slac summer institute 2009
DESCRIPTION
A summer school lecture at the SLAC summer Institute in 2009 on "New Physics Scenarios".TRANSCRIPT
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New Physics Scenarios
Jay WackerSLAC
SLAC Summer InstituteAugust 5&6, 2009
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Any minute now!When’s the revolution?
An unprecedented moment
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What is a “New Physics Scenario”?
“New Physics”:
A structural change to the Standard Model Lagrangian
“Scenario”:
“A sequence of events especially when imagined”
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Why New Physics?Four Paradigms
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Why New Physics?Four Paradigms
Experiment doesn’t match theoretical predictionsBest motivation
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Why New Physics?Four Paradigms
Experiment doesn’t match theoretical predictionsBest motivation
Parameters are “Unnatural”Well defined and have good theoretical motivation
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Why New Physics?Four Paradigms
Experiment doesn’t match theoretical predictionsBest motivation
Parameters are “Unnatural”Well defined and have good theoretical motivation
Reduce/Explain the multitude of parametersTypically has limited success, frequently untestable
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Why New Physics?Four Paradigms
Experiment doesn’t match theoretical predictionsBest motivation
Parameters are “Unnatural”Well defined and have good theoretical motivation
Reduce/Explain the multitude of parametersTypically has limited success, frequently untestable
To know what is possibleLet’s us know what we can look for in experiments
Limited only by creativity and taste
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The PlanBeyond 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 principlesused in a half dozen paradigmsthat created hundreds of models
and spawned thousands of papers
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Outline
The Standard Model
Motivation for Physics Beyond the SM
Organizing Principles for New Physics
New Physics ScenariosSupersymmetry
Extra DimensionsStrong Dynamics
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Standard Model: a story of economysymmetry unification!
15 Particles, 12 Force carriers! 2700 !V !! Couplings
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Standard Model: a story of economy
!eL eL eR uL uR dRdLuLuL uRuR dL dL dR dR
symmetry unification!15 Particles, 12 Force carriers! 2700 !V !! Couplings
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Standard Model: a story of economy
!eL 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 !V !! Couplings
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Standard Model: a story of economy
!eL 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 !V !! Couplings
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The Standard Model... where we stand today
LSM = LGauge + LFermion + LHiggs + LYukawa
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The Standard Model... where we stand today
LSM = LGauge + LFermion + LHiggs + LYukawa
LGauge = !14Bµ!
2 ! 14W a
µ!2 ! 1
4GA
µ!2
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The Standard Model... where we stand today
LSM = LGauge + LFermion + LHiggs + LYukawa
LGauge = !14Bµ!
2 ! 14W a
µ!2 ! 1
4GA
µ!2
LFermion = QiiD! Qi + U ci iD! U c
i + Dci iD! Dc
i + LiiD! Li + Eci iD! Ec
i
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The Standard Model... where we stand today
LSM = LGauge + LFermion + LHiggs + LYukawa
LGauge = !14Bµ!
2 ! 14W a
µ!2 ! 1
4GA
µ!2
LFermion = QiiD! Qi + U ci iD! U c
i + Dci iD! Dc
i + LiiD! Li + Eci iD! Ec
i
LHiggs = |DµH|2 ! !(|H|2 ! v2/2)2
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The Standard Model... where we stand today
LSM = LGauge + LFermion + LHiggs + LYukawa
LGauge = !14Bµ!
2 ! 14W a
µ!2 ! 1
4GA
µ!2
LFermion = QiiD! Qi + U ci iD! U c
i + Dci iD! Dc
i + LiiD! Li + Eci iD! Ec
i
LHiggs = |DµH|2 ! !(|H|2 ! v2/2)2
LYuk = yiju QiU
cj H + yij
d QiDcjH
! + yije LiE
cjH
!
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Q
U c
Dc
Ec
L
3
331
1
11
1
2
2
+16
!23
+13
!12
+1
Field Color Weak Hypercharge
Standard Model Charges
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Motivations for Physics Beyond the Standard Model
The Hierarchy Problem
Dark Matter
Exploration
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The Hierarchy ProblemThe SM suffers from a stability crisis
!µ2
!3y2t !2
t
16!2
+34g2!2
W
16!2
+14g!2!2
B
16!2
+!!2
H
16"2
Higgs vev determined by effective mass, not bare massMany contributions that must add up to -(100 GeV)2
=
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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)
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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
!
2001: Universal Extra Dimensions (Appelquist, Cheng, Dobrescu)
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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
!M2Composite
Why hadrons are lighter than Planck Scale
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A New Symmetryµ2 = 0 not specialUV dynamics at
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A New Symmetry
Scalar
Fermion
!
! Supersymmetry
!! "#Scalar Mass related to Fermion Mass
µ2 = 0 not specialUV dynamics at
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A New Symmetry
Scalar
Fermion
!
! Supersymmetry
!! "#Scalar Mass related to Fermion Mass
!
Scalar
Scalar
!Shift Symmetry
!! ! + "Scalar Mass forbidden
µ2 = 0 not specialUV dynamics at
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A New Symmetry
Scalar
Fermion
!
! Supersymmetry
!! "#Scalar Mass related to Fermion Mass
!
Scalar
Scalar
!Shift Symmetry
!! ! + "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
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Dark Matter85% of the mass of the Universe is not described by the SM
There must be physics beyond the Standard Model
Cold dark matterElectrically & Color Neutral
Cold/SlowRelatively small self interactions
Interacts very little with SM particles
No SM particle fits the bill
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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
log
Y(x
)/Y
(x=
0)
x ! m/T
!!Annv"
Incr
easi
ng
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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
log
Y(x
)/Y
(x=
0)
x ! m/T
!!Annv"
Incr
easi
ng
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The WIMP Miracle DM was in equilibrium with SM in the Early Universe
T ! mDM
T ! mDMReverse process energetically disfavored
1 3 10 30 100 300 1000!20
!15
!10
!5
0
log
Y(x
)/Y
(x=
0)
x ! m/T
!!Annv"
Incr
easi
ng
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The WIMP Miracle DM was in equilibrium with SM in the Early Universe
T ! mDM
T ! mDMReverse process energetically disfavored
1 3 10 30 100 300 1000!20
!15
!10
!5
0
log
Y(x
)/Y
(x=
0)
x ! m/T
!!Annv"
Incr
easi
ng
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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 ! mDMReverse process energetically disfavored
1 3 10 30 100 300 1000!20
!15
!10
!5
0
log
Y(x
)/Y
(x=
0)
x ! m/T
!!Annv"
Incr
easi
ng
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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 ! mDMReverse process energetically disfavored
Relic density is “frozen in”
1 3 10 30 100 300 1000!20
!15
!10
!5
0
log
Y(x
)/Y
(x=
0)
x ! m/T
!!Annv"
Incr
easi
ng
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Boltzmann Equation Solves for
! = "DM/"baryon ! 6
Frozen out when nDM !v ! H!ann =
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Boltzmann Equation Solves for
! = "DM/"baryon ! 6
Frozen out when nDM !v ! H!ann =
H ! T 2/MPlnDM = !
mp
mDM"s
s ! T 3 TFO ! mDM
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Boltzmann Equation Solves for
! = "DM/"baryon ! 6
!v =1
"mpMPl#! 3" 10!26cm3/s
Frozen out when nDM !v ! H!ann =
H ! T 2/MPlnDM = !
mp
mDM"s
s ! T 3 TFO ! mDM
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Boltzmann Equation Solves for
! = "DM/"baryon ! 6
!v =1
"mpMPl#! 3" 10!26cm3/s
Frozen out when
mDM ! !" 20 TeV! ! "2
m2DM
=!
nDM !v ! H!ann =
H ! T 2/MPlnDM = !
mp
mDM"s
s ! T 3 TFO ! mDM
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We want to see what’s there!
Muon, Strange particles, Tau leptonnot predicted before discovery
Serendipity favors the prepared!
Exploration
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Chirality
Anomaly Cancellation
Flavor Symmetries
Gauge Coupling Unification
Effective Field Theory
Organizing Principlesfor going beyond the SM
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ChiralityA symmetry acting a fermions that forbids masses
! =!
ffc
"M!! = M(ff c + f fc)
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ChiralityA symmetry acting a fermions that forbids masses
! =!
ffc
"M!! = M(ff c + f fc)
f ! ei!f fc ! ei!c
fc
Can do independent phase rotations
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ChiralityA symmetry acting a fermions that forbids masses
! =!
ffc
"M!! = M(ff c + f fc)
! = !!cVector symmetry
Allows mass
JµV = !!µ!
f ! ei!f fc ! ei!c
fc
Can do independent phase rotations
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ChiralityA symmetry acting a fermions that forbids masses
! =!
ffc
"M!! = M(ff c + f fc)
! = !!cVector symmetry
Allows mass
JµV = !!µ!
! = !cAxial symmetry
Forbids mass
JµA = !!5!
µ!
f ! ei!f fc ! ei!c
fc
Can do independent phase rotations
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The Standard Model is a Gauged Chiral Theory
All masses are forbidden by a gauge symmetry
15 different bilinears all forbidden
QU c ! (1, 2)! 12 QEc ! (3, 2) 7
6
DcEc ! (3, 1) 43
U cL ! (3, 2)! 53
EcEc ! (1, 1)+2
LL ! (1, 1)!1QQ ! (3, 3) 1
3
DcDc ! (3, 1) 23
DcL ! (3, 2)! 16
etc...
The Standard Model force carriers forbid fermion masses
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Electroweak Symmetry BreakingBreaking of Chiral Symmetry
SU(2)L ! U(1)Y " U(1)EM!H" #!
0v
"V (H) = !|H|4 ! µ2|H|2
LYuk = yiju QiU
cj H + yij
d QiDcjH
! + yije LiE
cjH
!
Q =!
UD
"L =
!!E
"
LYuk = miju UiU
cj + mij
d DiDcj + mij
e EiEcj
Fermions pick up Dirac Masses
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Effective Field Theory
Take a theory with light and heavy particlesLFull = Llight(!) + Lheavy(!,!)
If we only can ask questions in the range!
s" !cut o!<#M"
!cut o!
!s
m!
M!
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Effective Field Theory
Take a theory with light and heavy particlesLFull = Llight(!) + Lheavy(!,!)
If we only can ask questions in the range!
s" !cut o!<#M"
!cut o!
!s
m!
M!
with n > 0
Dynamics of light fields described by
Lfull(!) = Llight(!) + "L(!) !L ! O(")/!ncut o!
Only contribute as !" !! "
s
!cut o!
"n
known as “irrelevant operators”
Nonrenomalizable
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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 asan “Effective Theory” that describes the dynamics
Shouldn’t be constrained by renormalizability
One way of looking for new physics is bylooking for these nonrenormalizable operators
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Limits on Non-Renormalizable Operators
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Limits on Non-Renormalizable Operators
Baryon Number Violation QQQL/!2
! >! 1016 GeV
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Limits on Non-Renormalizable Operators
Baryon Number Violation QQQL/!2
! >! 1016 GeV
Lepton Number Violation (LH)2/!! ! 1015 GeV
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Limits on Non-Renormalizable Operators
Baryon Number Violation QQQL/!2
! >! 1016 GeV
Lepton Number Violation (LH)2/!! ! 1015 GeV
Flavor Violation H†(L2!µ!Ec
1)Bµ!/!2Dc
1Dc1D
c2D
c2/!2
! >! 106 GeV ! >! 106 GeV
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Limits on Non-Renormalizable Operators
Baryon Number Violation QQQL/!2
! >! 1016 GeV
Lepton Number Violation (LH)2/!! ! 1015 GeV
Flavor Violation H†(L2!µ!Ec
1)Bµ!/!2Dc
1Dc1D
c2D
c2/!2
! >! 106 GeV ! >! 106 GeV
CP Violation iH†(L1!µ!Ec
1)Bµ!/!2
! >! 106 GeV
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Limits on Non-Renormalizable Operators
Baryon Number Violation QQQL/!2
! >! 1016 GeV
Lepton Number Violation (LH)2/!! ! 1015 GeV
Flavor Violation H†(L2!µ!Ec
1)Bµ!/!2Dc
1Dc1D
c2D
c2/!2
! >! 106 GeV ! >! 106 GeV
CP Violation iH†(L1!µ!Ec
1)Bµ!/!2
! >! 106 GeVPrecision Electroweak |H†DµH|2/!2
! >! 3" 103 GeV
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Limits on Non-Renormalizable Operators
Baryon Number Violation QQQL/!2
! >! 1016 GeV
Lepton Number Violation (LH)2/!! ! 1015 GeV
Flavor Violation H†(L2!µ!Ec
1)Bµ!/!2Dc
1Dc1D
c2D
c2/!2
! >! 106 GeV ! >! 106 GeV
CP Violation iH†(L1!µ!Ec
1)Bµ!/!2
! >! 106 GeVPrecision Electroweak |H†DµH|2/!2
! >! 3" 103 GeV
Contact Operators (L1L1)2/!2
! >! 3" 103 GeV
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Limits on Non-Renormalizable Operators
Baryon Number Violation QQQL/!2
! >! 1016 GeV
Lepton Number Violation (LH)2/!! ! 1015 GeV
Flavor Violation H†(L2!µ!Ec
1)Bµ!/!2Dc
1Dc1D
c2D
c2/!2
! >! 106 GeV ! >! 106 GeV
CP Violation iH†(L1!µ!Ec
1)Bµ!/!2
! >! 106 GeVPrecision Electroweak |H†DµH|2/!2
! >! 3" 103 GeV
Contact Operators (L1L1)2/!2
! >! 3" 103 GeV
Generic Operators Gµ!G!"Gµ"/!2
! >! 3" 102 GeV
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Flavor SymmetriesSymmetries that interchange fermions
Turn off all the interactions of the SM = Free Theory
L = !i i"! !i !i ! U ji !j U(N) symmetry
![Page 61: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/61.jpg)
Flavor SymmetriesSymmetries that interchange fermions
Turn off all the interactions of the SM = Free Theory
Q,U c, Dc, L,Ec = 15 Fermions/Generation
45 Total fermions that look the same in the free theoryglobal symmetry! U(45)
L = !i i"! !i !i ! U ji !j U(N) symmetry
![Page 62: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/62.jpg)
Flavor SymmetriesSymmetries that interchange fermions
Turn off all the interactions of the SM = Free Theory
Q,U c, Dc, L,Ec = 15 Fermions/Generation
45 Total fermions that look the same in the free theoryglobal 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 = !i i"! !i !i ! U ji !j U(N) symmetry
![Page 63: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/63.jpg)
Prevents Flavor Changing Neutral CurrentsImagine two scalars with two sources of flavor breaking
LYuk = yijH!i!cj + "ij#!i!
cj
H = v + h mij = yijv
![Page 64: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/64.jpg)
Prevents Flavor Changing Neutral CurrentsImagine two scalars with two sources of flavor breaking
LYuk = yijH!i!cj + "ij#!i!
cj
H = v + h mij = yijv
Can diagonalize mass matrix with unitary transformations!i ! U j
i !j !ci ! V j
i !cj mij ! (UT mV )ij = Mi!
ij
LYuk !Mi!ij"i"
cj(1 + h/v) + (UT #V )ij$"i"j
![Page 65: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/65.jpg)
Prevents Flavor Changing Neutral CurrentsImagine two scalars with two sources of flavor breaking
LYuk = yijH!i!cj + "ij#!i!
cj
H = v + h mij = yijv
Higgs doesn’t change flavor, but other scalar field is a disaster
K0K0
d s
sd
!
! ! yUnless m!
!>! 100 TeVor
Can diagonalize mass matrix with unitary transformations!i ! U j
i !j !ci ! V j
i !cj mij ! (UT mV )ij = Mi!
ij
LYuk !Mi!ij"i"
cj(1 + h/v) + (UT #V )ij$"i"j
![Page 66: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/66.jpg)
Anomaly CancellationQuantum violation of current conservation
!µJaµ ! Tr T aT bT c (F bF c)
T a
T b
T c
!
An anomaly leads to a mass for a gauge boson
m2 =!
g2
16!2
"3
!2
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Anomaly cancellation:
One easy way: only vector-like gauge couplings
!, !c
(+1)3 + (!1)3 = 0
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Anomaly cancellation:
but the Standard Model is chiral
One easy way: only vector-like gauge couplings
!, !c
(+1)3 + (!1)3 = 0
![Page 69: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/69.jpg)
Anomaly cancellation:
but the Standard Model is chiral
One easy way: only vector-like gauge couplings
!, !c
(+1)3 + (!1)3 = 0
SU(3)SU(3)
SU(3)
U(1)U(1)
U(1)
U(1)SU(3)
SU(3)
6!
16
"3
+ 3!!2
3
"3
+ 3!
13
"3
+ 2!!1
2
"3
+ (1)3 = 0
2(1)3 + (!1)3 + (!1)3 + 0 + 0 = 0
2!
16
"+
!!2
3
"+
!13
"+ 0 + 0 = 0
Q U c Dc L Ec
It works, but is a big constraint!
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Gauge coupling unification: Our Microscope
!!1
E103 106 109 1012 1015
(GeV)
30
40
20
10
sin2 !w
1
2
3
EGUT
d
dt!!1 =
b0
2"Counts charged matter
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Gauge coupling unification: Our Microscope
!!1
E103 106 109 1012 1015
(GeV)
30
40
20
10
sin2 !w
1
2
3
EGUT
!!13 (t) = !!1
3 (t") +b3 0
2"(t! t")
!!12 (t) = !!1
2 (t") +b2 0
2"(t! t")
!!11 (t) = !!1
1 (t") +b1 0
2"(t! t")
d
dt!!1 =
b0
2"Counts charged matter
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Gauge coupling unification: Our Microscope
!!1
E103 106 109 1012 1015
(GeV)
30
40
20
10
sin2 !w
1
2
3
EGUT
!!13 (t) = !!1
3 (t") +b3 0
2"(t! t")
!!12 (t) = !!1
2 (t") +b2 0
2"(t! t")
!!11 (t) = !!1
1 (t") +b1 0
2"(t! t")
d
dt!!1 =
b0
2"Counts charged matter
A3221 = 0.714
!!13 (t)! !!1
2 (t)!!1
2 (t)! !!11 (t)
=b3 0 ! b2 0
b2 0 ! b1 0
Weak scale measurementHigh scale particle contentB32
21 = 0.528
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!eL 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
![Page 74: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/74.jpg)
!eL 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
![Page 75: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/75.jpg)
!eL eL eR uL uR dRdLuLuL uRuR dL dL dR dR
Grand Unification
! e q u d
5 10 SU(5)
!eR
! SO(10)
SU(3)! SU(2)! U(1)
Gauge coupling unification indicates forces arise from single entity
![Page 76: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/76.jpg)
Standard Model Summary
The Standard Model is chiral gauge theory
It is an effective field theory
It is anomaly free & anomaly cancellationrestricts new charged particles
Making sure that there is no new sourcesof flavor violation ensures that new theories are
not horribly excluded
SM Fermions fit into GUT multiplets,but gauge coupling unification doesn’t quite work
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The Scenarios
Supersymmetry
Little Higgs Theories
Extra Dimensions
Technicolor
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SupersymmetryDoubles Standard Model particles
Q,U c, Dc, L,Ec
Q, U c, Dc, L, Ec
H
Hu,Hd
Hu, Hd
g,W,B
g, W , B
Dirac pair of Higgsinos GauginosSfermions
Squarks, Sleptons Gluino, Wino, Bino
Fermions Higgs Gauge
(1, 2) 12
(1, 2)! 12
Susy Taxonomy
Needed for anomaly cancellation
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Susy Gauge Coupling Unification
A3221 = 0.714
!!13 (t)! !!1
2 (t)!!1
2 (t)! !!11 (t)
=b3 0 ! b2 0
b2 0 ! b1 0
B3221 =
4285
= 0.714
Too good!(Two loop beta functions, etc)
But significantly better than SM or any other BSM theory
Only need to add in particles that contribute to the relative runningGauge Bosons, Gauginos, Higgs & Higgsinos
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SUSY Interactions
Rule of thumb: take 2 and flip spins
q
q
gg
Q
U c
U c
HH
Q
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SUSY BreakingSUSY is not an exact symmetry
We don’t know how SUSY is broken, butSUSY breaking effects can be parameterized in the Lagrangian
Lsoft = Lm20+ Lm 1
2+ LA + LB
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SUSY BreakingSUSY is not an exact symmetry
We don’t know how SUSY is broken, butSUSY breaking effects can be parameterized in the Lagrangian
Lsoft = Lm20+ Lm 1
2+ LA + LB
Lm20
= m2!
ij !†
i !j
+m2Hu
|Hu|2 + m2Hd
|Hd|2! ! Q,U c, Dc, L,Ec
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SUSY BreakingSUSY is not an exact symmetry
We don’t know how SUSY is broken, butSUSY breaking effects can be parameterized in the Lagrangian
Lsoft = Lm20+ Lm 1
2+ LA + LB
Lm 12
= m1BB + m2WW + m3gg
Lm20
= m2!
ij !†
i !j
+m2Hu
|Hu|2 + m2Hd
|Hd|2! ! Q,U c, Dc, L,Ec
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SUSY BreakingSUSY is not an exact symmetry
We don’t know how SUSY is broken, butSUSY breaking effects can be parameterized in the Lagrangian
Lsoft = Lm20+ Lm 1
2+ LA + LB
Lm 12
= m1BB + m2WW + m3gg
LA = aiju QiU
cj Hu + aij
d QiDcjHd + aij
e LiEcjHd
Lm20
= m2!
ij !†
i !j
+m2Hu
|Hu|2 + m2Hd
|Hd|2! ! Q,U c, Dc, L,Ec
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SUSY BreakingSUSY is not an exact symmetry
We don’t know how SUSY is broken, butSUSY breaking effects can be parameterized in the Lagrangian
Lsoft = Lm20+ Lm 1
2+ LA + LB
Lm 12
= m1BB + m2WW + m3gg
LA = aiju QiU
cj Hu + aij
d QiDcjHd + aij
e LiEcjHd
LB = Bµ HuHd
Lm20
= m2!
ij !†
i !j
+m2Hu
|Hu|2 + m2Hd
|Hd|2! ! Q,U c, Dc, L,Ec
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Problem with Parameterized SUSY Breaking
There are over 100 parameters onceSupersymmetry no longer constrains interactions
Most of these are new flavor violation parametersor CP violating phases
Horribly excluded
Susy breaking is not generic!
m2ijQ
†i Q
j Qi ! U ji Qj
gs g Q†iQ
i ! gs g Q†i (U
†U)ijQ
j
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Soft Susy Breaking
i.e. Super-GIM mechanismUniversality of soft terms
d
d s
s
g gd, s, b
d, s, b
K0 K0
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Soft Susy Breaking
i.e. Super-GIM mechanismUniversality of soft terms
d
d s
s
g gd, s, b
d, s, b
K0 K0
Need to be Flavor Universal Couplings
A ! 11m2
0 ! 11Scalar MassesTrilinear A-Terms
Approximate degeneracy of scalars
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Proton StabilityNew particles ⇒ new ways to mediate proton decay
Dangerous couplings
Prot
on Pionu u
u
d
d
u
e+
LRPV = !BU cDcDc + !LQLDc
Supersymmetric couplings that violate SM symmetries
A new symmetry forbids these couplings: (!1)3B+L+2s
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Proton StabilityNew particles ⇒ new ways to mediate proton decay
Lightest Supersymmetric Particle is stable
Dangerous couplings
Prot
on Pionu u
u
d
d
u
e+
LRPV = !BU cDcDc + !LQLDc
Supersymmetric couplings that violate SM symmetries
A new symmetry forbids these couplings: (!1)3B+L+2s
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Proton StabilityNew particles ⇒ new ways to mediate proton decay
Lightest Supersymmetric Particle is stable
Dangerous couplings
Must be neutral and colorless -- Dark Matter
Prot
on Pionu u
u
d
d
u
e+
LRPV = !BU cDcDc + !LQLDc
Supersymmetric couplings that violate SM symmetries
A new symmetry forbids these couplings: (!1)3B+L+2s
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Mediation of Susy Breaking
MSSM PrimoridalSusy BreakingMediation
Susy breaking doesn’t occur inside the MSSMFelt through interactions of intermediate particles
Studied to reduce the number of parametersGauge Mediation
Universal “Gravity” MediationAnomaly Mediation
Usually only 4 or 5 parameters...but for phenomenology, these are too restrictive
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The Phenomenological MSSMThe set of parameters that are:
Not strongly constrainedEasily 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
55334
20 Total Parameters
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Charginos & NeutralinosThe Higgsinos, Winos and Binos
Hu ! 2 12" 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 = µHuHd + m2WW + m1BB
+(H†uHu + H†
dHd)(gW + g!B)
(2)
All mix together, but typically mixture is small
Tend find charginos next to their neutralino brethren
Neutralinos are good DM candidates
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Elementary Phenomenology
Neutralinos Charginos Sleptons Squarks Gluinos
Mas
s
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Collider signatures
q
q
!0
!0
!02
!+1
!
!!
!
!
!
Trileptons+MET: If sleptons are availableN
eutra
linos
Cha
rgin
os
Slep
tons
Mas
s
3 Leptons + MET
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Collider signatures
9 RESULTS AND LIMITS 13
)2Chargino Mass (GeV/c100 110 120 130 140 150 160 170
3l)
(p
b)
!± 1"#
0 2" ~
BR
($
%
0
0.2
0.4
0.6
0.8
1
1.2
-1CDF Run II Preliminary, 3.2 fb
)2Chargino 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
Figure 6: Expected and observed limit for the mSugra model M0 =60, tan! = 3, A0 = 0, (µ) > 0. In red is the theoretical " ! BR and inblack is our expected limit with one and two " errors. We expect to set alimit of about 156 GeV/c2, and observe a limit of 164 GeV/c2.
q
q
!0
!0
!02
!+1
!
!!
!
!
!
Trileptons+MET: If sleptons are availableN
eutra
linos
Cha
rgin
os
Slep
tons
Mas
s
3 Leptons + MET
![Page 98: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/98.jpg)
Collider signaturesTrileptons+MET
Without sleptons in the decay chainN
eutra
linos
Cha
rgin
os
Slep
tons
Mas
s q
q
!0
!0
!02
!+1 !
!!!W+
Z0
30% leptonic Br of W, 10% leptonic Br of Z3% Total Branching Rate
![Page 99: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/99.jpg)
7
Cro
ss S
ecti
on [p
b]
]2 [GeV/cg~
M]2 [GeV/cq~
M
2 = 230 GeV/cg~
M
q~ = M
g~M
2 = 370 GeV/cq~
M
2 = 460 GeV/cq~
M
Theoretical uncertainties not included in the calculation of the limit
<0µ = 5, ! = 0, tan0A -1L = 2.0 fb
NLO Prospino Ren.)"syst. uncert. (PDF
expected limit 95% C.L.
observed limit 95% C.L.
-110
1
10
210
-110
1
10
210
300 400 500
-210
-110
1
10
300 400 500
-210
-110
1
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 gluinoproduction cross sections as a function of M!q (left) and
M!g (right) in di!erent regions of the squark-gluino mass
plane, compared to NLO mSUGRA predictions (dashed-dotted lines). The shaded bands denote the total uncertaintyon the theory.
0 100 200 300 400 500 6000
100
200
300
400
500
600
no mSUGRA
solution
LEP
UA
1
UA
2
g~
= M
q~M
0 100 200 300 400 500 6000
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 [G
eV/c
q~M
FIG. 3: Exclusion plane at 95 % C.L. as a function of squarkand gluino masses in an mSUGRA scenario with A0 = 0,µ < 0 and tan! = 5. The observed (solid line) and expected(dashed line) upper limits are compared to previous resultsfrom SPS [30] and LEP [31] experiments at CERN (shadedbands), and from the Run I at the Tevatron [2] (dashed-dottedline). The hatched area indicates the region in the plane withno mSUGRA solution.
Japan; the Natural Sciences and Engineering ResearchCouncil of Canada; the National Science Council of theRepublic of China; the Swiss National Science Founda-tion; the A.P. Sloan Foundation; the Bundesministeriumfur Bildung und Forschung, Germany; the Korean Sci-ence and Engineering Foundation and the Korean Re-search Foundation; the Science and Technology FacilitiesCouncil and the Royal Society, UK; the Institut Nationalde Physique Nucleaire et Physique des Particules/CNRS;the Russian Foundation for Basic Research; the Ministe-rio de Ciencia e Innovacion, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; and the
Academy of Finland.
[1] H. E. Haber and G. L. Kane, Phys. Rep. 117, 75 (1985).[2] T. A!older et al. (CDF Collaboration), Phys. Rev. Lett.
88, 041801 (2002); S. Abachi et al. (D0 Collaboration),ibid. 75, 618 (1995).
[3] V.M. Abazov et al. (D0 Collaboration), Phys. Lett. B660, 449 (2008).
[4] H. P. Nilles, Phys. Rep. 110, 1 (1984).[5] CDF uses a cylindrical coordinate system about the beam
axis with polar angle " and azimuthal angle #. We definetransverse energy ET = E sin", transverse momentumpT = p sin", pseudorapidity $ = !ln(tan( !
2 )), and rapid-
ity y = 12 ln(E+pz
E!pz
). The missing transverse energy E/T is
defined as the norm of !"
iEi
·%ni, where %ni is the com-ponent in the azimuthal plane of the unit vector pointingfrom the interaction point to the i-th calorimeter tower.
[6] D. Acosta et al. (CDF Collaboration), Phys. Rev. D 71,032001 (2005).
[7] D. Acosta et al., Nucl. Instrum. Methods, A 494, 57(2002).
[8] T. Sjostrand et al., Comp. Phys. Comm. 135, 238 (2001).[9] T. A!older et al. (CDF Collaboration), Phys. Rev. D 65,
092002 (2002).[10] M. Cacciari et al., J. High Energy Phys. 0404, 068
(2004).[11] J. M.Campbell and R. K. Ellis, Phys. Rev. D60, 113006
(1999).[12] M.L. Mangano et al., J. High Energy Phys. 07, 001
(2003).[13] A Abulencia et al. (CDF Collaboration), J. Phys. G:
Nucl. Part. Phys. 34, 2457 (2007).[14] F. Maltoni and T. Stelzer, J. High Energy Phys. 02, 027
(2003).[15] B. W. Harris et al., Phys. Rev. D66, 054024 (2002).[16] B. C. Allanach et al., Eur. Phys. J. C25, 113 (2002).[17] W. Beenakker et al., Nucl. Phys. B492, 51 (1997).[18] F. Paige and S. Protopopescu, in Supercollider Physics,
p. 41, ed. D. Soper (World Scientific, 1986).[19] J. Pumplin et al., J. High Energy Phys. 0207, 012 (2002).[20] Pole masses are considered. The squark mass is averaged
over the first two squark generations.[21] R. Brun et al., Tech. Rep. CERN-DD/EE/84-1, 1987.[22] G. Grindhammer, M. Rudowicz, and S. Peters, Nucl. In-
strum. Methods A 290, 469 (1990).[23] F. Abe et al. (CDF Collaboration), Phys. Rev. D 45,
1448 (1992).[24] A. Bhatti et al., Nucl. Instrum. Methods A 566, 375
(2006).[25] Charge conjugation is implied throughout the paper.[26] The sum runs over the selected jets. In the four-jets case,
the first three leading jets are considered.[27] X. Portell, Ph.D. Thesis, U.A.B., Barcelona (2007).[28] G. De Lorenzo, Master Thesis, U.A.B., Barcelona (2008).[29] R. Cousins, Am. J. Phys. 63, 398 (1995).[30] C. Albajar et al. (UA1 Collaboration), Phys. Lett. B198,
261 (1987); J. Alitti et al. (UA2 Collaboration), ibid.B235, 363 (1990).
[31] LEPSUSYWG/02-06.2, http://lepsusy.web.cern.ch/lepsusy/.
Collider signaturesGluino Pairs: 4j +MET Squark Pairs: 2j +MET Squark-Gluino Pairs: 3j +MET
q
q
g
g
q
q
q
q
!0
!0
q
q
q
q
q q
!0
!0
q
q
q
qq gq
g
!0
!0
q
mSUGRA Searchm3 : m2 : m1 = 6 : 2 : 1
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Away from mSUGRA Gluino Search
Out[27]=
XX
100 200 300 400 5000
50
100
150
Gluino Mass !GeV"
BinoMass!GeV
"mg ! 130 GeVmg ! 120 GeV
g ! qqB
g ! qqW ! qqBW
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The Higgs Mass ProblemVHiggs = !|H|4 + µ2|H|2m2
h0 = 2!v2 = !2µ2
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The Higgs Mass ProblemVHiggs = !|H|4 + µ2|H|2m2
h0 = 2!v2 = !2µ2
mh0 !MZ0!susy =18
!g2 + g!2" cos2 2"
Need a susy copy of quartic coupling, only gauge coupling works in MSSM
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The Higgs Mass Problemm2
h0 = 2!v2 = !2µ2
H
t t
H
!" =3y4
top
8#2log
mstop
mtop
mh0 !MZ0!susy =18
!g2 + g!2" cos2 2"
Need a susy copy of quartic coupling, only gauge coupling works in MSSM
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The Higgs Mass Problem
!µ2 = !3y2
top
8"2m2
stopH t tH
m2h0 = 2!v2 = !2µ2
H
t t
H
!" =3y4
top
8#2log
mstop
mtop
mh0 !MZ0!susy =18
!g2 + g!2" cos2 2"
Need a susy copy of quartic coupling, only gauge coupling works in MSSM
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The Higgs Mass Problem
!µ2 = !3y2
top
8"2m2
stopH t tH
Higgs mass gain is only logFine tuning loss is quadratic
Difficult to make the Higgs heavier than 125 GeV in MSSM
FT !m2
h0
!µ2
m2h0 = 2!v2 = !2µ2
H
t t
H
!" =3y4
top
8#2log
mstop
mtop
mh0 !MZ0!susy =18
!g2 + g!2" cos2 2"
Need a susy copy of quartic coupling, only gauge coupling works in MSSM
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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 mSUGRAare still being explored
A lot of the qualitative signatures of Susyappear in other models
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Extra Dimensions Taxonomy
Large TeV Small
Flat Curved
UEDs RS Models GUT ModelsADD Models
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Kaluza-Klein ModesThe general method to analyze higher dimensional theories
S =!
d4x
!dy |!M"(x, y)|2 !M2|"(x, y)|2
y
xµ
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Kaluza-Klein ModesThe general method to analyze higher dimensional theories
S =!
d4x
!dy |!M"(x, y)|2 !M2|"(x, y)|2
y
xµ
(!µ!µ ! !25 + M2)"(x, y) = 0
Equations of Motion
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Kaluza-Klein ModesThe general method to analyze higher dimensional theories
S =!
d4x
!dy |!M"(x, y)|2 !M2|"(x, y)|2
y
xµ
(!µ!µ ! !25 + M2)"(x, y) = 0
Equations of Motion
!(x, y) =!
n
!n(x)fn(y)!
!µ!µ + M2 +"
2"n
R
#2$
#n(x) = 0
One 5D field = tower of 4D fields
fn(y) =e2!iny/R
!2!R
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Large Extra Dimensions
GravitySM
Integrate out extra dimension
S4+n =!
d4x
!dny!
g M2+n! R4+n + !n(y)LSM
S4 e! =!
d4x!
g M4+n! Ln R4 + LSM
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Large Extra Dimensions
GravitySM
Integrate out extra dimension
S4+n =!
d4x
!dny!
g M2+n! R4+n + !n(y)LSM
S4 e! =!
d4x!
g M4+n! Ln R4 + LSM
M2Pl = M2+n
! Ln
Identify new Planck Mass
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Large Extra Dimensions
GravitySM
Integrate out extra dimension
S4+n =!
d4x
!dny!
g M2+n! R4+n + !n(y)LSM
S4 e! =!
d4x!
g M4+n! Ln R4 + LSM
M2Pl = M2+n
! Ln
Identify new Planck Massn L1 1010 km
2 1 mm
3 10nm
4 10-2nm
5 100fm
6 1fmM! ! 1 TeVSet
If fundamental Planck mass is weakscale, there is no hierarchy problem!
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Large Extra Dimension Signatures
Monophoton+MET
6
Background EventsZ ! !! 388 ± 30W ! "! 187 ± 14W ! µ! 117 ± 9W ! e! 58 ± 4Z ! ## 8 ± 1
Multi-jet 23 ± 20$+jet 17 ± 5
Non-collision 10 ± 10Total predicted 808 ± 62Data observed 809
TABLE II: Number of observed events and expected SM back-grounds in the jet + E/T candidate sample.
mates and the number of observed events are shown inTable II, and a comparison of the expected and observedleading jet ET distributions is shown in Fig. 2.
(GeV)TLeading Jet E100 150 200 250 300 350 400
Eve
nts
/ 1
0 G
eV
0
50
100
150
200
250
300
Data
SM Prediction
=1TeV)DSM + LED (n=2,M
)-1
CDF II ( 1.1 fb
FIG. 2: Predicted and observed leading jet ET distributionsfor the jet + E/T candidate sample. The expected LED signalcontribution for the case of n = 2 and MD = 1.0 TeV is alsoshown.
Based on the observed agreement with the SM expecta-tion in both the ! + E/T and jet + E/T candidate samples,we proceed to set lower limits on MD for the LED model.The limits are obtained solely from the total number ofobserved events in each of the samples (no kinematicshape information is incorporated). In order to estimateour sensitivity to the ADD model we simulate expectedsignals in both final states using the pythia [12] eventgenerator in conjunction with a geant [13] based de-tector simulation. For each extra dimension scenario wesimulate event samples for MD ranging between 0.7 and2 TeV. In the case of the ! + E/T analysis, the final kine-matic selection requirements for the candidate sampleare determined by optimizing the expected cross sectionlimit without looking at the data. The jet + E/T anal-ysis was done as a generic search for new physics usingthree sets of kinematic cuts, the most sensitive of which isused here. To compute the expected 95% C.L. cross sec-tion upper limits we combine the predicted ADD signal
$ + E/T Jet + E/T Combinedn % Mobs
D % MobsD Mobs
D
2 7.2 1080 9.9 1310 14003 7.2 1000 11.1 1080 11504 7.6 970 12.6 980 10405 7.3 930 12.1 910 9806 7.2 900 12.3 880 940
TABLE III: Percentage of signal events passing the candidatesample selection criteria (%) and observed 95% C.L. lowerlimits on the e!ective Planck scale in the ADD model (Mobs
D )in GeV/c2 as a function of the number of extra dimensions inthe model (n) for both individual and the combined analysis.
Number of Extra Dimensions2 3 4 5 6
Lo
we
r L
imit (
Te
V)
DM
0.6
0.8
1
1.2
1.4
1.6
Number of Extra Dimensions2 3 4 5 6
Lo
we
r L
imit (
Te
V)
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
FIG. 3: 95 % C.L. lower limits on MD in the ADD model asa function of the number of extra dimensions in the model.
and background estimates with systematic uncertaintieson the acceptance using a Bayesian method with a flatprior [14]. The acceptance is found to be almost indepen-dent (within 2%) of the mass MD. The total systematicuncertainties on the number of expected signal events are5.7% and 12.4% for the ! + E/T and jet + E/T candidatesamples respectively. The largest systematic uncertain-ties arise from modeling of initial/final state radiationconvoluted with jet veto requirements, choice of renor-malization and factorization scales, modeling of partondistribution functions, modeling of the jet energy scale(jet + E/T sample only), and the luminosity measurement.
Since the underlying graviton production mechanismis equivalent for both final states, the combination of theindependent limits obtained from the two candidate sam-ples is based on the predicted relative contributions ofthe four graviton production processes. Systematic un-certainties on the signal acceptances are treated as 100%correlated, while uncertainties on background estimates,obtained in most cases from data, are considered to beuncorrelated. The 95% C.L. lower limits on MD fromeach candidate sample and the combined limits are givenin Table III and plotted with LEP limits [15] in Fig. 3.
In conclusion, the CDF experiment has recently com-pleted searches for new physics in the ! + E/T and jet +E/T final states using data corresponding to 2.0 fb!1 and
q
q
!
G
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Large Extra Dimension SignaturesBlack 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
Table 1: The black hole production cross sections at the LHC for MPL = 1 TeV as given byCHARYBDIS. Note that CHARYBDIS does not include the form factors mentioned in section 7.
in order for our analyses to be as widely applicable as possible. In this section we review
these uncertainties.
4.1 Production cross section
The process of black hole production in hadron collisions is subject to a number of basic
uncertainties. The order of magnitude of the parton-level cross section should be given by
equation 2.1, but the form factor relating the left- and right-hand sides is uncertain and
would be expected to be n-dependent. Classical numerical simulations [26] suggest values
in the range 0.5–2, increasing with n. These values are not included in the CHARYBDIS
generator, but we take them into account when cross section data are used in our analysis
(in sections 7 and 8).
More fundamentally, the transition from the parton-level to the hadron-level cross
section is based on the factorization formula
!(S) =
!
dx1 dx2 f(x1)f(x2)!(s = x1x2S) (4.1)
where f(x) is the parton distribution function (PDF) summed over parton flavours. The
validity of this formula in the trans-Planckian energy region is unclear. Even if factoriza-
tion remains valid, the extrapolation of the PDFs into this region based on Standard Model
evolution from present energies is questionable. Also, comparison to Standard Model pro-
cesses in the trans-Planckian regime would be di!cult since perturbative physics would be
suppressed.
4.2 The first stages of decay
CHARYBDIS does not model the initial balding or spin-down phases of the black hole decay.
The amount of energy emitted from the black hole during these phases is expected to be
small [8] so such an omission should not be significant. However, it is probable that the
energy spectrum will be modified at low energies.
– 5 –
Rs(!
s) = M!1"
!!s
M"
" 1n+1!
s"M!for !BH ! R2s
BHs decaythermally, violating all
global conservation laws
High multiplicity eventswith lots of energy
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Universal Extra Dimensions
+GravitySM
Standard Model has KK modes
S5D =!
d5x F 2MN + !iD! ! + · · ·
!12R " x5 "
12R
All fields go in the bulk
R!1 >! 500 GeV
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Universal Extra Dimensions
+GravitySM
Standard Model has KK modes
S5D =!
d5x F 2MN + !iD! ! + · · ·
!12R " x5 "
12R
All fields go in the bulkM
ass
g W B Q U c Dc L Ec H
n = 1
n = 2n = 3· · ·
n = 0
f(x5)
1
sin(x5/R)
cos(2x5/R)sin(3x5/R)
Impose Dirichlet Boundary Conditions
R!1 >! 500 GeV
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UED KK Spectra
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
Levels are degenerate at tree level
All masses within 30% of each other!(This is a widely spaced example!)
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KK Parityx5 ! "x5
All odd-leveled KK modes are oddSM and even-leveled KK modes are even
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KK Parityx5 ! "x5
All odd-leveled KK modes are oddSM and even-leveled KK modes are even
LKP is stable!
Usually KK partner of Hypercharge Gauge boson
g0,0,1 !! R/2
!R/2dx5 f0(x5)f0(x5)f1(x5) "
!dx5 1 · 1 · sin(!x5/R)
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KK Parityx5 ! "x5
All odd-leveled KK modes are oddSM and even-leveled KK modes are even
Looks like a degenerate Supersymmetry spectrumuntil you can see 2nd KK level
LKP is stable!
Usually KK partner of Hypercharge Gauge boson
g0,0,1 !! R/2
!R/2dx5 f0(x5)f0(x5)f1(x5) "
!dx5 1 · 1 · sin(!x5/R)
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Typical UED EventPair produce colored 1st KK level
Each side decays separately
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
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Typical UED EventPair produce colored 1st KK level
Each side decays separately
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
g1 ! q1q
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Typical UED EventPair produce colored 1st KK level
Each side decays separately
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
q1 ! B1q
g1 ! q1q
![Page 125: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/125.jpg)
Typical UED EventPair produce colored 1st KK level
Each side decays separately
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
q1 ! B1q
g1 ! q1q
2j + ET!
![Page 126: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/126.jpg)
Typical UED EventPair produce colored 1st KK level
Each side decays separately
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
g1 ! q1q
q1 ! B1q
g1 ! q1q
2j + ET!
![Page 127: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/127.jpg)
Typical UED EventPair produce colored 1st KK level
Each side decays separately
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
g1 ! q1q
q1 ! B1q
g1 ! q1q
q1 !W 31 q
2j + ET!
![Page 128: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/128.jpg)
Typical UED EventPair produce colored 1st KK level
Each side decays separately
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
g1 ! q1q
q1 ! B1q
g1 ! q1q
q1 !W 31 q
W 31 ! !1!
2j + ET!
![Page 129: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/129.jpg)
Typical UED EventPair produce colored 1st KK level
Each side decays separately
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
g1 ! q1q
q1 ! B1q
g1 ! q1q
q1 !W 31 q
W 31 ! !1!
!1 ! !B1
2j + ET!
![Page 130: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/130.jpg)
Typical UED EventPair produce colored 1st KK level
Each side decays separately
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
g1 ! q1q
q1 ! B1q
g1 ! q1q
q1 !W 31 q
W 31 ! !1!
!1 ! !B1
2j + ET! 2j + ! + ! + ET!
![Page 131: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/131.jpg)
Typical UED EventPair produce colored 1st KK level
Each side decays separately
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,
!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.
R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary
terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections
and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the
lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an
interesting dark matter candidate. The corrections to the masses of the other first level KK
states are generally large enough that they will have prompt cascade decays down to !1.3
Therefore KK production at colliders results in generic missing energy signatures, similar
to supersymmetric models with stable neutralino LSP. Collider searches for this scenario
appear to be rather challenging because of the KK mass degeneracy and will be discussed
in a separate publication [13].
V. CONCLUSIONS
Loop corrections to the masses of Kaluza-Klein excitations can play an important role
in the phenomenology of extra dimensional theories. This is because KK states of a given
level are all nearly degenerate, so that small corrections can determine which states decay
and which are stable.
3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)
could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-
logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting
consequences for cosmology.
20
g1 ! q1q
q1 ! B1q
g1 ! q1q
q1 !W 31 q
W 31 ! !1!
!1 ! !B1
2j + ET! 2j + ! + ! + ET!
Difficult is in Soft Spectra
![Page 132: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/132.jpg)
Randall Sundrum ModelsTeV Scale Curved Extra Dimensions
ds2 = e!2kydx24 ! 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
![Page 133: Slac Summer Institute 2009](https://reader038.vdocuments.site/reader038/viewer/2022103018/5588e70cd8b42a11448b4590/html5/thumbnails/133.jpg)
Effects of the Warping
S5 =!
d4xdy!
g5 !(y " y0)"gµ!5 "µ#"!# + m2#2 + g#3 + $#4
#
gµ!5 = e2ky0!µ!!
g5 = e!4ky0
An IR brane scalar
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Effects of the Warping
S5 =!
d4xdy!
g5 !(y " y0)"gµ!5 "µ#"!# + m2#2 + g#3 + $#4
#
gµ!5 = e2ky0!µ!!
g5 = e!4ky0
S4 =!
d4x e!4ky0"e2ky0(!")2 + m2"2 + g"3 + #"4
#
Need to go to canonical normalization !! eky0!
An IR brane scalar
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Effects of the Warping
S5 =!
d4xdy!
g5 !(y " y0)"gµ!5 "µ#"!# + m2#2 + g#3 + $#4
#
gµ!5 = e2ky0!µ!!
g5 = e!4ky0
S4 =!
d4x e!4ky0"e2ky0(!")2 + m2"2 + g"3 + #"4
#
Need to go to canonical normalization !! eky0!
S4 =!
d4x (!")2 + m2e!2ky0"2 + ge!ky0"3 + #"4
All mass scales on IR brane got crunched by warp factor
Super-heavy IR brane Higgs becomes light!
An IR brane scalar
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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 parityResonances not evenly spaced either
Get light KK copies of right-handed top
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Tonnes of Theory & Pheno and Models for RS Models!
AdS/CFTTheories 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
!IR = e!ky0!UV
!QCD = e!2!"!1
3 (MGUT)b0 MGUT
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Technicolor TheoriesImagine there was no Higgs
QCD still gets strong and quarks condense
!QQc" #= 0 Qc = (U c, Dc)
QQc ! (1, 2) 12
Condensate has SM gauge quantum numbers
Like the Higgs!QCD confinement/chiral symmetry breaking
breaks electroweak symmetry
Technicolor is a scaled-up version of QCDRS Models are the modern versions of Technicolor
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In Technicolor theoriesNot necessarily a Higgs boson
Technirhos usually first resonance
OS =H†Wµ!HBµ!
!2
Mediate contributions to
! >! 3 TeVwithW±, Z0
!T
!T
90 GeV
800 GeV
etcNeed to be lighter than 1 TeV
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In Technicolor theoriesNot necessarily a Higgs boson
Technirhos usually first resonance
OS =H†Wµ!HBµ!
!2
Mediate contributions to
! >! 3 TeVwithW±, Z0
!T
!T
90 GeV
800 GeV
etcNeed to be lighter than 1 TeV
W±, Z0
!T!T
90 GeV
3 TeV
etc
Can push off the Technirhosusually a scalar resonance becomes narrow
600 GeV !T
!T starts playing the role of the HiggsRequires assumptions about
technicolor dynamics
Would like to get scalars lightwithout dynamical assumptions
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Higgs as a Goldstone boson!T !" "T
Higgs boson is a technipion
Pions are light because the areGoldstone bosons of approximate symmetries
V (!T ) ! m2f2 cos !T /f
f set by Technicolor scale
!!T " = 0,!f
Goldstone bosons only have periodic potentials
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Little Higgs TheoriesSpecial type of symmetry breaking
V (!T ) ! f4 sin4 !T /f + m2f2 cos !T /f
Looks like normal “Mexican hat” potential
Lots of group theory to get specific examples
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Little Higgs TheoriesSpecial type of symmetry breaking
V (!T ) ! f4 sin4 !T /f + m2f2 cos !T /f
Looks like normal “Mexican hat” potential
Lots of group theory to get specific examples
[SU(3)! SU(3)/SU(3)]4SU(5)/SO(5)
SU(6)/Sp(6) [SO(5)! SO(5)/SO(5)]4
[SU(4)/SU(3)]4SU(9)/SU(8)
SO(9)/SO(5)! SO(4)
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All have some similar features
New gauge sectors
Vector-like copies of the top quarksQ3 & Qc
3 U c3 & U3
There are extended Higgs sectors SU(2)L singlets, doublets & triplets
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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 theorieshave something to do with the weak scale
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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