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A summer school lecture at the SLAC summer Institute in 2009 on "New Physics Scenarios".

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- 1. New Physics Scenarios Jay Wacker SLAC SLAC Summer Institute August 5&6, 2009
- 2. Any minute now!When’s the revolution? An unprecedented moment
- 3. What is a “New Physics Scenario”? “New Physics”: A structural change to the Standard Model Lagrangian “Scenario”: “A sequence of events especially when imagined”
- 4. Why New Physics? Four Paradigms
- 5. Why New Physics? Four Paradigms Experiment doesn’t match theoretical predictions Best motivation
- 6. Why New Physics? Four Paradigms Experiment doesn’t match theoretical predictions Best motivation Parameters are “Unnatural” Well defined and have good theoretical motivation
- 7. Why New Physics? Four Paradigms Experiment doesn’t match theoretical predictions Best motivation Parameters are “Unnatural” Well defined and have good theoretical motivation Reduce/Explain the multitude of parameters Typically has limited success, frequently untestable
- 8. Why New Physics? Four Paradigms Experiment doesn’t match theoretical predictions Best motivation Parameters are “Unnatural” Well defined and have good theoretical motivation Reduce/Explain the multitude of parameters Typically has limited success, frequently untestable To know what is possible Let’s us know what we can look for in experiments Limited only by creativity and taste
- 9. The Plan Beyond the SM Physics is 30+ years old There is no one leading candidate for new physics New physics models draw upon all corners of the SM In 2 hours there will be a sketch some principles used in a half dozen paradigms that created hundreds of models and spawned thousands of papers
- 10. Outline The Standard Model Motivation for Physics Beyond the SM Organizing Principles for New Physics New Physics Scenarios Supersymmetry Extra Dimensions Strong Dynamics
- 11. Standard Model: a story of economy symmetry unification→ 15 Particles, 12 Force carriers ↔ 2700 ¯ψV ψ Couplings
- 12. Standard Model: a story of economy νe L eL eR uL uR dRdLuLuL uRuR dL dL dR dR symmetry unification→ 15 Particles, 12 Force carriers ↔ 2700 ¯ψV ψ Couplings
- 13. Standard Model: a story of economy νe L eL eR uL uR dRdLuLuL uRuR dL dL dR dR e q u d 5 Particles 3 Couplings symmetry unification→ 15 Particles, 12 Force carriers ↔ 2700 ¯ψV ψ Couplings
- 14. Standard Model: a story of economy νe L eL eR uL uR dRdLuLuL uRuR dL dL dR dR e q u d 5 Particles 3 Couplings symmetry unification→ 4 forces, 20 particles, 20 parameters x 3 Mystery of Generations: 15 Particles, 12 Force carriers ↔ 2700 ¯ψV ψ Couplings
- 15. The Standard Model ... where we stand today LSM = LGauge + LFermion + LHiggs + LYukawa
- 16. The Standard Model ... where we stand today LSM = LGauge + LFermion + LHiggs + LYukawa LGauge = − 1 4 Bµν 2 − 1 4 Wa µν 2 − 1 4 GA µν 2
- 17. The Standard Model ... where we stand today LSM = LGauge + LFermion + LHiggs + LYukawa LGauge = − 1 4 Bµν 2 − 1 4 Wa µν 2 − 1 4 GA µν 2 LFermion = ¯QiiD Qi + ¯Uc i iD Uc i + ¯Dc i iD Dc i + ¯LiiD Li + ¯Ec i iD Ec i
- 18. The Standard Model ... where we stand today LSM = LGauge + LFermion + LHiggs + LYukawa LGauge = − 1 4 Bµν 2 − 1 4 Wa µν 2 − 1 4 GA µν 2 LFermion = ¯QiiD Qi + ¯Uc i iD Uc i + ¯Dc i iD Dc i + ¯LiiD Li + ¯Ec i iD Ec i LHiggs = |DµH|2 − λ(|H|2 − v2 /2)2
- 19. The Standard Model ... where we stand today LSM = LGauge + LFermion + LHiggs + LYukawa LGauge = − 1 4 Bµν 2 − 1 4 Wa µν 2 − 1 4 GA µν 2 LFermion = ¯QiiD Qi + ¯Uc i iD Uc i + ¯Dc i iD Dc i + ¯LiiD Li + ¯Ec i iD Ec i LHiggs = |DµH|2 − λ(|H|2 − v2 /2)2 LYuk = yij u QiUc j H + yij d QiDc jH∗ + yij e LiEc j H∗
- 20. Q Uc Dc Ec L 3 ¯3 ¯3 1 1 1 1 1 2 2 + 1 6 − 2 3 + 1 3 − 1 2 +1 Field Color Weak Hypercharge Standard Model Charges
- 21. Motivations for Physics Beyond the Standard Model The Hierarchy Problem Dark Matter Exploration
- 22. The Hierarchy Problem The SM suffers from a stability crisis −µ2 − 3y2 t Λ2 t 16π2 + 3 4 g2 Λ2 W 16π2 + 1 4 g 2 Λ2 B 16π2 + λΛ2 H 16π2 Higgs vev determined by effective mass, not bare mass Many contributions that must add up to -(100 GeV)2 =
- 23. A recasting of the problem: Why is gravity so weak? GN GF = 10−32 Explain how to make GF large (i.e. v small) Explain why GN is so small (i.e. MPl large)
- 24. 1998: Large Extra Dimensions (Arkani-Hamed, Dimopoulos, Dvali) High scale is a “mirage” Gravity is strong at the weak scale Need to explain how gravity is weakened MPlanckMWeak α 2001: Universal Extra Dimensions (Appelquist, Cheng, Dobrescu)
- 25. 1978: Technicolor (Weinberg, Susskind) 1999: Warped Gravity (Randall, Sundrum) 2001: Little Higgs (Arkani-Hamed, Cohen, Georgi) The Higgs is composite h Resolve substructure at small distances αM2 Composite Why hadrons are lighter than Planck Scale
- 26. A New Symmetry µ2 = 0 not specialUV dynamics at
- 27. A New Symmetry Scalar Fermion φ ψ Supersymmetry φ → ψ Scalar Mass related to Fermion Mass µ2 = 0 not specialUV dynamics at
- 28. A New Symmetry Scalar Fermion φ ψ Supersymmetry φ → ψ Scalar Mass related to Fermion Mass φ Scalar Scalar φ Shift Symmetry φ → φ + Scalar Mass forbidden µ2 = 0 not specialUV dynamics at
- 29. A New Symmetry Scalar Fermion φ ψ Supersymmetry φ → ψ Scalar Mass related to Fermion Mass φ Scalar Scalar φ Shift Symmetry φ → φ + Scalar Mass forbidden 1981: Supersymmetric Standard Model (Dimopoulos, Georgi) 2001: Little Higgs (Arkani-Hamed, Cohen, Georgi) 1974: Higgs as Goldstone Boson (Georgi, Pais) µ2 = 0 not specialUV dynamics at
- 30. Dark Matter 85% of the mass of the Universe is not described by the SM There must be physics beyond the Standard Model Cold dark matter Electrically & Color Neutral Cold/Slow Relatively small self interactions Interacts very little with SM particles No SM particle fits the bill
- 31. The WIMP Miracle DM was in equilibrium with SM in the Early Universe 1 3 10 30 100 300 1000 −20 −15 −10 −5 0 logY(x)/Y(x=0) x ≡ m/T σAnnv Increasing
- 32. The WIMP Miracle DM was in equilibrium with SM in the Early Universe T mDM 1 3 10 30 100 300 1000 −20 −15 −10 −5 0 logY(x)/Y(x=0) x ≡ m/T σAnnv Increasing
- 33. The WIMP Miracle DM was in equilibrium with SM in the Early Universe T mDM T ∼ mDM Reverse process energetically disfavored 1 3 10 30 100 300 1000 −20 −15 −10 −5 0 logY(x)/Y(x=0) x ≡ m/T σAnnv Increasing
- 34. The WIMP Miracle DM was in equilibrium with SM in the Early Universe T mDM T ∼ mDM Reverse process energetically disfavored 1 3 10 30 100 300 1000 −20 −15 −10 −5 0 logY(x)/Y(x=0) x ≡ m/T σAnnv Increasing
- 35. The WIMP Miracle DM was in equilibrium with SM in the Early Universe T mDM T mDM DM too dilute to find each other T ∼ mDM Reverse process energetically disfavored 1 3 10 30 100 300 1000 −20 −15 −10 −5 0 logY(x)/Y(x=0) x ≡ m/T σAnnv Increasing
- 36. The WIMP Miracle DM was in equilibrium with SM in the Early Universe T mDM T mDM DM too dilute to find each other T ∼ mDM Reverse process energetically disfavored Relic density is “frozen in” 1 3 10 30 100 300 1000 −20 −15 −10 −5 0 logY(x)/Y(x=0) x ≡ m/T σAnnv Increasing
- 37. Boltzmann Equation Solves for ξ = ρDM/ρbaryon 6 Frozen out when nDM σv ∼ HΓann =
- 38. Boltzmann Equation Solves for ξ = ρDM/ρbaryon 6 Frozen out when nDM σv ∼ HΓann = H T2 /MPl nDM = ξ mp mDM ηs s ∼ T3 TFO ∼ mDM
- 39. Boltzmann Equation Solves for ξ = ρDM/ρbaryon 6 σv = 1 ξmpMPlη 3 × 10−26 cm3 /s Frozen out when nDM σv ∼ HΓann = H T2 /MPl nDM = ξ mp mDM ηs s ∼ T3 TFO ∼ mDM
- 40. Boltzmann Equation Solves for ξ = ρDM/ρbaryon 6 σv = 1 ξmpMPlη 3 × 10−26 cm3 /s Frozen out when mDM ∼ α × 20 TeVσ α2 m2 DM =⇒ nDM σv ∼ HΓann = H T2 /MPl nDM = ξ mp mDM ηs s ∼ T3 TFO ∼ mDM
- 41. We want to see what’s there! Muon, Strange particles, Tau lepton not predicted before discovery Serendipity favors the prepared! Exploration
- 42. Chirality Anomaly Cancellation Flavor Symmetries Gauge Coupling Unification Effective Field Theory Organizing Principles for going beyond the SM
- 43. Chirality A symmetry acting a fermions that forbids masses Ψ = f ¯fc M ¯ΨΨ = M(ffc + ¯f ¯fc )
- 44. Chirality A symmetry acting a fermions that forbids masses Ψ = f ¯fc M ¯ΨΨ = M(ffc + ¯f ¯fc ) f → eiα f fc → eiαc fc Can do independent phase rotations
- 45. Chirality A symmetry acting a fermions that forbids masses Ψ = f ¯fc M ¯ΨΨ = M(ffc + ¯f ¯fc ) α = −αc Vector symmetry Allows mass Jµ V = ¯Ψγµ Ψ f → eiα f fc → eiαc fc Can do independent phase rotations
- 46. Chirality A symmetry acting a fermions that forbids masses Ψ = f ¯fc M ¯ΨΨ = M(ffc + ¯f ¯fc ) α = −αc Vector symmetry Allows mass Jµ V = ¯Ψγµ Ψ α = αc Axial symmetry Forbids mass Jµ A = ¯Ψγ5γµ Ψ f → eiα f fc → eiαc fc Can do independent phase rotations
- 47. The Standard Model is a Gauged Chiral Theory All masses are forbidden by a gauge symmetry 15 different bilinears all forbidden QUc ∼ (1, 2)− 1 2 QEc ∼ (3, 2)7 6 Dc Ec ∼ (¯3, 1)4 3 Uc L ∼ (¯3, 2)− 5 3 Ec Ec ∼ (1, 1)+2 LL ∼ (1, 1)−1 QQ ∼ (¯3, 3)1 3 Dc Dc ∼ (3, 1)2 3 Dc L ∼ (3, 2)− 1 6 etc... The Standard Model force carriers forbid fermion masses
- 48. Electroweak Symmetry Breaking Breaking of Chiral Symmetry SU(2)L × U(1)Y → U(1)EMH ∼ 0 v V (H) = λ|H|4 − µ2 |H|2 LYuk = yij u QiUc j H + yij d QiDc jH∗ + yij e LiEc j H∗ Q = U D L = ν E LYuk = mij u UiUc j + mij d DiDc j + mij e EiEc j Fermions pick up Dirac Masses
- 49. Effective Field Theory Take a theory with light and heavy particles LFull = Llight(ψ) + Lheavy(Ψ, ψ) If we only can ask questions in the range √ s Λcut oﬀ < ∼ MΨ Λcut oﬀ √ s mψ MΨ
- 50. Effective Field Theory Take a theory with light and heavy particles LFull = Llight(ψ) + Lheavy(Ψ, ψ) If we only can ask questions in the range √ s Λcut oﬀ < ∼ MΨ Λcut oﬀ √ s mψ MΨ with n > 0 Dynamics of light fields described by Lfull(ψ) = Llight(ψ) + δL(ψ) δL ∼ O(ψ)/Λn cut oﬀ Only contribute as δσ ∼ √ s Λcut oﬀ n known as “irrelevant operators” Nonrenomalizable
- 51. We have only tested the SM to certain precision How do we know that there aren’t those effects? We know the SM isn’t the final theory of nature We should view any theory we test as an “Effective Theory” that describes the dynamics Shouldn’t be constrained by renormalizability One way of looking for new physics is by looking for these nonrenormalizable operators
- 52. Limits on Non-Renormalizable Operators
- 53. Limits on Non-Renormalizable Operators Baryon Number Violation QQQL/Λ2 Λ > ∼ 1016 GeV
- 54. Limits on Non-Renormalizable Operators Baryon Number Violation QQQL/Λ2 Λ > ∼ 1016 GeV Lepton Number Violation (LH)2 /Λ Λ 1015 GeV
- 55. Limits on Non-Renormalizable Operators Baryon Number Violation QQQL/Λ2 Λ > ∼ 1016 GeV Lepton Number Violation (LH)2 /Λ Λ 1015 GeV Flavor Violation H† (L2σµν Ec 1)Bµν/Λ2¯Dc 1 ¯Dc 1Dc 2Dc 2/Λ2 Λ > ∼ 106 GeV Λ > ∼ 106 GeV
- 56. Limits on Non-Renormalizable Operators Baryon Number Violation QQQL/Λ2 Λ > ∼ 1016 GeV Lepton Number Violation (LH)2 /Λ Λ 1015 GeV Flavor Violation H† (L2σµν Ec 1)Bµν/Λ2¯Dc 1 ¯Dc 1Dc 2Dc 2/Λ2 Λ > ∼ 106 GeV Λ > ∼ 106 GeV CP Violation iH† (L1σµν Ec 1)Bµν/Λ2 Λ > ∼ 106 GeV
- 57. Limits on Non-Renormalizable Operators Baryon Number Violation QQQL/Λ2 Λ > ∼ 1016 GeV Lepton Number Violation (LH)2 /Λ Λ 1015 GeV Flavor Violation H† (L2σµν Ec 1)Bµν/Λ2¯Dc 1 ¯Dc 1Dc 2Dc 2/Λ2 Λ > ∼ 106 GeV Λ > ∼ 106 GeV CP Violation iH† (L1σµν Ec 1)Bµν/Λ2 Λ > ∼ 106 GeV Precision Electroweak |H† DµH|2 /Λ2 Λ > ∼ 3 × 103 GeV
- 58. Limits on Non-Renormalizable Operators Baryon Number Violation QQQL/Λ2 Λ > ∼ 1016 GeV Lepton Number Violation (LH)2 /Λ Λ 1015 GeV Flavor Violation H† (L2σµν Ec 1)Bµν/Λ2¯Dc 1 ¯Dc 1Dc 2Dc 2/Λ2 Λ > ∼ 106 GeV Λ > ∼ 106 GeV CP Violation iH† (L1σµν Ec 1)Bµν/Λ2 Λ > ∼ 106 GeV Precision Electroweak |H† DµH|2 /Λ2 Λ > ∼ 3 × 103 GeV Contact Operators (¯L1L1)2 /Λ2 Λ > ∼ 3 × 103 GeV
- 59. Limits on Non-Renormalizable Operators Baryon Number Violation QQQL/Λ2 Λ > ∼ 1016 GeV Lepton Number Violation (LH)2 /Λ Λ 1015 GeV Flavor Violation H† (L2σµν Ec 1)Bµν/Λ2¯Dc 1 ¯Dc 1Dc 2Dc 2/Λ2 Λ > ∼ 106 GeV Λ > ∼ 106 GeV CP Violation iH† (L1σµν Ec 1)Bµν/Λ2 Λ > ∼ 106 GeV Precision Electroweak |H† DµH|2 /Λ2 Λ > ∼ 3 × 103 GeV Contact Operators (¯L1L1)2 /Λ2 Λ > ∼ 3 × 103 GeV Generic Operators GµνGνσ Gµ σ/Λ2 Λ > ∼ 3 × 102 GeV
- 60. Flavor Symmetries Symmetries that interchange fermions Turn off all the interactions of the SM = Free Theory L = ¯ψi i∂ ψi ψi → Uj i ψj U(N) symmetry
- 61. Flavor Symmetries Symmetries that interchange fermions Turn off all the interactions of the SM = Free Theory Q, Uc , Dc , L, Ec = 15 Fermions/Generation 45 Total fermions that look the same in the free theory global symmetry⇒ U(45) L = ¯ψi i∂ ψi ψi → Uj i ψj U(N) symmetry
- 62. Flavor Symmetries Symmetries that interchange fermions Turn off all the interactions of the SM = Free Theory Q, Uc , Dc , L, Ec = 15 Fermions/Generation 45 Total fermions that look the same in the free theory global symmetry⇒ U(45) Gauge interactions destroy most of this symmetry U(3)5 = U(3)Q × U(3)Uc × U(3)Dc × U(3)L × U(3)Ec Yukawa couplings break the rest... but they are the only source of U(3)5 breaking L = ¯ψi i∂ ψi ψi → Uj i ψj U(N) symmetry
- 63. Prevents Flavor Changing Neutral Currents Imagine two scalars with two sources of flavor breaking LYuk = yij Hψiψc j + κij φψiψc j H = v + h mij = yij v
- 64. Prevents Flavor Changing Neutral Currents Imagine two scalars with two sources of flavor breaking LYuk = yij Hψiψc j + κij φψiψc j H = v + h mij = yij v Can diagonalize mass matrix with unitary transformations ψi → Uj i ψj ψc i → V j i ψc j mij → (UT mV )ij = Miδij LYuk → Miδij ψiψc j (1 + h/v) + (UT κV )ij φψiψj
- 65. Prevents Flavor Changing Neutral Currents Imagine two scalars with two sources of flavor breaking LYuk = yij Hψiψc j + κij φψiψc j H = v + h mij = yij v Higgs doesn’t change flavor, but other scalar field is a disaster K0 ¯K0 d s ¯s¯d φ κ ∝ yUnless mφ κ > ∼ 100 TeVor Can diagonalize mass matrix with unitary transformations ψi → Uj i ψj ψc i → V j i ψc j mij → (UT mV )ij = Miδij LYuk → Miδij ψiψc j (1 + h/v) + (UT κV )ij φψiψj
- 66. Anomaly Cancellation Quantum violation of current conservation ∂µ Ja µ ∝ Tr Ta Tb Tc (Fb ˜Fc ) Ta Tb Tc ψ An anomaly leads to a mass for a gauge boson m2 = g2 16π2 3 Λ2
- 67. Anomaly cancellation: One easy way: only vector-like gauge couplings ψ, ψc (+1)3 + (−1)3 = 0
- 68. Anomaly cancellation: but the Standard Model is chiral One easy way: only vector-like gauge couplings ψ, ψc (+1)3 + (−1)3 = 0
- 69. Anomaly cancellation: but the Standard Model is chiral One easy way: only vector-like gauge couplings ψ, ψc (+1)3 + (−1)3 = 0 SU(3) SU(3) SU(3) U(1) U(1) U(1) U(1) SU(3) SU(3) 6 1 6 3 + 3 − 2 3 3 + 3 1 3 3 + 2 − 1 2 3 + (1) 3 = 0 2(1)3 + (−1)3 + (−1)3 + 0 + 0 = 0 2 1 6 + − 2 3 + 1 3 + 0 + 0 = 0 Q Uc Dc L Ec It works, but is a big constraint!
- 70. Gauge coupling unification: Our Microscope α−1 E 103 106 109 1012 1015 (GeV) 30 40 20 10 sin2 θw 1 2 3 EGUT d dt α−1 = b0 2π Counts charged matter
- 71. Gauge coupling unification: Our Microscope α−1 E 103 106 109 1012 1015 (GeV) 30 40 20 10 sin2 θw 1 2 3 EGUT α−1 3 (t) = α−1 3 (t∗) + b3 0 2π (t − t∗) α−1 2 (t) = α−1 2 (t∗) + b2 0 2π (t − t∗) α−1 1 (t) = α−1 1 (t∗) + b1 0 2π (t − t∗) d dt α−1 = b0 2π Counts charged matter
- 72. Gauge coupling unification: Our Microscope α−1 E 103 106 109 1012 1015 (GeV) 30 40 20 10 sin2 θw 1 2 3 EGUT α−1 3 (t) = α−1 3 (t∗) + b3 0 2π (t − t∗) α−1 2 (t) = α−1 2 (t∗) + b2 0 2π (t − t∗) α−1 1 (t) = α−1 1 (t∗) + b1 0 2π (t − t∗) d dt α−1 = b0 2π Counts charged matter A32 21 = 0.714 α−1 3 (t) − α−1 2 (t) α−1 2 (t) − α−1 1 (t) = b3 0 − b2 0 b2 0 − b1 0 Weak scale measurement High scale particle content B32 21 = 0.528
- 73. νe L eL eR uL uR dRdLuLuL uRuR dL dL dR dR Grand Unification e q u d SU(3) × SU(2) × U(1) Gauge coupling unification indicates forces arise from single entity
- 74. νe L eL eR uL uR dRdLuLuL uRuR dL dL dR dR Grand Unification e q u d ¯5 10 SU(5) SU(3) × SU(2) × U(1) Gauge coupling unification indicates forces arise from single entity
- 75. νe L eL eR uL uR dRdLuLuL uRuR dL dL dR dR Grand Unification e q u d ¯5 10 SU(5) νe R Ψ SO(10) SU(3) × SU(2) × U(1) Gauge coupling unification indicates forces arise from single entity
- 76. Standard Model Summary The Standard Model is chiral gauge theory It is an effective field theory It is anomaly free & anomaly cancellation restricts new charged particles Making sure that there is no new sources of flavor violation ensures that new theories are not horribly excluded SM Fermions fit into GUT multiplets, but gauge coupling unification doesn’t quite work
- 77. The Scenarios Supersymmetry Little Higgs Theories Extra Dimensions Technicolor
- 78. Supersymmetry Doubles Standard Model particles Q, Uc , Dc , L, Ec ˜Q, ˜Uc, ˜Dc , ˜L, ˜Ec H Hu, Hd ˜Hu, ˜Hd g, W, B ˜g, ˜W, ˜B Dirac pair of Higgsinos GauginosSfermions Squarks, Sleptons Gluino, Wino, Bino Fermions Higgs Gauge (1, 2)1 2 (1, 2)− 1 2 Susy Taxonomy Needed for anomaly cancellation
- 79. Susy Gauge Coupling Unification A32 21 = 0.714 α−1 3 (t) − α−1 2 (t) α−1 2 (t) − α−1 1 (t) = b3 0 − b2 0 b2 0 − b1 0 B32 21 = 4 28 5 = 0.714 Too good! (Two loop beta functions, etc) But significantly better than SM or any other BSM theory Only need to add in particles that contribute to the relative running Gauge Bosons, Gauginos, Higgs & Higgsinos
- 80. SUSY Interactions Rule of thumb: take 2 and flip spins q ¯q ¯q ˜q ˜g g Q Uc ˜Uc ˜H H Q
- 81. 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 Lsoft = Lm2 0 + Lm 1 2 + LA + LB
- 82. 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 Lsoft = Lm2 0 + Lm 1 2 + LA + LB Lm2 0 = m2 ψ i j ˜ψ† i ˜ψj +m2 Hu |Hu|2 + m2 Hd |Hd|2 ψ ∈ Q, Uc , Dc , L, Ec
- 83. 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 Lsoft = Lm2 0 + Lm 1 2 + LA + LB Lm 1 2 = m1 ˜B ˜B + m2 ˜W ˜W + m3˜g˜g Lm2 0 = m2 ψ i j ˜ψ† i ˜ψj +m2 Hu |Hu|2 + m2 Hd |Hd|2 ψ ∈ Q, Uc , Dc , L, Ec
- 84. 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 Lsoft = Lm2 0 + Lm 1 2 + LA + LB Lm 1 2 = m1 ˜B ˜B + m2 ˜W ˜W + m3˜g˜g LA = aij u ˜Qi ˜Uc j Hu + aij d ˜Qi ˜Dc jHd + aij e ˜Li ˜Ec j Hd Lm2 0 = m2 ψ i j ˜ψ† i ˜ψj +m2 Hu |Hu|2 + m2 Hd |Hd|2 ψ ∈ Q, Uc , Dc , L, Ec
- 85. 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 Lsoft = Lm2 0 + Lm 1 2 + LA + LB Lm 1 2 = m1 ˜B ˜B + m2 ˜W ˜W + m3˜g˜g LA = aij u ˜Qi ˜Uc j Hu + aij d ˜Qi ˜Dc jHd + aij e ˜Li ˜Ec j Hd LB = Bµ HuHd Lm2 0 = m2 ψ i j ˜ψ† i ˜ψj +m2 Hu |Hu|2 + m2 Hd |Hd|2 ψ ∈ Q, Uc , Dc , L, Ec
- 86. Problem with Parameterized SUSY Breaking There are over 100 parameters once Supersymmetry no longer constrains interactions Most of these are new flavor violation parameters or CP violating phases Horribly excluded Susy breaking is not generic! m2i j ˜Q† i ˜Qj ˜Qi → ˜Uj i ˜Qj gs ˜g ˜Q† i Qi → gs ˜g ˜Q† i ( ˜U† U)i jQj
- 87. Soft Susy Breaking i.e. Super-GIM mechanism Universality of soft terms d ¯d ¯s s ˜g ˜g ˜d, ˜s,˜b ˜d, ˜s,˜b K0 K 0
- 88. Soft Susy Breaking i.e. Super-GIM mechanism Universality of soft terms d ¯d ¯s s ˜g ˜g ˜d, ˜s,˜b ˜d, ˜s,˜b K0 K 0 Need to be Flavor Universal Couplings A ∝ 11 m2 0 ∝ 11Scalar Masses Trilinear A-Terms Approximate degeneracy of scalars
- 89. Proton Stability New particles new ways to mediate proton decay Dangerous couplings Proton Pion u u u d ˜d ¯u e+ LRPV = λBUc Dc ˜Dc + λLQL ˜Dc Supersymmetric couplings that violate SM symmetries A new symmetry forbids these couplings: (−1)3B+L+2s
- 90. Proton Stability New particles new ways to mediate proton decay Lightest Supersymmetric Particle is stable Dangerous couplings Proton Pion u u u d ˜d ¯u e+ LRPV = λBUc Dc ˜Dc + λLQL ˜Dc Supersymmetric couplings that violate SM symmetries A new symmetry forbids these couplings: (−1)3B+L+2s
- 91. Proton Stability New particles new ways to mediate proton decay Lightest Supersymmetric Particle is stable Dangerous couplings Must be neutral and colorless -- Dark Matter Proton Pion u u u d ˜d ¯u e+ LRPV = λBUc Dc ˜Dc + λLQL ˜Dc Supersymmetric couplings that violate SM symmetries A new symmetry forbids these couplings: (−1)3B+L+2s
- 92. Mediation of Susy Breaking MSSM Primoridal Susy BreakingMediation Susy breaking doesn’t occur inside the MSSM Felt through interactions of intermediate particles Studied to reduce the number of parameters Gauge Mediation Universal “Gravity” Mediation Anomaly Mediation Usually only 4 or 5 parameters... but for phenomenology, these are too restrictive
- 93. The Phenomenological MSSM The set of parameters that are: Not strongly constrained Easily visible at colliders First 2 generation sfermions are degenerate 3rd generation sfermions in independent Gaugino masses are free Independent A-terms proportional to Yukawas Higgs Masses are Free 5 5 3 3 4 20 Total Parameters
- 94. Charginos & Neutralinos The Higgsinos, Winos and Binos ˜Hu ∼ 21 2 → 0, +1 ˜Hd ∼ 2− 1 2 → 0, −1 ˜W ∼ 30 → 0, +1, −1 ˜B ∼ 10 → 0 After EWSB: 2 Charge +1 Dirac Fermions 4 Charge 0 Majorana Fermions L = µ ˜Hu ˜Hd + m2 ˜W ˜W + m1 ˜B ˜B +(H† u ˜Hu + H† d ˜Hd)(g ˜W + g ˜B) All mix together, but typically mixture is small Tend find charginos next to their neutralino brethren Neutralinos are good DM candidates
- 95. Elementary Phenomenology Neutralinos Charginos Sleptons Squarks Gluinos Mass
- 96. Collider signatures q ¯q ˜χ0 ˜χ0 χ0 2 χ+ 1 ˜ ˜ν ν Trileptons+MET: If sleptons are availableNeutralinos Charginos Sleptons Mass 3Leptons+MET
- 97. Collider signatures 9 RESULTS AND LIMITS 13 )2 Chargino Mass (GeV/c 100 110 120 130 140 150 160 170 3l)(pb)! ± 1 "#0 2 "~BR($% 0 0.2 0.4 0.6 0.8 1 1.2 -1 CDF Run II Preliminary, 3.2 fb )2 Chargino Mass (GeV/c LEP 2 direct limit BR$NLO %Theory %1±Expected Limit %2±Expected Limit 95% CL Upper Limit: expected Observed Limit ) > 0µ=0, ( 0 =3, A&=60, tan 0 mSugra M q ¯q ˜χ0 ˜χ0 χ0 2 χ+ 1 ˜ ˜ν ν Trileptons+MET: If sleptons are availableNeutralinos Charginos Sleptons Mass 3Leptons+MET
- 98. Collider signatures Trileptons+MET Without sleptons in the decay chain Neutralinos Charginos Sleptons Mass q ¯q ˜χ0 ˜χ0 χ0 2 χ+ 1 ν W+ Z0 30% leptonic Br of W, 10% leptonic Br of Z 3% Total Branching Rate
- 99. ]2 [GeV/cg~M]2 [GeV/cq~M q~= Mg~M 2 = 460 GeV/cq~M 300 400 500 -2 10 300 400 500 -2 10 200 300 400 500200 300 400 500 FIG. 2: Observed (solid lines) and expected (dashed lines) 95% C.L. upper limits on the inclusive squark and gluino production cross sections as a function of Mq (left) and Mg (right) in diﬀerent regions of the squark-gluino mass plane, compared to NLO mSUGRA predictions (dashed- dotted lines). The shaded bands denote the total uncertainty on the theory. 0 100 200 300 400 500 600 0 100 200 300 400 500 600 no mSUGRA solution LEP UA1 UA2 g~ = M q~ M 0 100 200 300 400 500 600 0 100 200 300 400 500 600 observed limit 95% C.L. expected limit FNAL Run I ) -1 <0 (L=2.0fbµ=5,!=0, tan0A ] 2 [GeV/cg ~M ] 2 [GeV/cq ~M 6 [4] H [5] C a t p i d p f [6] D 0 [7] D ( [8] T [9] T 0 [10] M ( [11] J ( [12] M ( [13] A N [14] F ( [15] B [16] B Collider signatures Gluino Pairs: 4j +MET Squark Pairs: 2j +MET Squark-Gluino Pairs: 3j +MET q ¯q ˜g ˜g q q ¯q ¯q ˜χ0 ˜χ0 ˜q ˜q q q ¯q ¯q ˜χ0 ˜χ0 ˜q ˜q q qq ˜g ¯q g ˜χ0 ˜χ0 ˜q ˜q ˜q mSUGRA Search m3 : m2 : m1 = 6 : 2 : 1
- 100. Away from mSUGRA Gluino Search Out[27]= XX 100 200 300 400 500 0 50 100 150 Gluino Mass GeV BinoMassGeV m˜g ∼ 130 GeVm˜g ∼ 120 GeV ˜g → q¯q ˜B ˜g → q¯q ˜W → q¯q ˜BW
- 101. The Higgs Mass Problem VHiggs = λ|H|4 + µ2 |H|2 m2 h0 = 2λv2 = −2µ2
- 102. The Higgs Mass Problem VHiggs = λ|H|4 + µ2 |H|2 m2 h0 = 2λv2 = −2µ2 mh0 ≤ MZ0λsusy = 1 8 g2 + g 2 cos2 2β Need a susy copy of quartic coupling, only gauge coupling works in MSSM
- 103. The Higgs Mass Problem m2 h0 = 2λv2 = −2µ2 H t ˜t H δλ = 3y4 top 8π2 log mstop mtop mh0 ≤ MZ0λsusy = 1 8 g2 + g 2 cos2 2β Need a susy copy of quartic coupling, only gauge coupling works in MSSM
- 104. The Higgs Mass Problem δµ2 = − 3y2 top 8π2 m2 stop H t ˜t H m2 h0 = 2λv2 = −2µ2 H t ˜t H δλ = 3y4 top 8π2 log mstop mtop mh0 ≤ MZ0λsusy = 1 8 g2 + g 2 cos2 2β Need a susy copy of quartic coupling, only gauge coupling works in MSSM
- 105. The Higgs Mass Problem δµ2 = − 3y2 top 8π2 m2 stop H t ˜t H Higgs mass gain is only log Fine tuning loss is quadratic Difficult to make the Higgs heavier than 125 GeV in MSSM FT ∼ m2 h0 δµ2 m2 h0 = 2λv2 = −2µ2 H t ˜t H δλ = 3y4 top 8π2 log mstop mtop mh0 ≤ MZ0λsusy = 1 8 g2 + g 2 cos2 2β Need a susy copy of quartic coupling, only gauge coupling works in MSSM
- 106. Susy is the leading candidate for BSM Physics Dark Matter candidate Gauge Coupling Unification Compelling structure Become the standard lamppost Basic Susy Signatures away from mSUGRA are still being explored A lot of the qualitative signatures of Susy appear in other models
- 107. Extra Dimensions Taxonomy Large TeV Small Flat Curved UEDs RS Models GUT ModelsADD Models
- 108. Kaluza-Klein Modes The general method to analyze higher dimensional theories S = d4 x dy |∂M φ(x, y)|2 − M2 |φ(x, y)|2 y xµ
- 109. Kaluza-Klein Modes The general method to analyze higher dimensional theories S = d4 x dy |∂M φ(x, y)|2 − M2 |φ(x, y)|2 y xµ (∂µ∂µ − ∂2 5 + M2 )φ(x, y) = 0 Equations of Motion
- 110. Kaluza-Klein Modes The general method to analyze higher dimensional theories S = d4 x dy |∂M φ(x, y)|2 − M2 |φ(x, y)|2 y xµ (∂µ∂µ − ∂2 5 + M2 )φ(x, y) = 0 Equations of Motion φ(x, y) = n φn(x)fn(y) ∂µ∂µ + M2 + 2πn R 2 φn(x) = 0 One 5D field = tower of 4D fields fn(y) = e2πiny/R √ 2πR
- 111. Large Extra Dimensions Gravity SM Integrate out extra dimension S4+n = d4 x dn y √ g M2+n ∗ R4+n + δn (y)LSM S4 eﬀ = d4 x √ g M4+n ∗ Ln R4 + LSM
- 112. Large Extra Dimensions Gravity SM Integrate out extra dimension S4+n = d4 x dn y √ g M2+n ∗ R4+n + δn (y)LSM S4 eﬀ = d4 x √ g M4+n ∗ Ln R4 + LSM M2 Pl = M2+n ∗ Ln Identify new Planck Mass
- 113. Large Extra Dimensions Gravity SM Integrate out extra dimension S4+n = d4 x dn y √ g M2+n ∗ R4+n + δn (y)LSM S4 eﬀ = d4 x √ g M4+n ∗ Ln R4 + LSM M2 Pl = M2+n ∗ Ln Identify new Planck Mass n L 1 1010 km 2 1 mm 3 10nm 4 10-2nm 5 100fm 6 1fm M∗ 1 TeVSet If fundamental Planck mass is weak scale, there is no hierarchy problem!
- 114. Large Extra Dimension Signatures Monophoton+MET M back- own in served TABLE III: Percentage of signal events passing the candidate sample selection criteria (α) and observed 95% C.L. lower limits on the eﬀective Planck scale in the ADD model (Mobs D ) in GeV/c2 as a function of the number of extra dimensions in the model (n) for both individual and the combined analysis. Number of Extra Dimensions 2 3 4 5 6 LowerLimit(TeV)DM 0.6 0.8 1 1.2 1.4 1.6 Number of Extra Dimensions 2 3 4 5 6 LowerLimit(TeV)DM 0.6 0.8 1 1.2 1.4 1.6 TE+!CDF II Jet/ ) -1 (2.0 fbTE+!CDF II ) -1 (1.1 fbTECDF II Jet + LEP Combined q ¯q γ G
- 115. Large Extra Dimension Signatures Black Holes at the LHC Topology Total Cross Section (fb) n = 2 62, 000 5 TeV black hole n = 4 37, 000 n = 6 34, 000 n = 2 580 8 TeV black hole n = 4 310 n = 6 270 n = 2 6.7 10 TeV black hole n = 4 3.4 n = 6 2.9 Rs( √ s) = M−1 ∗ √ s M∗ 1 n+1√ s M∗for σBH ∼ R2 s BHs decay thermally, violating all global conservation laws High multiplicity events with lots of energy q q
- 116. Universal Extra Dimensions +Gravity SM Standard Model has KK modes S5D = d5 x F2 MN + ¯ΨiD Ψ + · · · − 1 2 R ≤ x5 ≤ 1 2 R All fields go in the bulk R−1 > ∼ 500 GeV
- 117. Universal Extra Dimensions +Gravity SM Standard Model has KK modes S5D = d5 x F2 MN + ¯ΨiD Ψ + · · · − 1 2 R ≤ x5 ≤ 1 2 R All fields go in the bulk Mass g W B Q Uc Dc L Ec H n = 1 n = 2 n = 3· · · n = 0 f(x5) 1 sin(x5/R) cos(2x5/R) sin(3x5/R) Impose Dirichlet Boundary Conditions R−1 > ∼ 500 GeV
- 118. UED KK Spectra e ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. Levels are degenerate at tree level All masses within 30% of each other! (This is a widely spaced example!)
- 119. KK Parity x5 → −x5 All odd-leveled KK modes are odd SM and even-leveled KK modes are even
- 120. KK Parity x5 → −x5 All odd-leveled KK modes are odd SM and even-leveled KK modes are even LKP is stable! Usually KK partner of Hypercharge Gauge boson g0,0,1 ∝ R/2 −R/2 dx5 f0(x5)f0(x5)f1(x5) ∼ dx5 1 · 1 · sin(πx5/R)
- 121. KK Parity x5 → −x5 All odd-leveled KK modes are odd SM and even-leveled KK modes are even Looks like a degenerate Supersymmetry spectrum until you can see 2nd KK level LKP is stable! Usually KK partner of Hypercharge Gauge boson g0,0,1 ∝ R/2 −R/2 dx5 f0(x5)f0(x5)f1(x5) ∼ dx5 1 · 1 · sin(πx5/R)
- 122. Typical UED Event Pair produce colored 1st KK level Each side decays separately The spectrum of the ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, mh = 120 GeV, m2 H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. tree level and (b) one-loop, for R−1 = 500 GeV, anishing boundary terms at the cut-oﬀ scale Λ.
- 123. Typical UED Event Pair produce colored 1st KK level Each side decays separately The spectrum of the ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, mh = 120 GeV, m2 H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. tree level and (b) one-loop, for R−1 = 500 GeV, anishing boundary terms at the cut-oﬀ scale Λ. g1 → q1 ¯q
- 124. Typical UED Event Pair produce colored 1st KK level Each side decays separately The spectrum of the ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, mh = 120 GeV, m2 H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. tree level and (b) one-loop, for R−1 = 500 GeV, anishing boundary terms at the cut-oﬀ scale Λ. q1 → B1q g1 → q1 ¯q
- 125. Typical UED Event Pair produce colored 1st KK level Each side decays separately The spectrum of the ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, mh = 120 GeV, m2 H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. tree level and (b) one-loop, for R−1 = 500 GeV, anishing boundary terms at the cut-oﬀ scale Λ. q1 → B1q g1 → q1 ¯q 2j + ET
- 126. Typical UED Event Pair produce colored 1st KK level Each side decays separately The spectrum of the ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, mh = 120 GeV, m2 H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. tree level and (b) one-loop, for R−1 = 500 GeV, anishing boundary terms at the cut-oﬀ scale Λ. g1 → q1 ¯q q1 → B1q g1 → q1 ¯q 2j + ET
- 127. Typical UED Event Pair produce colored 1st KK level Each side decays separately The spectrum of the ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, mh = 120 GeV, m2 H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. tree level and (b) one-loop, for R−1 = 500 GeV, anishing boundary terms at the cut-oﬀ scale Λ. g1 → q1 ¯q q1 → B1q g1 → q1 ¯q q1 → W3 1 q 2j + ET
- 128. Typical UED Event Pair produce colored 1st KK level Each side decays separately The spectrum of the ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, mh = 120 GeV, m2 H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. tree level and (b) one-loop, for R−1 = 500 GeV, anishing boundary terms at the cut-oﬀ scale Λ. g1 → q1 ¯q q1 → B1q g1 → q1 ¯q q1 → W3 1 q W3 1 → 1 ¯ 2j + ET
- 129. Typical UED Event Pair produce colored 1st KK level Each side decays separately The spectrum of the ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, mh = 120 GeV, m2 H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. tree level and (b) one-loop, for R−1 = 500 GeV, anishing boundary terms at the cut-oﬀ scale Λ. g1 → q1 ¯q q1 → B1q g1 → q1 ¯q q1 → W3 1 q W3 1 → 1 ¯ 1 → B1 2j + ET
- 130. Typical UED Event Pair produce colored 1st KK level Each side decays separately The spectrum of the ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, mh = 120 GeV, m2 H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. tree level and (b) one-loop, for R−1 = 500 GeV, anishing boundary terms at the cut-oﬀ scale Λ. g1 → q1 ¯q q1 → B1q g1 → q1 ¯q q1 → W3 1 q W3 1 → 1 ¯ 1 → B1 2j + ET 2j + + ¯+ ET
- 131. Typical UED Event Pair produce colored 1st KK level Each side decays separately The spectrum of the ﬁrst KK level at (a) tree level and (b) one-loop, for R−1 = 500 GeV, mh = 120 GeV, m2 H = 0, and assuming vanishing boundary terms at the cut-oﬀ scale Λ. tree level and (b) one-loop, for R−1 = 500 GeV, anishing boundary terms at the cut-oﬀ scale Λ. g1 → q1 ¯q q1 → B1q g1 → q1 ¯q q1 → W3 1 q W3 1 → 1 ¯ 1 → B1 2j + ET 2j + + ¯+ ET Difficult is in Soft Spectra
- 132. Randall Sundrum Models TeV Scale Curved Extra Dimensions ds2 = e−2ky dx2 4 − dy2 Warp factor UV Brane IR Brane y 0 ≤ y ≤ y0 At each point of the 5th dimension, there is a different normalization of 4D lengths
- 133. Effects of the Warping S5 = d4 xdy √ g5 δ(y − y0) gµν 5 ∂µφ∂νφ + m2 φ2 + gφ3 + λφ4 gµν 5 = e2ky0 ηµν√ g5 = e−4ky0 An IR brane scalar
- 134. Effects of the Warping S5 = d4 xdy √ g5 δ(y − y0) gµν 5 ∂µφ∂νφ + m2 φ2 + gφ3 + λφ4 gµν 5 = e2ky0 ηµν√ g5 = e−4ky0 S4 = d4 x e−4ky0 e2ky0 (∂φ)2 + m2 φ2 + gφ3 + λφ4 Need to go to canonical normalization φ → eky0 φ An IR brane scalar
- 135. Effects of the Warping S5 = d4 xdy √ g5 δ(y − y0) gµν 5 ∂µφ∂νφ + m2 φ2 + gφ3 + λφ4 gµν 5 = e2ky0 ηµν√ g5 = e−4ky0 S4 = d4 x e−4ky0 e2ky0 (∂φ)2 + m2 φ2 + gφ3 + λφ4 Need to go to canonical normalization φ → eky0 φ S4 = d4 x (∂φ)2 + m2 e−2ky0 φ2 + ge−ky0 φ3 + λφ4 All mass scales on IR brane got crunched by warp factor Super-heavy IR brane Higgs becomes light! An IR brane scalar
- 136. Can put all fields on IR brane... but just like low dimension operators get scrunched, high dimension operators get enlarged! Motivated putting SM fields in bulk except for the Higgs UV Brane IR Brane SM Gauge + Fermions Higgs boson Now have SM KK modes, but no KK parity Resonances not evenly spaced either Get light KK copies of right-handed top
- 137. Tonnes of Theory & Pheno and Models for RS Models! AdS/CFT Theories in Anti-de Sitter space (RS metric) Equivalent to 4D theories that are conformal (scale invariant) 5D description is way of mocking up complicated 4D physics! Warping is Dimensional Transmutation IR Brane is breaking of conformal symmetry ΛIR = e−ky0 ΛUV ΛQCD = e− 2πα −1 3 (MGUT) b0 MGUT
- 138. Technicolor Theories Imagine there was no Higgs QCD still gets strong and quarks condense QQc = 0 Qc = (Uc , Dc ) QQc ∼ (1, 2)1 2 Condensate has SM gauge quantum numbers Like the Higgs! QCD confinement/chiral symmetry breaking breaks electroweak symmetry Technicolor is a scaled-up version of QCD RS Models are the modern versions of Technicolor
- 139. In Technicolor theories Not necessarily a Higgs boson Technirhos usually first resonance OS = H† Wµν HBµν Λ2 Mediate contributions to Λ > ∼ 3 TeVwith W± , Z0 ρT ωT 90 GeV 800 GeV etc Need to be lighter than 1 TeV
- 140. In Technicolor theories Not necessarily a Higgs boson Technirhos usually first resonance OS = H† Wµν HBµν Λ2 Mediate contributions to Λ > ∼ 3 TeVwith W± , Z0 ρT ωT 90 GeV 800 GeV etc Need to be lighter than 1 TeV W± , Z0 ρT ωT 90 GeV 3 TeV etc Can push off the Technirhos usually a scalar resonance becomes narrow 600 GeV σT σT starts playing the role of the Higgs Requires assumptions about technicolor dynamics Would like to get scalars light without dynamical assumptions
- 141. Higgs as a Goldstone boson σT −→ πT Higgs boson is a technipion Pions are light because the are Goldstone bosons of approximate symmetries V (πT ) m2 f2 cos πT /f f set by Technicolor scale πT = 0, πf Goldstone bosons only have periodic potentials
- 142. Little Higgs Theories Special type of symmetry breaking V (πT ) f4 sin4 πT /f + m2 f2 cos πT /f Looks like normal “Mexican hat” potential Lots of group theory to get specific examples
- 143. Little Higgs Theories Special type of symmetry breaking V (πT ) f4 sin4 πT /f + m2 f2 cos πT /f Looks like normal “Mexican hat” potential Lots of group theory to get specific examples [SU(3) × SU(3)/SU(3)]4 SU(5)/SO(5) SU(6)/Sp(6) [SO(5) × SO(5)/SO(5)]4 [SU(4)/SU(3)]4 SU(9)/SU(8) SO(9)/SO(5) × SO(4)
- 144. All have some similar features New gauge sectors Vector-like copies of the top quarks Q3 & Qc 3 Uc 3 & U3 There are extended Higgs sectors SU(2)L singlets, doublets & triplets
- 145. Conclusion Beyond the Standard Model Physics is rich and diverse Within the diversity there are many similar themes These lectures were just an entry way into the phenomenology of new physics We’ll soon know which parts of these theories have something to do with the weak scale
- 146. References S. P. Martin hep-ph/9709356 C. Csaki et al “Supersymmetry Primer” “TASI lectures on electroweak symmetry breaking from extra dimensions” hep-ph/0510275 M. Schmaltz, D. Tucker-Smith “Little Higgs Review” hep-ph/0502182 I. Rothstein hep-ph/0308286 “TASI Lectures on Effective Field Theory” G. Kribs “TASI 2004 Lectures on the pheomenology of extra dimensions” hep-ph/0605325 J. Wells hep-ph/0512342 “TASI Lecture Notes: Introduction to Precision Electroweak Analysis” R. Sundrum “TASI 2004: To the Fifth Dimension and Back” hep-ph/0508134

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