Non-SUSY Physics Beyond
the Standard Model
J. Hewett, Pre-SUSY 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!
The Standard Model
Brief review of features which guide & restrict BSM
physics
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]
)
Standard Model predictions well described by data!
EW measurements agree with
SM predictions @ 2+ loop level
Pull
Jet production rates @
Tevatron agree with QCD
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
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!
Symmetries of the 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
Symmetries of the 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
SM is valid
Particle masses
All interactions consistent with gauge symmetries
are permitted, including higher dimensional
operators whose mass dimension is compensated
by powers of 
Constraints on Higher Dimensional Operators
Baryon Number Violation
Λ ≳ 1016 GeV
Lepton Number Violation
Λ ≳ 1015 GeV
Flavor Violation
CP Violation
Precision Electroweak
Λ ≳ 106 GeV
Λ ≳ 106 GeV
Λ ≳ 103 GeV
Contact Operators
Λ ≳ 103 GeV
Generic Operators
Λ ≳ 3x102 GeV
• 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
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
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)
New Physics @ LHC7
Supermodel Discovery
Criteria:
• Large σLHC giving ≥ 10
events at ℒ = 10 pb-1
• Small σTevatron giving ≤ 10
events with ℒ = 10 fb-1
• Large BF to easy to detect
final state
• Consistency with other
bounds
Bauer etal 0909.5213
Most cases controlled by
Parton flux
Solid:
7 TeV vs Tevatron
Dashed: 10 TeV vs Tevatron
New Physics @ LHC7
Supermodel Discovery
Criteria:
• Large σLHC giving ≥ 10
events at ℒ = 10 pb-1
• Small σTevatron giving ≤ 10
events with ℒ = 10 fb-1
• Large BF to easy to detect
final state
• Consistency with other
bounds
Naive, but a reasonable guide
Bauer etal 0909.5213
Most cases controlled by
Parton flux
Solid:
7 TeV vs Tevatron
Dashed: 10 TeV vs Tevatron
QCD Pair Production Reach @ LHC7
•gg,qq → QQ
•Assumes 100%
reconstruction efficiencies
•No background
Tevatron
exclusion
Bauer etal 0909.5213
Current Tevatron bound
On 4th generation T’ quark:
~ 335 GeV (4.6 fb-1)
LHC7 should cover entire
4th generation expected
region!
High Mass Resonances
Z’ Resonance: GUT Models
E6 GUTS
LRM
LHC7
Tevatron Bounds
Rizzo
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 infinite, 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, 5d scalar becomes a 4d tower of scalars
• Recall:
4-vector
tensor
• 5d:
Lorentz (4d)
scalar
Aμ
Fμν
5d
scalar
vector AM
tensor hMN
↔
↔
Rotations (3d)
scalar
→
A, Φ
→ →
E, B
4d
(scalar)n
(Aμ, A5)n
(hμν, hμ5, h55)n
KK towers
Higher Dimensional Field Decomposition
• As we saw, 5d scalar becomes a 4d tower of scalars
• Recall:
4-vector
tensor
• (4+δ)d:
Lorentz (4d)
scalar
Aμ
Fμν
(4+δ)d
scalar
vector AM
tensor hMN
↔
↔
Rotations (3d)
scalar
→
A, Φ
→ →
E, B
4d (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
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
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
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
Summary of Theory & Experimental Constraints
LHC can cover entire allowed parameter space!!
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
Schematic of Wavefunctions
Can reproduce
Fermion mass
hierarchy
Planck brane
TeV brane
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
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
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:
Naïve = 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!
Naïve ~ n for large n
1 per sec at LHC!
MD = 1.5 TeV
JLH, Lillie, Rizzo
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
Cosmic Ray Sensitivity to Black Hole Production
No suppression
Ringwald, Tu
Anchordoqui etal
Summary of Exp’t Constraints on MD
Anchordoqui, Feng
Goldberg, Shapere
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