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**Non-SUSY Physics Beyond**

the Standard Model J. Hewett, Pre-SUSY 2010

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**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!

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

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**The Standard Model on One Page**

SGauge = d4x FY FY + F F + Fa Fa SFermions = d4x fDf SHiggs = d4x (DH)†(DH) – m2|H|2 + |H|4 SYukawa = d4x YuQucH + YdQdcH† + YeLecH† ( SGravity = d4x g [MPl2 R + CC4] ) Generations f = Q,u,d, L,e The

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**Standard Model predictions well described by data!**

EW measurements agree with SM 2+ loop level Jet production Tevatron agree with QCD Pull

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**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)

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**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

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**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

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**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! - - - - - -

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**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

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**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!

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**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

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**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

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**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

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**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

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**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

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**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

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**The naturalness problem that has had the greatest impact on collider physics is:**

The Higgs (mass)2 problem or The hierarchy problem

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**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

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**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

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**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

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**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)

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**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

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**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

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**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

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High Mass Resonances

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**Z’ Resonance: GUT Models**

LRM E6 GUTS LHC7 Tevatron Bounds Rizzo

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**Extra Dimensions Taxonomy**

Large TeV Small Flat Curved UEDs RS Models GUT Models ADD Models

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**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

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**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

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**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

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**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

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**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.

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**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

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**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

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

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**Masses of KK modes are determined by the interval BC**

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**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

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**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 → → →

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**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 → → →

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**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

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**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!

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**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? …

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**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?

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**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

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**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

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**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

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**Constraints from Cavendish-type exp’ts**

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**Bulk Metric: Linearized Quantum Gravity**

Perform Graviton KK reduction Expand hAB into KK tower SM on 3-brane Set T = AB (ya) Pick a gauge Integrate over dy Interactions of Graviton KK states with SM fields on 3-brane

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**Feyman Rules: Graviton KK Tower**

Massless 0-mode + KK states have indentical coupling to matter Han, Lykken, Zhang; Giudice, Rattazzi, Wells

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Collider Tests

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**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)

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**Graviton Exchange Forward-Backward Asymmetry Drell-Yan Spectrum @ LHC**

MD = 2.5 TeV 4.0 JLH Graviton Exchange

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**Graviton Exchange @ 7 TeV LHC**

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**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):

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**Graviton Emission @ LHC**

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**Graviton Emission @ LHC @ 7 TeV**

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**Detailed LHC/ATLAS MC Study**

The 14 TeV LHC is seen to have considerable search reach for KK Graviton production Hinchliffe, Vacavant

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**Current Bounds on Graviton Emission**

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**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

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**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

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**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!

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**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

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**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

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Interactions Recall = MPlekr ~ TeV

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**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

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**Tevatron limits on RS Gravitons**

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**Summary of Theory & Experimental Constraints**

LHC can cover entire allowed parameter space!!

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**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….

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**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

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**Derivation of Bulk Gauge KK Spectrum**

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**Schematic of Wavefunctions**

Can reproduce Fermion mass hierarchy Planck brane TeV brane

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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

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**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/

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**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 = FnRs2(E), details show this holds up to a factor of a few

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**Blackhole Formation Factor**

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**Potential Corrections to Classical Approximation**

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

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**Production rate is enormous!**

Naïve ~ n for large n 1 per sec at LHC! MD = 1.5 TeV JLH, Lillie, Rizzo

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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

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**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/

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**Grey-body Factors Particle multiplicity in decay: = grey-body factor**

Contain energy & anglular emission information

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**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

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**Black Hole event simulation @ LHC**

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**Cosmic Ray Sensitivity to Black Hole Production**

No suppression Ringwald, Tu Anchordoqui etal

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**Summary of Exp’t Constraints on MD**

Anchordoqui, Feng Goldberg, Shapere

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**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!!

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**Fine-tuning does occur in nature**

2001 solar eclipse as viewed from Africa

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**Most Likely Scenario @ LHC:**

H. Murayama Most Likely LHC:

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