Download Standard Model is an Effective Theory

Physics Beyond the Standard Model
J. Hewett, ITEP Winter School 2010
Why New Physics @ the Terascale?
• Electroweak Symmetry breaks at
energies ~ 1 TeV
(SM Higgs or ???)
• WW Scattering unitarized at energies ~ 1 TeV
(SM Higgs or ???)
• Gauge Hierarchy: Nature is fine-tuned or
Higgs mass must be stabilized by
New Physics ~ 1 TeV
• Dark Matter: Weakly Interacting Massive
Particle must have mass ~ 1 TeV to
reproduce observed DM density
All things point to the Terascale!
A Revolution is Upon Us!
Science Timeline: The Tools
WMAP
Auger
PLANCK
LSST/JDEM
Fermi
Tevatron
2005
LHC
2007
B-Factories
2010
2012
2015
Underground & IndirectDark Matter Searches
2020
ILC
LHCb
Numi/Minos
Super-K
Kamland
2018
LHC
Upgrade
T2K/Noa
0
Science Timeline: The Tools
WMAP
Auger
PLANCK
LSST/JDEM
Fermi
Tevatron
2005
LHC
2007
B-Factories
2010
2012
2015
Underground & IndirectDark Matter Searches
2020
ILC
LHCb
Numi/Minos
Super-K
Kamland
2018
LHC
Upgrade
T2K/Noa
0
The Standard Model
Brief review of features which guide & restrict BSM
physics
The Standard Model of Particle Physics
Building Blocks of Matter:
Symmetry:
SU(3)C x SU(2)L x U(1)Y
QCD
Electroweak
Spontaneously Broken
to QED
This structure is
experimentally confirmed!
The Standard Model on One Page
SGauge =  d4x FY FY + F F + Fa Fa
SFermions =  d4x 
Generations

f = Q,u,d,
L,e
fDf
SHiggs =  d4x (DH)†(DH) – m2|H|2 + |H|4
SYukawa =  d4x YuQucH + YdQdcH† + YeLecH†
( SGravity =  d4x g [MPl2 R
+ CC4]
)
Gauged Symmetries
Color
Matter
Fermions
SU(3)C
Electroweak
x
SU(2)L x U(1)Y
Q
3
2
+1/6
uc
3
1
-2/3
dc
3
1
+1/3
L
1
2
-1/2
ec
1
1
+1
Standard Model predictions well described by data!
EW measurements agree with
SM predictions @ 2+ loop level
Pull
Jet production rates @
Tevatron agree with QCD
Search for the Higgs Boson:
Tevatron Search
Direct Searches at LEP:
mH > 114.4 GeV
Indirect Searches at
LEP/SLC:
mH < 186 GeV @ 95% CL
Higgs
Z
Z
Z
Global Flavor Symmetries
SM matter secretly has a large symmetry:
Q1
u1
d1
L1
e1
.
.2
.
.3
U(45)
Rotate 45 fermions into
each other
Explicitly broken by gauging 3x2x1
U(3)Q x U(3)u x U(3)d x U(3)L x U(3)e
Explicitly
broken by
quark Yukawas
+ CKM
Rotate among
generations
Explicitly broken by
charged lepton
Yukawas
U(1)B
Baryon Number
U(1)e x U(1) x U(1) Explicitly broken
Lepton
Number
by neutrino
masses
U(1)L
(or nothing)
(Dirac)
(Majorana)
Global Symmetries of Higgs Sector
1 + i2
3 + i4
Higgs Doublet:
Secretly transforms as a
4 of SO(4)
1
2
3
4
Decomposes into
subgroups
(2,2) SU(2) x SU(2)
SU(2)L of EW
Left-over Global Symmetry
Four real degrees
of freedom
Global Symmetries of Higgs Sector
Secretly transforms as a
4 of SO(4)
Four real degrees
of freedom
1 + i2
3 + i4
Higgs Doublet:
1
2
3
4
Decomposes into
subgroups
(2,2) SU(2) x SU(2)
SU(2)L of EW
Remaining Global Symmetry
Gauging U(1)Y explicitly breaks
SU(2)Global  Nothing
Size of this breaking given by
Hypercharge coupling g’
MW2
MZ2
=
g2
g2 + (g’)2
 1 as g’0
New Physics may excessively
break SU(2)Global
Custodial Symmetry
Standard Model Fermions are Chiral
Fermions cannot simply ‘pair up’ to form mass terms
i.e., mfLfR is forbidden
Standard Model Fermions are Chiral
Fermions cannot simply ‘pair up’ to form mass terms
i.e., mfLfR is forbidden
Try it!
SU(3)C
(Quc)
(Qdc)
(QL)
(Qe)
(ucdc)
(ucL)
(uce)
(dcL)
(dce)
(Le)
1
1
3
3
-3x3
3
3
3
3
1
SU(2)L U(1)Y
2
2
1
2
1
2
1
2
1
2
-1/2
+1/2
-1/3
+7/6
-1/3
-7/6
+1/3
-5/6
+4/3
+1/2
Fermion masses must be
generated by Dimension-4
(Higgs) or higher
operators to respect SM
gauge invariance!
Anomaly Cancellation
Quantum violation of current conservation
An anomaly leads to a mass for a gauge boson
Anomaly Cancellation
SU(3)
SU(3)
SU(2)L
SU(2)L
U(1)Y
U(1)Y
g
g
U(1)Y
3[ 2‧(1/6) – (2/3) + (1/3)] = 0
Q
uc
dc
U(1)Y
3[3‧(1/6) – (1/2)] = 0
Q
L
U(1)Y
3[ 6‧(1/6)3 + 3‧(-2/3)3 + 3‧(1/3)3
+ 2‧(-1/2)3 + 13] = 0
U(1)Y
3[(1/6) – (2/3) + (1/3) – (1/2) +1]
=0
Q
uc
dc
L
e
Can’t add any new fermion  must be chiral or vector-like!
Standard Model Summary
• Gauge Symmetry
SU(3)C x SU(2)L x U(1)Y
Exact
Broken to U(1)QED
• Flavor Symmetry
U(3)5  U(1)B x U(1)L (?)
Explicitly broken by Yukawas
• Custodial Symmetry
SU(2)Custodial of Higgs sector
Broken by hypercharge so  = 1
• Chiral Fermions
Need Higgs or Higher
order operators
• Gauge Anomalies
Restrict quantum
numbers of new fermions
Standard Model Summary
• Gauge Symmetry
SU(3)C x SU(2)L x U(1)Y
Exact
Broken to U(1)QED
• Flavor Symmetry
U(3)5  U(1)B x U(1)L (?)
Explicitly broken by Yukawas
• Custodial Symmetry
SU(2)Custodial of Higgs sector
Broken by hypercharge so  = 1
• Chiral Fermions
Need Higgs or Higher
order operators
• Gauge Anomalies
Restrict quantum
numbers of new fermions
Any model with New Physics must respect these symmetries
Standard Model is an Effective field theory
An effective field theory has a finite range of
applicability in energy:
, Cutoff scale
Energy
Theory is valid
Particle masses
All interactions consistent with gauged
symmetries are permitted, including higher
dimensional operators whose mass dimension is
compensated for by powers of 
Constraints on Higher Dimensional Operators
Baryon Number Violation
Lepton Number Violation
Flavor Violation
CP Violation
Precision Electroweak
Contact Operators
Generic Operators
Gauge coupling unification: Our Telescope
Counts charged
matter
4
0
3
0
2
0
1
0
1
2
3
(GeV)
Weak scale measurement
High scale particle content
Telescope to Unification
Unification of Weak and
Electromagnetic forces
demonstrated at HERA
ep collider at DESY
 Electroweak theory!
Grand Unification
Gauge coupling unification indicates forces arise from
single entity
16
• What sets the cutoff scale  ?
• What is the theory above the cutoff?
New Physics, Beyond the Standard Model!
Three paradigms:
1. SM parameters are unnatural
 New physics introduced to “Naturalize”
2. SM gauge/matter content complicated
 New physics introduced to simplify
3. Deviation from SM observed in experiment
 New physics introduced to explain
How unnatural are the SM parameters?
Technically Natural
– Fermion masses
(Yukawa Couplings)
– Gauge couplings
– CKM
Logarithmically
sensitive to the cutoff
scale
Technically Unnatural
•Higgs mass
•Cosmological constant
•QCD vacuum angle
Power-law sensitivity to
the cutoff scale
The naturalness problem that has had the greatest
impact on collider physics is:
The Higgs (mass)2 problem
or
The hierarchy problem
Do we really need a Higgs?
Higgs
Higgs
Bad violation of unitarity
Restores unitarity
A = a s/MW2 + …
A = - a (s – mh2)/MW2
+…
Expand cross section into partial waves
Unitarity bound (Optical theorem!)  Gives mh < 4MW
LHC is designed to explore this entire region!
The Hierarchy
Energy (GeV)
Planck
GUT
10
Weak
desert
1019
1016
Future
Collider
Energies
3
All of
known
physics
10-18
Solar System
Gravity
The Hierarchy Problem
Energy (GeV)
Planck
GUT
10
Weak
Quantum Corrections:
Virtual Effects drag
Weak Scale to MPl
desert
1019
1016
Future
Collider
Energies
3
mH2 ~
All of
known
physics
10-18
Solar System
Gravity
~ MPl2
Electroweak Hierarchy Problem
Higgs (mass)2 is quadratically divergent
In the SM, mh is naturally ~ Λ, the largest energy scale
mh ~ 100 GeV & Λ ~ MPl ~ 1019 GeV → cancellation in one part of 1034
A Cellar of New Ideas
’67
The Standard Model
’77
Vin de Technicolor
’70’s
’90’s
Supersymmetry: MSSM
SUSY Beyond MSSM
a classic!
aged to perfection
better drink now
mature, balanced, well
developed - the Wino’s choice
svinters blend
CP Violating Higgs
all upfront, no finish
lacks symmetry
’98
Extra Dimensions
bold, peppery, spicy
uncertain terrior
’02
Little Higgs
’90’s
’03
’03
’04
’05
Fat Higgs
Higgsless
Split Supersymmetry
Twin Higgs
complex structure
young, still tannic
needs to develop
sleeper of the vintage
what a surprise!
finely-tuned
double the taste
J. Hewett
Last Minute Model Building
Anything Goes!
•
•
•
•
•
•
•
Non-Communtative Geometries
Return of the 4th Generation
Hidden Valleys
Quirks – Macroscopic Strings
Lee-Wick Field Theories
Unparticle Physics
…..
(We stilll have a bit more time)
A Cellar of New Ideas
’67
The Standard Model
’77
Vin de Technicolor
’70’s
’90’s
Supersymmetry: MSSM
SUSY Beyond MSSM
a classic!
aged to perfection
better drink now
mature, balanced, well
developed - the Wino’s choice
svinters blend
CP Violating Higgs
all upfront, no finish
lacks symmetry
’98
Extra Dimensions
bold, peppery, spicy
uncertain terrior
’02
Little Higgs
’90’s
’03
’03
’04
’05
Fat Higgs
Higgsless
Split Supersymmetry
Twin Higgs
complex structure
young, still tannic
needs to develop
sleeper of the vintage
what a surprise!
finely-tuned
double the taste
J. Hewett
The Hierarchy Problem: Supersymmetry
Energy (GeV)
Planck
GUT
Quantum Corrections:
Virtual Effects drag
Weak Scale to MPl
desert
1019
1016
Future
Collider
Energies
boson
10
3
Weak
fermion
mH2 ~
All of
known
physics
10-18
~ MPl2
mH2 ~
Solar System
Gravity
~ - MPl2
Large virtual effects cancel
order by order in
perturbation theory
Supersymmetry
Supersymmetry is a new symmetry that relates
fermions ↔ bosons
Superpartners
• Translations:
Particle P at point x → Particle P at point x’
• Supersymmetry:
~
Particle P at point x → Particle P at point x
~
– P and P differ by spin ½: fermions ↔ bosons
~
– P and P are identical in all other ways (mass, couplings….)
γ
~
γ
~
γ
Supersymmetry and Naturalness
Dependence on Λ is softened to a logarithm
SUSY solves hierarchy problem, if sparticle masses <1 TeV
Supersymmetry: Recap
•Symmetry between fermions and bosons
•Predicts that every particle has a superpartner of
equal mass
•Suppresses quantum effects
•Can make quantum mechanics consistent with
gravity (with other ingredients)
Supersymmetry: Recap
•Symmetry between fermions and bosons
•Predicts that every particle has a superpartner of
equal mass (  SUSY is broken: many competing models!)
•Suppresses quantum effects
•Can make quantum mechanics consistent with
gravity (with other ingredients)
Higgs Doubling
• SUSY requires 2 Higgs doublets to cancel anomalies and to give
mass to both up- and down-type particles
• Anomaly cancellation requires Σ Y3 = 0, where Y is hypercharge
and the sum is over all fermions
• SUSY adds an extra fermion with Y = -1
• To cancel this anomaly, we add another Higgs doublet with Y = +1
Supersymmetric Parameters
Minimal Supersymmetric Standard Model
Conserved multiplicative quantum number (R-parity)
•Superpartners are produced in pairs
•Heavier Superpartners decay to the Lightest
•Lightest Superpartner is stable
Collider signatures dependent on this assumption
and on model of SUSY breaking
R-Parity: New Multiplicative Quantum Number
• One problem: proton decay!
• Forbid this with R-parity conservation: Rp = (-1)3(B-L)+2S
~
– P has Rp = +1; P has Rp = -1
– Requires 2 superpartners in each interaction
• Consequence: the Lightest Supersymmetric Particle (LSP)
is stable and cosmologically significant.
• What is the LSP?
Neutral SUSY Particles
Electroweak Symmetry Breaking
Telescope to Unification
• Superpartners modify the scale dependence of couplings
• With TeV superpartners, the forces are unified!
• Unification scale ~ 1016 GeV
Telescope to Unification
• All parameters have scale dependence
• Superpartner mass determinations provide tests for
unification
Evolution of superpartner masses to high scale:
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
Parameterized SUSY Breaking
There are over 100 parameters!
Most of these are new flavor violation parameters
or CP violating phases
Causes difficulties in the flavor sector
Need some simplifying assumptions
SUSY Effects in FCNC
Super-GIM mechanism
Must be Flavor Universal Couplings
Scalar Masses
Trilinear A-Terms
Scalar particles are approximately degenerate!
Mediation of SUSY Breaking
SUSY breaking occurs through interactions of
Intermediate particles
Weak Scale
MSSM
Mediation
Susy Breaking
Hidden Sector
Theoretical assumptions @ the GUT scale reduce the
number of parameters
3 Popular SUSY breaking scenarios:
Gravity Mediation (mSUGRA)
Gauge Mediation
Anomaly Mediation
Gravity Mediated SUSY Breaking (mSUGRA)
Two MSSM Model Frameworks
• The constrained MSSM (CMSSM)
– Based on mSUGRA
– Common masses & couplings at the GUT scale
– m0, m1/2, A0, tanβ = v2/v1, sign μ
• The phenomenological MSSM (pMSSM)
– 19 real, weak-scale parameters
scalars:
mQ1, mQ3, mu1, md1, mu3, md3, mL1, mL3, me1, me3
gauginos: M1, M2, M3
tri-linear couplings: Ab, At, Aτ
Higgs/Higgsino: μ, MA, tanβ
Predictions for Lightest Higgs Mass in the
CMSSM Framework
• CMSSM: m0, m1/2, A0, tanβ, sign μ
• Χ2 fit to some global data set
Fit to EW precision, B-physics observables, & WMAP
Ellis etal arXiv:0706.0652
Predictions for Lightest Higgs Mass in the
pMSSM
Models consistent with EW Precision, B Physics, Cosmology,
and Collider data
Berger, Gainer, JLH, Rizzo 0812.0980
Squarks & Gluinos @ the Tevatron
mSUGRA limits
Gluinos at the Tevatron
• Tevatron gluino/squark analyses performed
for mSUGRA – constant ratio mgluino : mBino ≃ 6 : 1
Distribution of Gluino Masses
Gluino-Bino mass
ratio determines
kinematics
x
Berger, Gainer, JLH, Rizzo 0812.0980
Production cross section (pb)
Supersymmetry at the LHC
Sparticle mass (GeV)
Supersymmetry at the LHC
SUSY discovery generally
‘easy’ at LHC: Multijets
+ missing ET
LHC mSUGRA Discovery Reach (14 TeV)
Sample pMSSM Results
14 TeV, 1 fb-1
Conley, Gainer, JLH, Le, Rizzo In progress
SUSY Mass Scale from Inclusive Analysis
Reconstruction of Sparticle Masses at LHC
Squarks and Gluinos have
complicated decay chains
Main analysis tool: dilepton edge in 02  01l+ lProportional to Sparticle mass
differences
Introduces strong mass correlations
The ATLAS SUSY analyses:
• 2,3,4-jet +MET
• 1l, ≥4-jet +MET
• Same Sign Di-Lepton
• Opposite Sign Di-Lepton
• Trileptons + (0,1)-j +MET
•  +≥ 4j +MET
• ≥4j w/ ≥ 2btags + MET
• Stable particle search
Some Results From 70k pMSSM Models
*
*
 ID & reconstruction in PGS is a bit too optimistic & needs to be
Conley, Gainer, JLH, Le, Rizzo In progress
reaccessed
Supersymmetry at the ILC
ILC Studies superpartners individually via
Determines
•Quantum numbers (spin!)
•Supersymmetric relation
of couplings

Selectron pair production
=e
e + e-
-
SS
~
Ratio of Coupling Stregths
M1 (GeV)
2% accuracy in
determination of
Supersymmetric
coupling strength
Proof that it IS
Supersymmetry!
~

= 2e
Precise Mass Measurements of Superpartners
~ ~
Example: e  e + 
Fixed center of mass energy
gives flat energy distribution in
the laboratory for final state e-
e
Endpoints can be used to
determine superpartner masses
to part-per-mil accuracy
A realistic simulation:
Determines Superpartner
masses of the electron and
photon to 0.05%
SUSY parameter determination: Fittino SPS1a’
Bechtle, Desch, Wienemann, hep-ph/0506244
Precise
determination
of parameters
only possible
with LHC + ILC
Reconstruction
of SUSY
Lagrangian
(without
assumptions)
becomes
possible!
Dark Matter Candidates
• The observational
constraints are no
match for the
creativity of theorists
SUSY
• Masses and interaction
strengths span many,
many orders of
magnitude, but not all
candidates are equally
motivated
• Weakly Interacting
Massive Particle (WIMP)
HEPAP/AAAC DMSAG Subpanel (2007)
The WIMP ‘Miracle’
(1) Assume a new (heavy)
particle  is initially in
thermal equilibrium:
(1)
(2)
 ↔ f f
(2) Universe cools:
ff
→
/
←

(3) s “freeze out”:

→
/
←/
Zeldovich et al. (1960s)
ff
(3)
• The amount of dark matter
left over is inversely
proportional to the
annihilation cross section:
WDM ~ <sAv>-1
s A ~  2/ m 2
HEPAP LHC/ILC Subpanel (2006)
[band width from k = 0.5 – 2, S and P wave]
Remarkable “coincidence”:
WDM ~ 0.1 for m ~ 100 GeV – 1 TeV WIMP!
particle physics independently predicts particles with about the
right density to be dark matter !
Relic Density: Neutralino LSP
Contributions to Neutralino WIMP Annihilation
Cosmologically Preferred SUSY: mSUGRA
Relic Density Determinations
Identifying Dark Matter
J. Feng
Dark Matter Detection
  photons, positrons , anti-protons…. ‘in the sky’ right now
may be seen by PAMELA, FERMI & other experiments
N N (elastic) scattering may be detected on earth in deep
underground experiments
If  is really a WIMP it may be directly produced at the LHC !
Direct Detection Prospects
mSUGRA
pMSSM
Berger, Gainer, JLH, Rizzo 0812.0980
Supersymmetry Summary
• SUSY solves many questions:
–
–
–
–
Gauge hierarchy
EWSB
Gauge coupling unification
Dark Matter candidate
• SUSY has some issues:
– 120 free parameters
– In most natural case, we would have discovered it already
– Has problems fitting indirect DM search data (PAMELA,
Fermi)
• LHC will tell us if SUSY is relevant to the weak scale
or not! (If the signal isn’t missed….)
Extra Dimensions Taxonomy
Large
ADD Models
TeV
Small
Flat
Curved
UEDs
RS Models
GUT Models
Extra dimensions can be difficult to visualize
•One picture: shadows of higher dimensional
objects
2-dimensional shadow of a
rotating cube
3-dimensional shadow of a rotating hypercube
Extra dimensions can be difficult to visualize
• Another picture: extra dimensions are too small
for us to observe  they are
‘curled up’ and compact
The tightrope walker only
sees one dimension:
back & forth.
The ants see two
dimensions: back & forth
and around the circle
Every point in spacetime has curled up
extra dimensions associated with it
One extra dimension
is a circle
Two extra dimensions can
be represented by a sphere
Six extra dimensions can
be represented by a
Calabi-Yau space
The Braneworld Scenario
• Yet another picture
• We are trapped on a
3-dimensional spatial
membrane and cannot move
in the extra dimensions
• Gravity spreads out and
moves in the extra space
• The extra dimensions can
be either very small or
very large
Are Extra Dimensions Compact?
• QM tells us that the momentum of a particle traveling
along an infinite dimension takes a continuous set of
eigenvalues. So, if ED are not compact, SM fields must be
confined to 4D OTHERWISE we would observe states with
a continuum of mass values.
• If ED are compact (of finite size L), then QM tells us that
p5 takes on quantized values (n/L). Collider experiments
tell us that SM particles can only live in ED if 1/L > a few
100 GeV.
Kaluza-Klein tower of particles
E2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc2)2
Recall pextra = n/R
In 4 dimensions,
looks like a mass!
Tower of massive particles
Small radius
Large radius
Kaluza-Klein tower of particles
E2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc2)2
Recall pextra = n/R
Small radius
gives well
separated
Kaluza-Klein
particles
In 4 dimensions,
looks like a mass!
Tower of massive particles
Small radius
Large radius
Large
radius gives
finely
separated
KaluzaKlein
particles
Action Approach:
Consider a real,
massless scalar
in flat 5-d
Masses of KK modes are determined by the interval BC
Time-like or Space-like Extra Dimensions ?
Consider a massless particle, p2 =0, moving in flat 5-d
Then p2 = 0 = pμpμ ± p52
If the + sign is chosen, the extra dimension is time-like,
then in 4-d we would interpret p52 as a tachyonic mass
term, leading to violations of causality
Thus extra dimensions are usually considered to be
space-like
Higher Dimensional Field Decomposition
• As we saw, 5-d scalar becomes a 4-d tower of scalars
• Recall:
4-vector
tensor
• 5-d:
Lorentz (4-d)
scalar
Aμ
Fμν
5-d
scalar
vector AM
tensor hMN
↔
Rotations (3-d)
scalar
→
A, Φ
→ →
E, B
↔
4-d
(scalar)n
(Aμ, A5)n
(hμν, hμ5, h55)n
KK towers
Higher Dimensional Field Decomposition
• As we saw, 5-d scalar becomes a 4-d tower of scalars
• Recall:
4-vector
tensor
• 4+δ-d:
Lorentz (4-d)
scalar
Aμ
Fμν
4+δ-d
scalar
vector AM
tensor hMN
↔
Rotations (3-d)
scalar
→
A, Φ
→ →
E, B
↔
4-d (i=1…δ)
(δ scalars)n
(Aμ, Ai)ni
(hμν, hμi, hij)n
KK towers
1 tensor, δ 4-vectors, ½ δ(δ+1) scalars
• Experimental observation of KK states:
Signals evidence of extra dimensions
• Properties of KK states:
Determined by geometry of extra dimensions
 Measured by experiment!
The physics of extra dimensions is the
physics of the KK excitations
What are extra dimensions good for?
• Can unify the forces
• Can explain why gravity is weak (solve hierarchy
problem)
• Can break the electroweak force
• Contain Dark Matter Candidates
• Can generate neutrino masses
……
Extra dimensions can do everything SUSY can do!
If observed: Things we will want to know
•
•
•
•
•
•
How many extra dimensions are there?
How big are they?
What is their shape?
What particles feel their presence?
Do we live on a membrane?
…
If observed: Things we will want to know
•
•
•
•
•
•
•
•
How many extra dimensions are there?
How big are they?
What is their shape?
What particles feel their presence?
Do we live on a membrane?
…
Can we park in extra dimensions?
When doing laundry, is that where all the
socks go?
Searches for extra dimensions
Three ways we hope to see extra dimensions:
1. Modifications of gravity at short distances
1. Effects of Kaluza-Klein particles on
astrophysical/cosmological processes
1. Observation of Kaluza-Klein particles in high
energy accelerators
The Hierarchy Problem: Extra Dimensions
Energy (GeV)
Planck
GUT
Simplest Model:
Large Extra Dimensions
desert
1019
1016
Future
Collider
Energies
10
3
Weak – Quantum Gravity
= Fundamental scale in
4 +  dimensions
MPl2 = (Volume) MD2+
All of
known
physics
Gravity propagates in
D = 3+1 +  dimensions
10-18
Solar System
Gravity
Large Extra Dimensions
Arkani-Hamed, Dimopoulos, Dvali,
SLAC-PUB-7801
Motivation: solve the hierarchy problem by removing it!
SM fields confined to 3-brane
Gravity becomes strong in the bulk
Gauss’ Law:
MPl2 = V MD2+ , V = Rc 
MD = Fundamental scale in the bulk
~ TeV
Constraints from Cavendish-type exp’ts
Constraints from Astrophysics/Cosmology
• Supernova Cooling
Cullen, Perelstein
Barger etal, Savage etal
NN  NN + Gn can cool supernova too rapidly
• Cosmic Diffuse  Rays
NN  NN + Gn 
-  G  

n
• Matter Dominated Universe
Hannestad, Raffelt
Hall, Smith
Fairbairn
too many KK states
• Neutron Star Heat Excess
NN  NN + Gn
Hannestad, Raffelt
becomes trapped in neutron star halo
and heats it
Bulk Metric: Linearized Quantum Gravity
•Perform Graviton KK reduction
•Expand hAB into KK tower
•SM on 3-brane
Set T = AB (ya)
•Pick a gauge
•Integrate over dy
 Interactions of Graviton KK states
with SM fields on 3-brane
Feyman Rules: Graviton KK Tower
Massless 0-mode + KK states have
indentical coupling to matter
Han, Lykken, Zhang; Giudice, Rattazzi, Wells
Collider Tests
Graviton Tower Exchange: XX  Gn  YY
Giudice, Rattazzi, Wells
JLH
Search for 1) Deviations in SM processes
2) New processes! (gg  ℓℓ)
Angular distributions reveal spin-2 exchange
M
Gn are densely packed!
(s Rc) states are exchanged! (~1030 for =2 and s = 1 TeV)
Drell-Yan Spectrum @ LHC
Forward-Backward Asymmetry
MD = 2.5 TeV
4.0
JLH
Graviton Exchange
Graviton Exchange @ 7 TeV LHC
Issue: How to
determine spin of
exchanged particle?
Graviton Tower Emission
• e+e-  /Z + Gn
• qq  g + Gn
• Z  ff + Gn
Giudice, Ratazzi,Wells
Mirabelli,Perelstein,Peskin
Gn appears as missing energy
Model independent – Probes MD
directly
Sensitive to 
Parameterized by density of states:
Discovery reach for MD (TeV):
Graviton Emission @ LHC
Graviton Emission @ LHC @ 7 TeV
Detailed LHC/ATLAS MC Study
The 14 TeV LHC is seen
to have considerable search
reach for KK Graviton
production
Hinchliffe, Vacavant
Current Bounds on Graviton Emission
BEWARE!
• There is a subtlety in this calculation
• When integrating over the kinematics, we enter a
region where the collision energies EXCEED the
4+n-dimensional Planck scale
• This region requires Quantum Gravity or a UV
completion to the ADD model
• There are ways to handle this, which result in minor
modifications to the spectrum at large ET that may
be observable
Graviton Emission in e+e- Collisions
Giudice, Rattazzi, Wells
Dimopoulos, Landsberg
Giddings, Thomas
Black Hole Production @ LHC:
Black Holes produced when s > MD
Classical Approximation:
E/2
b
[space curvature << E]
b < Rs(E)  BH forms
E/2
^
MBH ~ s
Geometric Considerations:
sNaïve = FnRs2(E),
details show this holds up to a
factor of a few
Blackhole Formation Factor
Potential Corrections to Classical Approximation
1. Distortions from
finite Rc as Rs  Rc
Critical point for
instabilities for n=5:
(Rs/Rc)2 ~ 0.1 @ LHC
2. Quantum Gravity Effects
RS2/(2Rc)2
n = 2 - 20
n = 2 - 20
Higher curvature term
corrections
Gauss-Bonnet term
n2 ≤ 1 in string models
Production rate is enormous!
sNaïve ~ n for large n
1 per sec at LHC!
MD = 1.5 TeV
JLH, Lillie, Rizzo
Cosmic Ray Sensitivity to Black Hole Production
No suppression
Ringwald, Tu
Anchordoqui etal
Summary of Exp’t Constraints on MD
Anchordoqui, Feng
Goldberg, Shapere
Black Hole Decay
• Balding phase: loses ‘hair’ and
multiple moments by
gravitational radiation
• Spin-down phase: loses angular
momentum by Hawking radiation
• Schwarzschild phase: loses
mass by Hawking radiation –
radiates all SM particles
• Planck phase: final decay or
stable remnant determined by
quantum gravity
Decay Properties of Black Holes (after Balding):
Decay proceeds by thermal emission of Hawking radiation
Not very sensitive to BH rotation for n > 1
At fixed MBH, higher dimensional BH’s are hotter:
N ~ 1/T
 higher dimensional BH’s
emit fewer quanta, with each
quanta having higher energy
Multiplicity for n = 2 to n = 6
Harris etal hep-ph/0411022
Grey-body Factors
Particle multiplicity
in decay:
 = grey-body
factor
Contain energy & anglular emission information
pT distributions of Black Hole decays
Provide good discriminating power for value of n
Generated using modified CHARYBDIS linked to PYTHIA
with M* = 1 TeV
Black Hole event simulation @ LHC
LED: Is the hierarchy problem really solved?
M*Rc > 108 for n = 2-6
Disparate values for gravity
and EWK scales traded for
disparate values of M* and Rc
However,
1 < M*Rc < 10 for
n = 17 - 40
Large n offers true solution to hierarchy!
Collider Signatures Change with large n
Graviton KK states are now ‘invisible’
•m1 ~ TeV
•Couplings are still MPl-1
Collider searches are highly degraded!
For n = 2, M* up to 10 TeV
observable at ILC, LHC
Drops to < 1 TeV for
n = 20
Only viable collider
signature is Black Hole
production!
Questions you might ask about LED:
• Doesn’t string/M-theory fix  = 6,7?
• Aren’t there string-inspired models where SM
gauge fields have KK excitations?
• Do all  dimensions have to be the same size?
Flat TeV-1–size Extra Dimensions
Can arise naturally in string-inspired models
Antoniadis
The Standard Model goes into the bulk!
Model building choices:
• Gauge fields in the bulk
• Higgs in the bulk or on the brane?
• Fermions:
– Located at orbifold fixed points
– Localized to specific points inside the bulk (Split Fermions)
– Freely propagate inside the bulk (Universal Extra Dimensions)
Orbifolding in 1 Extra Dimension
y
Aside:
Double
Orbifolds!
Precision Electroweak Data (fermions @ fixed points)
Exchange of gauge KK excitations contribute to precision
EW observables
Contributions include:
– Tree-level KK interactions (e.g.,  decay)
– KK – zero mode mixing (e.g., affects Z-pole observables)
– Zero mode loop corrections
KK tower exchanges induce new dim-6 operators with
coefficients
Rizzo, Wells
Delgado, Pomerol
Perform full fit to global precision EW data set
Bound on compactification scale,
Mc > 4.5 TeV
degrades to Mc > 2-3 TeV for localized fermions
Searches @ Colliders
• Hadron Colliders:
-   /Z  ℓℓ
– qq
n
n
– qq  Wn  ℓ
– qq,gg  gn  jj
(fermions @ fixed points)
Drell-Yan /Z/W KK resonance
dijet g KK resonance
Bumps!
Tevatron Run I: Mc > 0.8 TeV
Run II Mc > 1.1 TeV
•
e+e-
Colliders:
e+e-
-
Indirect search in
 n/Zn  ff
Observe deviation from SM
Fit to sf, AFBf, ALRf, Apol
KK /Z Production @ LHC, Mc = 4 TeV
D = separation of fermions in 5th dimension
m2 = 2m1
Even spacing denotes flat space
ATLAS Simulation for /Z KK Production
Discovery Reach: Mc < 6.3 TeV
Azuelos, Polesello
Les Houches 01
KK gluon dijet mass bumps @ LHC
Localized Fermions in Extra Dimension
Arkani-Hamed, Schmaltz
kink
yf for each fermion. Overlap of Left- & Right-handed
wavefunctions give Yukawa couplings!
Proton Decay
Exponential Fall-off of Scattering Cross Sections
If collision energy is
high enough, the two
interacting partons will
probe separation
distance between them!
Exponential fall-off of cross section for
fermion pair production
Arkani-Hamed, Grossman, Schmaltz
s/sSM for  pair
production
Energy (TeV)
Universal Extra Dimensions
Appelquist, Cheng, Dobrescu
• All SM fields in TeV-1, 5d, S1/Z2 bulk
• No branes!  translational invariance is preserved
 tree-level conservation of p5
• KK number conserved at tree-level
•
broken at higher order by boundary terms
• KK parity conserved to all orders, (-1)n
Consequences:
1. KK excitations only produced in pairs
Relaxation of collider & precision EW constraints
Rc-1 ≥ 300 GeV!
2. Lightest KK particle is stable (LKP) and is Dark Matter
candidate
3. Boundary terms separate masses and give SUSY-like
spectrum
Universal Extra Dimensions: Bosonic SUSY
Phenomenology looks like
Supersymmetry:
Spectrum looks like SUSY !
Heavier particles cascade
down to LKP
LKP: Photon KK state
appears as missing ET
SUSY-like Spectroscopy
Confusion with SUSY if
discovered @ LHC !
Chang, Matchev,Schmaltz
How to distinguish SUSY from UED I:
Observe KK states in e+eannihilation
Measure their spin via:
•Threshold production, s-wave
vs p-wave
•Distribution of decay products
•However, could require CLIC
energies...
JLH, Rizzo, Tait
Datta, Kong, Matchev
How to distinguish SUSY from UED II:
Observe higher level (n = 2) KK
states:
– Pair production of q2q2, q2g2,
V2 V2
– Single production of V2 via
(1) small KK number
breaking couplings and (2)
from cascade decays of q2
Discovery reach @ LHC
Datta, Kong, Matchev
How to distinguish SUSY from UED III:
Measure the spins of the KK states @ LHC – Difficult!
Decay chains in SUSY and UED:
Form charge asymmetry:
Smillie, Webber
Works for some,
but not all,
regions of
parameter space
UED Dark Matter Candidate: 1
Calculate relic density from 1 annihilation and co-annihiliation
WMAP
Kong, Matchev
Tait, Servant
LED: Is the hierarchy problem really solved?
M*Rc > 108 for n = 2-6
Disparate values for gravity
and EWK scales traded for
disparate values of M* and Rc
However,
1 < M*Rc < 10 for
n = 17 - 40
Large n offers true solution to hierarchy!
Flat TeV-1–size Extra Dimensions
Can arise naturally in string-inspired models
Antoniadis
The Standard Model goes into the bulk!
Model building choices:
• Gauge fields in the bulk
• Higgs in the bulk or on the brane?
• Fermions:
– Located at orbifold fixed points
– Localized to specific points inside the bulk (Split Fermions)
– Freely propagate inside the bulk (Universal Extra Dimensions)
Orbifolding in 1 Extra Dimension
y
ATLAS Simulation for /Z KK Production
Discovery Reach: Mc < 6.3 TeV
Azuelos, Polesello
Les Houches 01
The Hierarchy Problem: Extra Dimensions
Energy (GeV)
Planck
GUT
desert
1019
1016
Future
Collider
Energies
Model II:
Warped Extra Dimensions
strong
curvature
10
3
Weak
All of
known
physics
10-18
Solar System
Gravity
wk = MPl e-kr
Non-Factorizable Curved Geometry: Warped Space
Area of each grid is equal
Field lines spread out
faster with more volume
 Drop to bottom brane
Gravity appears weak on top
brane!
Localized Gravity: Warped Extra Dimensions
Randall, Sundrum
Bulk = Slice of AdS5
5 = -24M53k2
k = curvature scale
Hierarchy is
generated by
exponential!
Naturally stablized
via Goldberger-Wise
4-d Effective Theory
Davoudiasl, JLH, Rizzo
Phenomenology
governed by two
parameters:
 ~ TeV
k/MPl ≲ 0.1
5-d curvature:
|R5| = 20k2 < M52
Interactions
Recall  = MPlekr ~ TeV
Randall-Sundrum Graviton KK spectrum
Davoudiasl, JLH, Rizzo
Unequal spacing signals curved space
e+e- →μ+μe+e- +-
LHC
pp → l+l-
Different curves for k/MPl =0.01 – 1.0
Tevatron limits on RS Gravitons
CDF Drell-Yan spectrum
Summary of Theory & Experimental Constraints
LHC can cover entire allowed parameter space!!
Graviton Branching Fractions
B = 2Bℓℓ
Measuring Graviton KK Properties
n=1,2 KK Graviton production
Spin determination
Davoudiasl, JLH, Rizzo
Extend Manifold: AdS5 x S
e+e- +-
Drell-Yan
Gives a forest of KK graviton resonances!
Davoudiasl, JLH, Rizzo
Problem with Higher Dimensional Operators
• Recall the higher dimensional operators that
mediate proton decay & FCNC
• These are supposed to be suppressed by some
high mass scale
• But all high mass scales present in any RS
Lagrangian are warped down to the TeV scale.
• ⇒ There is no mechanism to suppress these
dangerous operators!
• Could employ discrete symmetries ala SUSY – but
there is a more elegant solution….
Peeling the Standard Model off the Brane
• Model building scenarios
require SM bulk fields
–
–
–
–
–
Gauge coupling unification
Supersymmetry breaking
 mass generation
Fermion mass hierarchy
Suppression of higher
dimensional operators
Start with gauge fields in the bulk:
• Gauge boson KK towers have coupling gKK = 8.4gSM
• Precision EW Data Constrains: m1A > 25 TeV   >
100 TeV!
• SM gauge fields alone in the bulk violate custodial
symmetry
Davoudiasl, JLH, Rizzo
Pomarol
Derivation of Bulk Gauge KK Spectrum
Add Fermions in the Bulk
Grossman, Neubert
Ghergetta, Pomarol
Davoudiasl, JLH, Rizzo
• Each SM chiral fermion has a double KK tower of
fermions associated with it of both helicities
• Introduces new parameter, related to fermion Yukawa
– mfbulk = k, with  ~ O(1)
KK Spectra are related:
Add Fermions in the Bulk
• Zero-mode fermions couple weaker to gauge KK
states than brane fermions
towards Planck brane
towards TeV brane
Precision EW Constraints
Schematic of Wavefunctions
Can reproduce
Fermion mass
hierarchy
Planck brane
TeV brane
Collider Signals are more difficult
KK states must couple to gauge fields or top-quark to
be produced at observable rates
gg  Gn  ZZ
Agashe, Davoudiasl, Perez, Soni hep-ph/0701186
gg  gn  tt
Lillie, Randall, Wang, hep-ph/0701164
The Hierarchy Problem: Higgsless
Energy (GeV)
Planck
GUT
desert
1019
1016
Future
Collider
Energies
Warped Extra Dimensions
strong
curvature
10
3
Weak
wk = MPl e-kr
With NO Higgs boson!
All of
known
physics
10-18
Solar System
Gravity
Higgsless EWSB
Csaki, Grojean,Murayama, Pilo,
Terning
What good is a Higgs anyway??
• Generates W,Z Masses
• Generates fermion Masses
• Unitarizes scattering amplitudes (WLWL  WLW L )
Do we really need a Higgs?
And get everything we know right….
Our laboratory: Standard Model in 1 extra warped
dimension
 Minimal Particle Content!
Generating Masses
Consider a massless 5-d field
∂2 = (∂∂ - ∂5∂5 )  = 0
looks like
(∂∂ - mn2 )  = 0 in 4-d
(KK tower)
The curvature of the 5-d wavefunction (y) is related
to its mass in 4-d
Toy Example: Flat space with U(1) gauge field in
bulk with S1/Z2 Orbifold
A(y) ~ cos (ny/R)
A5(y) ~ sin (ny/R)
1st KK
0-mode
0-mode is flat & y independent
0
R
 m0 = 0
If The Same boundary conditions are applied at both boundaries,
0-mode is massless and U(1) remains unbroken
1st KK
Orbifold Boundary Conditions:
∂5A = 0
A5 = 0
0-mode
∂5
A=0
A cannot be flat with these
boundary conditions!
A=0
A(y) ~ n an cos(mny) + bn sin(mny)
∂5A(y) ~ mnn (-an sin(mny) + bn cos(mny)
BC’s:
A(y=0) = 0
 an = 0
∂5A(y=R) = 0  cos(mnR) = 0
mn = (n + ½)/R
The zero mode is massive!
A5 acts as a Goldstone
U(1) is broken
Agashe etal hep-ph/0308036
Csaki etal hep-ph/0308038
Realistic Framework:
SU(2)L x SU(2)R x U(1)B-L in 5-d Warped bulk
Planck
brane
TeV-brane
SU(2)L x SU(2)R
SU(2)R x U(1)B-L
U(1)Y
WR, ZR get Planck
scale masses
SU(2)D
BC’s restricted by variation
of the action at boundary
SU(2) Custodial Symmetry
is preserved!
W, Z get TeV scale masses
 left massless!
Parameters:  = g5R/g5L (restricted range)
L,Y,B,D brane kinetic terms
g5L fixed by GF, g5B/g5L fixed by MZ
Unitarity in Gauge Boson Scattering
•SM without Higgs violates perturbative unitarity in
WLWL  WLWL at s ~ 1.7 TeV
•Higgs restores unitarity if mH < TeV
What do we do without a Higgs??
Exchange gauge
KK towers:
Conditions on KK masses & couplings:
(g1111)2 = k (g11k)2
Csaki etal, hep-ph/0305237
4(g1111)2 M12 = k (g11k)2 Mk2
Necessary, but not sufficient, to guarantee perturbative unitarity!
Production of Gauge KK States @ LHC
gg, qq  g1  dijets
Davoudiasl, JLH, Lilllie, Rizzo
Balyaev, Christensen
What are the preferred gauge KK masses?
Tension Headache:
PUV in WW scattering
Colliders
Important direct
constraints
needs light KK’s
Precision EW
needs heavier KK’s
Is there a consistent region of parameter space?
What are the preferred gauge KK masses?
Tension Headache:
PUV in WW scattering
Colliders
Important direct
constraints
needs light KK’s
Precision EW
needs heavier KK’s
Is there a consistent region of parameter space?
Only if fermions are in the bulk at specific locations
Summary of Extra Dimensions
• Many models of extra dimensions exist!
• Extra dimensions were founded to resolve the
hierarchy, but now stand on their own for
answering many open questions of the Standard
Model
• Extra dimensions which resolve the gauge
hierarchy are testable at the LHC/ILC. These
models can be proved or disproved regarding their
relevance to the hierarchy
• If discovered, collider measurements can reveal
many properties of extra dimensions
• If discovered, our view of the universe will be
forever changed.
The Hierarchy Problem: Little Higgs
Energy (GeV)
Planck
GUT
Little Hierarchies!
desert
1019
1016
Future
Collider
Energies
104
New Physics!
10
Weak
3
Simplest Model:
The Littlest Higgs with
 ~ 10 TeV
No UV completion
All of
known
physics
10-18
Solar System
Gravity
The Hierarchy Problem: Little Higgs
Energy (GeV)
1019
1016
.
.
.
Future
Collider
Energies
Planck
GUT
106
105
104
New Physics!
New Physics!
New Physics!
10
Weak
3
All of
known
physics
10-18
Solar System
Gravity
Stacks of Little
Hierarchies
Simplest Model:
The Littlest Higgs with
1 ~ 10 TeV
2 ~ 100 TeV
3 ~ 1000 TeV
…..
Little Higgs: The Basics
• The Higgs becomes a component of a larger
multiplet of scalars, 
•  transforms non-linearly under a new global
symmetry
• New global symmetry undergoes SSB
 leaves Higgs as goldstone
• Part of global symmetry is gauged
 Higgs is pseudo-goldstone
• Careful gauging removes Higgs 1-loop divergences
 mh2 ~
2
(162)2
,
 > 10 TeV,
@ 2-loops!
Minimal Model: The Littlest Higgs
Arkani-Hamed,
Cohen, Katz, Nelson
 > 10 TeV: non-linear s model is strongly-coupled
 10 TeV:
• Global Symmetry: SU(5)  SO(5) via SSB with 0
(x) = e2i/f 0,  = a a(x)Xa  14 Goldstone Bosons
f ~ /4 = G.B. decay constant ~ TeV
• Gauged Symmetry: G1 x G2
[SU(2) x U(1)]2  SU(2)L x U(1)Y via SSB with 0
WH, ZH, BH acquire mass ~ f
W, W30, B0 remain massless
14 Goldstone Bosons  4 eaten under SSB
complex triplet 
complex doublet h
massless at
tree-level
 Acquires mass at 1-lopp via gauge interactions ~ f
h acquires mass at 2-loops ~ f/4
3-Scale Model
 > 10 TeV: New Strong Dynamics
? UV Completion ?
Global Symmetry
f ~ /4 ~ TeV:
v ~ f/4 ~ 100 GeV:
Sample Spectrum
Symmetires Broken
Pseudo-Goldstone Scalars
New Gauge Fields
New Fermions
Light Higgs
SM vector bosons & fermions
A UV Completion
Kaplan, Schmaltz, Skiba
Keep stacking Little Higgs Theories
• Upstairs Little Higgs: Strongly coupled @  ~ 100 TeV
non-linear s model
symmetry breaks @ F ~ 10 TeV
• Downstairs Little Higgs: Weakly coupled @  ~ 10 TeV
linear s model
symmetry breaks @ f ~ 1 TeV
Summary of Physics Beyond the Standard Model
• There are many ideas for scenarios with new
physics! Most of our thinking has been guided by
the hierarchy problem
• They must obey the symmetries of the SM
• They are testable at the LHC
• We are as ready for the LHC as we will ever be
• The most likely scenario to be discovered at the
LHC is the one we haven’t thought of yet.
Exciting times are about to begin.
Be prepared for the unexpected!!
Fine-tuning does occur in nature
2001 solar eclipse as viewed from Africa
Most Likely Scenario @ LHC:
H. Murayama