
2 1 mm
3 10nm
4 10-2nm
5 100fm
6 1fm
M∗ 1 TeVSet
If fundamental Planck mass is weak
scale, there is no hierarchy problem!
114. Large Extra Dimension Signatures
Monophoton+MET
M back-
own in
served
TABLE III: Percentage of signal events passing the candidate
sample selection criteria (α) and observed 95% C.L. lower
limits on the effective Planck scale in the ADD model (Mobs
D )
in GeV/c2
as a function of the number of extra dimensions in
the model (n) for both individual and the combined analysis.
Number of Extra Dimensions
2 3 4 5 6
LowerLimit(TeV)DM
0.6
0.8
1
1.2
1.4
1.6
Number of Extra Dimensions
2 3 4 5 6
LowerLimit(TeV)DM
0.6
0.8
1
1.2
1.4
1.6
TE+!CDF II Jet/
)
-1
(2.0 fbTE+!CDF II
)
-1
(1.1 fbTECDF II Jet +
LEP Combined
q
¯q
γ
G
115. Large Extra Dimension Signatures
Black Holes at the LHC
Topology Total Cross Section (fb)
n = 2 62, 000
5 TeV black hole n = 4 37, 000
n = 6 34, 000
n = 2 580
8 TeV black hole n = 4 310
n = 6 270
n = 2 6.7
10 TeV black hole n = 4 3.4
n = 6 2.9
Rs(
√
s) = M−1
∗
√
s
M∗
1
n+1√
s M∗for σBH ∼ R2
s
BHs decay
thermally, violating all
global conservation laws
High multiplicity events
with lots of energy
q
q
117. Universal Extra Dimensions
+Gravity
SM
Standard Model has KK modes
S5D = d5
x F2
MN + ¯ΨiD Ψ + · · ·
−
1
2
R ≤ x5 ≤
1
2
R
All fields go in the bulk
Mass
g W B Q Uc Dc
L Ec
H
n = 1
n = 2
n = 3· · ·
n = 0
f(x5)
1
sin(x5/R)
cos(2x5/R)
sin(3x5/R)
Impose Dirichlet Boundary Conditions
R−1 >
∼ 500 GeV
118. UED KK Spectra
e first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
Levels are degenerate at tree level
All masses within 30% of each other!
(This is a widely spaced example!)
119. KK Parity
x5 → −x5
All odd-leveled KK modes are odd
SM and even-leveled KK modes are even
120. KK Parity
x5 → −x5
All odd-leveled KK modes are odd
SM and even-leveled KK modes are even
LKP is stable!
Usually KK partner of Hypercharge Gauge boson
g0,0,1 ∝
R/2
−R/2
dx5 f0(x5)f0(x5)f1(x5) ∼ dx5 1 · 1 · sin(πx5/R)
121. KK Parity
x5 → −x5
All odd-leveled KK modes are odd
SM and even-leveled KK modes are even
Looks like a degenerate Supersymmetry spectrum
until you can see 2nd KK level
LKP is stable!
Usually KK partner of Hypercharge Gauge boson
g0,0,1 ∝
R/2
−R/2
dx5 f0(x5)f0(x5)f1(x5) ∼ dx5 1 · 1 · sin(πx5/R)
122. Typical UED Event
Pair produce colored 1st KK level
Each side decays separately
The spectrum of the first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
mh = 120 GeV, m2
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
tree level and (b) one-loop, for R−1 = 500 GeV,
anishing boundary terms at the cut-off scale Λ.
123. Typical UED Event
Pair produce colored 1st KK level
Each side decays separately
The spectrum of the first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
mh = 120 GeV, m2
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
tree level and (b) one-loop, for R−1 = 500 GeV,
anishing boundary terms at the cut-off scale Λ.
g1 → q1 ¯q
124. Typical UED Event
Pair produce colored 1st KK level
Each side decays separately
The spectrum of the first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
mh = 120 GeV, m2
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
tree level and (b) one-loop, for R−1 = 500 GeV,
anishing boundary terms at the cut-off scale Λ.
q1 → B1q
g1 → q1 ¯q
125. Typical UED Event
Pair produce colored 1st KK level
Each side decays separately
The spectrum of the first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
mh = 120 GeV, m2
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
tree level and (b) one-loop, for R−1 = 500 GeV,
anishing boundary terms at the cut-off scale Λ.
q1 → B1q
g1 → q1 ¯q
2j + ET
126. Typical UED Event
Pair produce colored 1st KK level
Each side decays separately
The spectrum of the first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
mh = 120 GeV, m2
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
tree level and (b) one-loop, for R−1 = 500 GeV,
anishing boundary terms at the cut-off scale Λ.
g1 → q1 ¯q
q1 → B1q
g1 → q1 ¯q
2j + ET
127. Typical UED Event
Pair produce colored 1st KK level
Each side decays separately
The spectrum of the first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
mh = 120 GeV, m2
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
tree level and (b) one-loop, for R−1 = 500 GeV,
anishing boundary terms at the cut-off scale Λ.
g1 → q1 ¯q
q1 → B1q
g1 → q1 ¯q
q1 → W3
1 q
2j + ET
128. Typical UED Event
Pair produce colored 1st KK level
Each side decays separately
The spectrum of the first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
mh = 120 GeV, m2
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
tree level and (b) one-loop, for R−1 = 500 GeV,
anishing boundary terms at the cut-off scale Λ.
g1 → q1 ¯q
q1 → B1q
g1 → q1 ¯q
q1 → W3
1 q
W3
1 → 1
¯
2j + ET
129. Typical UED Event
Pair produce colored 1st KK level
Each side decays separately
The spectrum of the first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
mh = 120 GeV, m2
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
tree level and (b) one-loop, for R−1 = 500 GeV,
anishing boundary terms at the cut-off scale Λ.
g1 → q1 ¯q
q1 → B1q
g1 → q1 ¯q
q1 → W3
1 q
W3
1 → 1
¯
1 → B1
2j + ET
130. Typical UED Event
Pair produce colored 1st KK level
Each side decays separately
The spectrum of the first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
mh = 120 GeV, m2
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
tree level and (b) one-loop, for R−1 = 500 GeV,
anishing boundary terms at the cut-off scale Λ.
g1 → q1 ¯q
q1 → B1q
g1 → q1 ¯q
q1 → W3
1 q
W3
1 → 1
¯
1 → B1
2j + ET 2j + + ¯+ ET
131. Typical UED Event
Pair produce colored 1st KK level
Each side decays separately
The spectrum of the first KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV,
mh = 120 GeV, m2
H = 0, and assuming vanishing boundary terms at the cut-off scale Λ.
tree level and (b) one-loop, for R−1 = 500 GeV,
anishing boundary terms at the cut-off scale Λ.
g1 → q1 ¯q
q1 → B1q
g1 → q1 ¯q
q1 → W3
1 q
W3
1 → 1
¯
1 → B1
2j + ET 2j + + ¯+ ET
Difficult is in Soft Spectra
132. Randall Sundrum Models
TeV Scale Curved Extra Dimensions
ds2
= e−2ky
dx2
4 − dy2
Warp factor
UV Brane IR Brane
y
0 ≤ y ≤ y0
At each point of the 5th dimension,
there is a different normalization of 4D lengths
133. Effects of the Warping
S5 = d4
xdy
√
g5 δ(y − y0) gµν
5 ∂µφ∂νφ + m2
φ2
+ gφ3
+ λφ4
gµν
5 = e2ky0
ηµν√
g5 = e−4ky0
An IR brane scalar
134. Effects of the Warping
S5 = d4
xdy
√
g5 δ(y − y0) gµν
5 ∂µφ∂νφ + m2
φ2
+ gφ3
+ λφ4
gµν
5 = e2ky0
ηµν√
g5 = e−4ky0
S4 = d4
x e−4ky0
e2ky0
(∂φ)2
+ m2
φ2
+ gφ3
+ λφ4
Need to go to canonical normalization φ → eky0
φ
An IR brane scalar
135. Effects of the Warping
S5 = d4
xdy
√
g5 δ(y − y0) gµν
5 ∂µφ∂νφ + m2
φ2
+ gφ3
+ λφ4
gµν
5 = e2ky0
ηµν√
g5 = e−4ky0
S4 = d4
x e−4ky0
e2ky0
(∂φ)2
+ m2
φ2
+ gφ3
+ λφ4
Need to go to canonical normalization φ → eky0
φ
S4 = d4
x (∂φ)2
+ m2
e−2ky0
φ2
+ ge−ky0
φ3
+ λφ4
All mass scales on IR brane got crunched by warp factor
Super-heavy IR brane Higgs becomes light!
An IR brane scalar
136. Can put all fields on IR brane...
but just like low dimension operators get
scrunched, high dimension operators get enlarged!
Motivated putting SM fields in bulk except for the Higgs
UV Brane IR Brane
SM Gauge
+ Fermions
Higgs boson
Now have SM KK modes, but no KK parity
Resonances not evenly spaced either
Get light KK copies of right-handed top
137. Tonnes of Theory & Pheno and Models for RS Models!
AdS/CFT
Theories in Anti-de Sitter space (RS metric)
Equivalent to 4D theories that are conformal (scale invariant)
5D description is way of mocking up complicated 4D physics!
Warping is Dimensional Transmutation
IR Brane is breaking of conformal symmetry
ΛIR = e−ky0
ΛUV
ΛQCD = e−
2πα
−1
3 (MGUT)
b0 MGUT
138. Technicolor Theories
Imagine there was no Higgs
QCD still gets strong and quarks condense
QQc
= 0 Qc
= (Uc
, Dc
)
QQc
∼ (1, 2)1
2
Condensate has SM gauge quantum numbers
Like the Higgs!
QCD confinement/chiral symmetry breaking
breaks electroweak symmetry
Technicolor is a scaled-up version of QCD
RS Models are the modern versions of Technicolor
139. In Technicolor theories
Not necessarily a Higgs boson
Technirhos usually first resonance
OS =
H†
Wµν
HBµν
Λ2
Mediate contributions to
Λ >
∼ 3 TeVwith
W±
, Z0
ρT
ωT
90 GeV
800 GeV
etc
Need to be lighter than 1 TeV
140. In Technicolor theories
Not necessarily a Higgs boson
Technirhos usually first resonance
OS =
H†
Wµν
HBµν
Λ2
Mediate contributions to
Λ >
∼ 3 TeVwith
W±
, Z0
ρT
ωT
90 GeV
800 GeV
etc
Need to be lighter than 1 TeV
W±
, Z0
ρT
ωT
90 GeV
3 TeV
etc
Can push off the Technirhos
usually a scalar resonance becomes narrow
600 GeV σT
σT starts playing the role of the Higgs
Requires assumptions about
technicolor dynamics
Would like to get scalars light
without dynamical assumptions
141. Higgs as a Goldstone boson
σT −→ πT
Higgs boson is a technipion
Pions are light because the are
Goldstone bosons of approximate symmetries
V (πT ) m2
f2
cos πT /f
f set by Technicolor scale
πT = 0, πf
Goldstone bosons only have periodic potentials
142. Little Higgs Theories
Special type of symmetry breaking
V (πT ) f4
sin4
πT /f + m2
f2
cos πT /f
Looks like normal “Mexican hat” potential
Lots of group theory to get specific examples
143. Little Higgs Theories
Special type of symmetry breaking
V (πT ) f4
sin4
πT /f + m2
f2
cos πT /f
Looks like normal “Mexican hat” potential
Lots of group theory to get specific examples
[SU(3) × SU(3)/SU(3)]4
SU(5)/SO(5)
SU(6)/Sp(6) [SO(5) × SO(5)/SO(5)]4
[SU(4)/SU(3)]4
SU(9)/SU(8)
SO(9)/SO(5) × SO(4)
144. All have some similar features
New gauge sectors
Vector-like copies of the top quarks
Q3 & Qc
3 Uc
3 & U3
There are extended Higgs sectors
SU(2)L singlets, doublets & triplets
145. Conclusion
Beyond the Standard Model Physics is rich and diverse
Within the diversity there are many similar themes
These lectures were just an entry way into
the phenomenology of new physics
We’ll soon know which parts of these theories
have something to do with the weak scale
146. References
S. P. Martin
hep-ph/9709356
C. Csaki et al
“Supersymmetry Primer”
“TASI lectures on electroweak symmetry breaking from extra dimensions”
hep-ph/0510275
M. Schmaltz, D. Tucker-Smith
“Little Higgs Review”
hep-ph/0502182
I. Rothstein
hep-ph/0308286
“TASI Lectures on Effective Field Theory”
G. Kribs
“TASI 2004 Lectures on the pheomenology of extra dimensions”
hep-ph/0605325
J. Wells
hep-ph/0512342
“TASI Lecture Notes: Introduction to Precision Electroweak Analysis”
R. Sundrum
“TASI 2004: To the Fifth Dimension and Back”
hep-ph/0508134