1. Non-SUSY Physics Beyond
the Standard Model
J. Hewett, Pre-SUSY 2010

2. 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!

3. The Standard Model
Brief review of features which guide & restrict BSM physics

4. The Standard Model on One Page
SGauge =  d4x FY FY + F F + Fa Fa
SFermions =  d4x   fDf
SHiggs =  d4x (DH)†(DH) – m2|H|2 + |H|4
SYukawa =  d4x YuQucH + YdQdcH† + YeLecH†
( SGravity =  d4x g [MPl2 R + CC4] )
Generations
f = Q,u,d,
L,e
The

5. Standard Model predictions well described by data!
EW measurements agree with
SM 2+ loop level
Jet production
Tevatron agree with QCD
Pull

6. Global Flavor Symmetries
SM matter secretly has a large symmetry: Q1 u1 d1 L1 e1 .
. 2
. 3
Rotate 45 fermions into each other
U(45)
Explicitly broken by gauging 3x2x1
Rotate among generations
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
Explicitly broken by charged lepton Yukawas
U(1)e x U(1) x U(1)
Explicitly broken by neutrino masses
U(1)B
Baryon Number
Lepton Number
U(1)L (Dirac)
(or nothing) (Majorana)

7. Global Symmetries of Higgs Sector
Four real degrees of freedom
Higgs Doublet:
Secretly transforms as a 1 2 3 4
4 of SO(4)
Decomposes into
subgroups
(2,2) SU(2) x SU(2)
SU(2)L of EW
Left-over Global Symmetry

8. Global Symmetries of Higgs Sector
Four real degrees of freedom
Higgs Doublet:
Secretly transforms as a
Gauging U(1)Y explicitly breaks
Size of this breaking given by Hypercharge coupling g’ 1 2 3 4
SU(2)Global  Nothing
4 of SO(4)
Decomposes into
subgroups
MW g2
=  1 as g’0
MZ g2 + (g’)2
(2,2) SU(2) x SU(2)
New Physics may excessively break SU(2)Global
SU(2)L of EW
Remaining Global Symmetry
Custodial Symmetry

9. Standard Model Fermions are Chiral
Fermions cannot simply ‘pair up’ to form mass terms
i.e., mfLfR is forbidden Try it!
(Quc) /2
(Qdc) /2
(QL) /3
(Qe) /6
(ucdc) x /3
(ucL) /6
(uce) /3
(dcL) /6
(dce) /3
(Le) /2 -
SU(3)C SU(2)L U(1)Y
Fermion masses must be generated by Dimension-4 (Higgs) or higher operators to respect SM gauge invariance! - - - - - -

10. Anomaly Cancellation An anomaly leads to a mass for a gauge boson
Quantum violation of current conservation
An anomaly leads to a mass for a gauge boson

11. Anomaly Cancellation SU(3) 3[ 2‧(1/6) – (2/3) + (1/3)] = 0 U(1)Y
SU(2)L
U(1)Y
g
3[ 2‧(1/6) – (2/3) + (1/3)] = 0
Q uc dc
U(1)Y
3[3‧(1/6) – (1/2)] = 0
Q L
3[ 6‧(1/6)3 + 3‧(-2/3)3 + 3‧(1/3)3
+ 2‧(-1/2)3 + 13] = 0
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!

12. Symmetries of the Standard Model: Summary
Gauge Symmetry
Flavor Symmetry
Custodial Symmetry
Chiral Fermions
Gauge Anomalies
SU(3)C x SU(2)L x U(1)Y
Exact
Broken to U(1)QED
U(3)5  U(1)B x U(1)L (?)
Explicitly broken by Yukawas
SU(2)Custodial of Higgs sector
Broken by hypercharge so  = 1
Need Higgs or Higher order operators
Restrict quantum numbers of new fermions

13. Symmetries of the Standard Model: Summary
Gauge Symmetry
Flavor Symmetry
Custodial Symmetry
Chiral Fermions
Gauge Anomalies
SU(3)C x SU(2)L x U(1)Y
Exact
Broken to U(1)QED
U(3)5  U(1)B x U(1)L (?)
Explicitly broken by Yukawas
SU(2)Custodial of Higgs sector
Broken by hypercharge so  = 1
Need Higgs or Higher order operators
Restrict quantum numbers of new fermions
Any model with New Physics must respect these symmetries

14. 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 

15. Constraints on Higher Dimensional Operators
Baryon Number Violation
Λ ≳ 1016 GeV
Lepton Number Violation
Λ ≳ 1015 GeV
Flavor Violation
Λ ≳ 106 GeV
CP Violation
Λ ≳ 106 GeV
Precision Electroweak
Λ ≳ 103 GeV
Contact Operators
Λ ≳ 103 GeV
Generic Operators
Λ ≳ 3x102 GeV

16. What sets the cutoff scale  ? What is the theory above the cutoff?
New Physics, Beyond the Standard Model!
Three paradigms:
SM parameters are unnatural
New physics introduced to “Naturalize”
SM gauge/matter content complicated
New physics introduced to simplify
Deviation from SM observed in experiment
 New physics introduced to explain

17. 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

18. The naturalness problem that has had the greatest impact on collider physics is:
The Higgs (mass)2 problem or
The hierarchy problem

19. The Hierarchy Energy (GeV) 1019 Planck 1016 GUT desert 103 Weak
Future Collider Energies
103
Weak
All of known physics
Solar System
Gravity
10-18

20. The Hierarchy Problem Energy (GeV) 1019 Planck Quantum Corrections:
Virtual Effects drag
Weak Scale to MPl
1016
GUT
desert
Future Collider Energies
mH2 ~
~ MPl2
103
Weak
All of known physics
Solar System
Gravity
10-18

21. A Cellar of New Ideas ’67 The Standard Model ’77 Vin de Technicolor
a classic!
aged to perfection
’ The Standard Model
’ Vin de Technicolor
’70’s Supersymmetry: MSSM
’90’s SUSY Beyond MSSM
’90’s CP Violating Higgs
’ Extra Dimensions
’ Little Higgs
’ Fat Higgs
’ Higgsless
’ Split Supersymmetry
’ Twin Higgs
better drink now
mature, balanced, well
developed - the Wino’s choice
svinters blend
all upfront, no finish
lacks symmetry
bold, peppery, spicy
uncertain terrior
complex structure
young, still tannic
needs to develop
sleeper of the vintage
what a surprise!
finely-tuned
double the taste
J. Hewett

22. 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)

23. 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
Most cases controlled by
Parton flux
Solid: TeV vs Tevatron
Dashed: 10 TeV vs Tevatron
Bauer etal

24. 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
Most cases controlled by
Parton flux
Naive, but a reasonable guide
Solid: TeV vs Tevatron
Dashed: 10 TeV vs Tevatron
Bauer etal

25. QCD Pair Production Reach @ LHC7- -
gg,qq → QQ
Assumes 100% reconstruction efficiencies
No background
Current Tevatron bound
On 4th generation T’ quark:
~ 335 GeV (4.6 fb-1)
Tevatron
exclusion
LHC7 should cover entire
4th generation expected
region!
Bauer etal

26. High Mass Resonances

27. Z’ Resonance: GUT Models
LRM
E6 GUTS
LHC7
Tevatron Bounds
Rizzo

28. Extra Dimensions Taxonomy
Large
TeV
Small
Flat
Curved
UEDs
RS Models
GUT Models
ADD Models

29. 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

30. 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

31. 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

32. 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

33. 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.

36. Kaluza-Klein tower of particles
E2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc2)2
In 4 dimensions, looks like a mass!
Recall pextra = n/R
Tower of massive particles
Small radius
Large radius

37. Kaluza-Klein tower of particles
E2 = (pxc)2 + (pyc)2 + (pzc)2 + (pextrac)2 + (mc2)2
In 4 dimensions, looks like a mass!
Recall pextra = n/R
Tower of massive particles
Small radius gives well separated Kaluza-Klein particles
Large radius gives finely separated Kaluza-Klein particles
Small radius
Large radius

38. Action Approach: Consider a real, massless scalar in flat 5-d

39. Masses of KK modes are determined by the interval BC

40. 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

41. Higher Dimensional Field Decomposition
As we saw, 5d scalar becomes a 4d tower of scalars
Recall: Lorentz (4d) ↔ Rotations (3d)
scalar scalar
4-vector Aμ A, Φ
tensor Fμν E, B
5d: d ↔ d
scalar (scalar)n
vector AM (Aμ, A5)n
tensor hMN (hμν, hμ5, h55)n
KK towers → → →

42. Higher Dimensional Field Decomposition
As we saw, 5d scalar becomes a 4d tower of scalars
Recall: Lorentz (4d) ↔ Rotations (3d)
scalar scalar
4-vector Aμ A, Φ
tensor Fμν E, B
(4+δ)d: (4+δ)d ↔ d (i=1…δ)
scalar (δ scalars)n
vector AM (Aμ, Ai)ni
tensor hMN (hμν, hμi, hij)n
KK towers
1 tensor, δ 4-vectors, ½ δ(δ+1) scalars → → →

43. 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

44. 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!

45. 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? …

46. 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?

47. Searches for extra dimensions
Three ways we hope to see extra dimensions:
Modifications of gravity at short distances
Effects of Kaluza-Klein particles on astrophysical/cosmological processes
Observation of Kaluza-Klein particles in high energy accelerators

48. The Hierarchy Problem: Extra Dimensions
Energy (GeV)
1019
Planck
Simplest Model:
Large Extra Dimensions
1016
GUT
desert
Future Collider Energies
103
Weak – Quantum Gravity
= Fundamental scale in
4 +  dimensions
MPl2 = (Volume) MD2+
Gravity propagates in
D =  dimensions
All of known physics
Solar System
Gravity
10-18

49. 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
LArg

50. Constraints from Cavendish-type exp’ts

51. 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

52. Feyman Rules: Graviton KK Tower
Massless 0-mode + KK states have indentical coupling to matter
Han, Lykken, Zhang; Giudice, Rattazzi, Wells

53. Collider Tests

54. 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)

56. Graviton Exchange Forward-Backward Asymmetry Drell-Yan Spectrum @ LHC
MD = 2.5 TeV
4.0
JLH
Graviton Exchange

57. Graviton Exchange @ 7 TeV LHC

59. Graviton Tower Emission
Giudice, Ratazzi,Wells
Mirabelli,Perelstein,Peskin
e+e-  /Z + Gn Gn appears as missing energy
qq  g + Gn Model independent – Probes MD
directly
Z  ff + Gn Sensitive to 
Parameterized by density of states: - -
Discovery reach for MD (TeV):

60. Graviton Emission @ LHC

61. Graviton Emission @ LHC @ 7 TeV

62. Detailed LHC/ATLAS MC Study
The 14 TeV LHC is seen
to have considerable search
reach for KK Graviton
production
Hinchliffe, Vacavant

63. Current Bounds on Graviton Emission

65. 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

66. The Hierarchy Problem: Extra Dimensions
Energy (GeV)
1019
Planck
Model II:
Warped Extra Dimensions
1016
GUT
strong curvature
desert
Future Collider Energies
103
Weak
wk = MPl e-kr
All of known physics
Solar System
Gravity
10-18

67. 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!

68. 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

69. 4-d Effective Theory Phenomenology governed by two parameters:
Davoudiasl, JLH, Rizzo
Phenomenology governed by two parameters:
 ~ TeV
k/MPl ≲ 0.1
5-d curvature:
|R5| = 20k2 < M52

70. Interactions
Recall  = MPlekr ~ TeV

72. Randall-Sundrum Graviton KK spectrum
Davoudiasl, JLH, Rizzo
Unequal spacing signals curved space
e+e- →μ+μ-
e+e- +-
LHC
pp → l+l-
Different curves for k/MPl =0.01 – 1.0

73. Tevatron limits on RS Gravitons

74. Summary of Theory & Experimental Constraints
LHC can cover entire allowed parameter space!!

75. 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….

76. 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

77. Derivation of Bulk Gauge KK Spectrum

78. Schematic of Wavefunctions
Can reproduce
Fermion mass
hierarchy
Planck brane
TeV brane

79. 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

80. Collider Signals are more difficult
KK states must couple to gauge fields or top-quark to
be produced at observable rates -
gg  Gn  ZZ
gg  gn  tt
Agashe, Davoudiasl, Perez, Soni hep-ph/
Lillie, Randall, Wang, hep-ph/

81. Black Hole Production @ LHC:
Dimopoulos, Landsberg
Giddings, Thomas
Black Holes produced when s > MD
Classical Approximation: [space curvature << E]
E/2
b < Rs(E)  BH forms b
E/2 ^
MBH ~ s
Geometric Considerations:
Naïve = FnRs2(E), details show this holds up to a
factor of a few

82. Blackhole Formation Factor

83. Potential Corrections to Classical Approximation
Distortions from
finite Rc as Rs  Rc
2. Quantum Gravity Effects
Higher curvature term
corrections
RS2/(2Rc)2
n =
Critical point for
instabilities for n=5:
(Rs/Rc)2 ~ @ LHC
n =
Gauss-Bonnet term
n2 ≤ 1 in string models

84. Production rate is enormous!
Naïve ~ n for large n
1 per sec at LHC!
MD = 1.5 TeV
JLH, Lillie, Rizzo

85. 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
Spin

86. 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/

87. Grey-body Factors Particle multiplicity in decay:  = grey-body factor
Contain energy & anglular emission information

90. 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

92. Black Hole event simulation @ LHC

93. Cosmic Ray Sensitivity to Black Hole Production
No suppression
Ringwald, Tu
Anchordoqui etal

94. Summary of Exp’t Constraints on MD
Anchordoqui, Feng
Goldberg, Shapere

95. 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!!

96. Fine-tuning does occur in nature
2001 solar eclipse as viewed from Africa

97. Most Likely Scenario @ LHC:
H. Murayama
Most Likely LHC: