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Non-SUSY Physics Beyond the Standard Model

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  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

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

  6. Global Flavor Symmetries Q1 u1 d1 L1 e1 . . 2 . . 3 Rotate 45 fermions into each other U(45) SM matter secretly has a large symmetry: 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 1 + i2 3 + i4 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 1 + i2 3 + i4 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 MW2 g2 =  1 as g’0 MZ2 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) 1 2 -1/2 (Qdc) 1 2 +1/2 (QL) 3 1 -1/3 (Qe) 3 2 +7/6 (ucdc) 3x3 1 -1/3 (ucL) 3 2 -7/6 (uce) 3 1 +1/3 (dcL) 3 2 -5/6 (dce) 3 1 +4/3 (Le) 1 2 +1/2 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. An anomaly leads to a mass for a gauge boson Anomaly Cancellation Quantum violation of current conservation

  11. Anomaly Cancellation SU(3) SU(3) SU(2)L SU(2)L U(1)Y U(1)Y g g 3[ 2‧(1/6) – (2/3) + (1/3)] = 0 Q uc dc U(1)Y U(1)Y U(1)Y 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 SU(3)C x SU(2)L x U(1)Y Exact Broken to U(1)QED • Gauge Symmetry • Flavor Symmetry • Custodial Symmetry • Chiral Fermions • Gauge Anomalies 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 SU(3)C x SU(2)L x U(1)Y Exact Broken to U(1)QED • Gauge Symmetry • Flavor Symmetry • Custodial Symmetry • Chiral Fermions • Gauge Anomalies 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. Lepton Number Violation Precision Electroweak Generic Operators Flavor Violation CP Violation Baryon Number Violation Contact Operators Constraints on Higher Dimensional Operators Λ≳ 1016 GeV Λ≳ 1015 GeV Λ≳ 106 GeV Λ≳ 106 GeV Λ≳ 103 GeV Λ≳ 103 GeV 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 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 a classic! aged to perfection better drink now mature, balanced, well developed - the Wino’s choice ’67 The Standard Model ’77 Vin de Technicolor ’70’s Supersymmetry: MSSM ’90’s SUSY Beyond MSSM ’90’s CP Violating Higgs ’98 Extra Dimensions ’02 Little Higgs ’03 Fat Higgs ’03 Higgsless ’04 Split Supersymmetry ’05 Twin Higgs 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 Most cases controlled by Parton flux 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 Solid: 7 TeV vs Tevatron Dashed: 10 TeV vs Tevatron Bauer etal 0909.5213

  24. New Physics @ LHC7 Most cases controlled by Parton flux 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 Solid: 7 TeV vs Tevatron Dashed: 10 TeV vs Tevatron Bauer etal 0909.5213

  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 0909.5213

  26. High Mass Resonances

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

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

  34. 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

  35. 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 Large radius gives finely separated Kaluza-Klein particles Small radius gives well separated Kaluza-Klein particles Small radius Large radius

  36. Action Approach:Consider a real, massless scalarin flat 5-d

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

  38. 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

  39. 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: 5d ↔ 4d scalar (scalar)n vector AM (Aμ, A5)n tensor hMN (hμν, hμ5, h55)n KK towers → → →

  40. 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 ↔ 4d (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 → → →

  41. 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

  42. 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!

  43. 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? • …

  44. 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?

  45. 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

  46. 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 = 3+1 +  dimensions All of known physics Solar System Gravity 10-18

  47. 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

  48. Constraints from Cavendish-type exp’ts