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STANDARD MODEL

STANDARD MODEL. Theoretical Constraints on Higgs Mass. Large M h → large self-coupling → blow up at low-energy scale Λ due to renormalization Small: renormalization due to t quark drives quartic coupling < 0 at some scale Λ → vacuum unstable

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STANDARD MODEL

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  1. STANDARD MODEL

  2. Theoretical Constraints on Higgs Mass • Large Mh → large self-coupling → blow up at low-energy scale Λ due to renormalization • Small: renormalization due to t quark drives quartic coupling < 0 at some scale Λ → vacuum unstable • Vacuum could be stabilized by supersymmetry LHC 95% exclusion Espinosa, JE, Giudice, Hoecker, Riotto, arXiv0906.0954

  3. Vacuum Stability vs Metastability • Dependence on scale up to which Standard Model remains • Stable • Metastable at non-zero temperature • Metastable at zero temperature

  4. What is the probable fate of the SM? Confidence Levels (CL) without/with Tevatron exclusion Confidence Levels (CL) for different fates Blow-up excluded at 99.2% CL CL as function of instability Scale Λ Espinosa, JE, Giudice, Hoecker, Riotto

  5. The LHC will Tell the Fate of the SM Examples with LHC measurement of mH = 120 or 115 GeV Espinosa, JE, Giudice, Hoecker, Riotto

  6. How to Stabilize a Light Higgs Boson? • Top quark destabilizes potential: introduce introduce stop-like scalar: • Can delay collapse of potential: • But new coupling must be fine-tuned to avoid blow-up: • Stabilize with new fermions: • just like Higgsinos • Very like Supersymmetry! JE + D. Ross

  7. Higgs mass χ2 price to pay if Mh = 125 GeV is < 2 Buchmueller, JE et al: arXiv:1112.3564 Favoured values of Mh ~ 119 GeV: Range consistent with evidence from LHC !

  8. Supersymmetry? • Would unify matter particles and force particles • Related particles spinning at different rates 0 - ½ - 1 - 3/2 - 2 Higgs - Electron - Photon - Gravitino - Graviton (Every particle is a ‘ballet dancer’) • Would help fix particle masses • Would help unify forces • Predicts light Higgs boson • Could provide dark matter for the astrophysicists and cosmologists

  9. Why Supersymmetry (Susy)? • Hierarchy problem:why is mW << mP ? (mP ~ 1019 GeV is scale of gravity) • Alternatively, why is GF = 1/ mW2 >> GN = 1/mP2 ? • Or, why is VCoulomb >> VNewton ? e2 >> G m2 = m2 / mP2 • Set by hand? What about loop corrections? δmH,W2 = O(α/π) Λ2 • Cancel boson loops  fermions • Need | mB2 – mF2| < 1 TeV2

  10. Loop Corrections to Higgs Mass2 • Consider generic fermion and boson loops: • Each is quadratically divergent: ∫Λd4k/k2 • Leading divergence cancelled if Supersymmetry! 2 x 2

  11. Other Reasons to like Susy It enables the gauge couplings to unify It predicts mH < 130 GeV As suggested by EW data

  12. Dark Matter in the Universe Astronomers say that most of the matter in the Universe is invisible Dark Matter Supersymmetricparticles ? We shall look for them with the LHC

  13. Minimal Supersymmetric Extension of Standard Model (MSSM) • Particles + spartners • 2 Higgs doublets, coupling μ, ratio of v.e.v.’s = tan β • Unknown supersymmetry-breaking parameters: Scalar massesm0, gaugino massesm1/2, trilinear soft couplingsAλ, bilinear soft couplingBμ • Often assume universality: Singlem0, singlem1/2, singleAλ,Bμ: not string? • Called constrained MSSM = CMSSM • Minimal supergravity also predicts gravitino mass m3/2 = m0,Bμ = Aλ – m0

  14. Why 2 Higgs Doublets? ~ H • Cancel anomalous Higgsino triangle diagrams • Superpotential must be analytic function of superfields: • Cannot use QUcH, QDcH* • Must use QUcHu, QDcHd • Two Higgs fields: • Coupling between them: μHuHd • Two different vev’s, ratio tan β • Five physical Higgs bosons: 3 neutrals, H± ~ H ~ H

  15. Non-Universal Scalar Masses? • Different sfermions with same quantum #s? e.g., d, s squarks? disfavoured by upper limits on flavour- changing neutral interactions • Squarks with different #s, squarks and sleptons? disfavoured in various GUT models e.g., dR = eL, dL = uL = uR = eR in SU(5), all in SO(10) • Non-universal susy-breaking masses for Higgses? No reason why not! NUHM

  16. MSSM: > 100 parameters String? SU(5) unification: 7 parameters NUHM2: 6 parameters NUHM1 = SO(10): 5 parameters CMSSM: 4 parameters Minimal Flavour Violation: 13 parameters (+ 6 violating CP) mSUGRA: 3 parameters

  17. Lightest Supersymmetric Particle • Stable in many models because of conservation of R parity: R = (-1) 2S –L + 3B where S = spin, L = lepton #, B = baryon # • Particles have R = +1, sparticles R = -1: Sparticles produced in pairs Heavier sparticles  lighter sparticles • Lightest supersymmetric particle (LSP) stable

  18. Possible Nature of LSP • No strong or electromagnetic interactions Otherwise would bind to matter Detectable as anomalous heavy nucleus • Possible weakly-interacting scandidates Sneutrino (Excluded by LEP, direct searches) Lightest neutralino χ(partner of Z, H, γ) Gravitino (nightmare for detection)

  19. Classic Supersymmetric Signature Missing transverse energy carried away by dark matter particles

  20. gμ - 2 Constraints on Supersymmetry • Absence of sparticles at LEP, Tevatron selectron, chargino > 100 GeV squarks, gluino > 300 GeV • Indirect constraints Higgs > 114 GeV, b -> s γ • Density of dark matter lightest sparticle χ: WMAP: 0.094 < Ωχh2 < 0.124

  21. Quo Vadisgμ - 2? Strong discrepancy between BNL experiment and e+e- data: now ~ 3.6 σ Better agreement between e+e- experiments Increased discrepancy between BNL experiment and μ decay data now ~ 2.4 σ Convergence between e+e- experiments and τ decay data More credibility?

  22. Impact of LHC on the CMSSM Assuming the lightest sparticle is a neutralino tan β = 10 ✕ gμ - 2 tan β = 55 ✓ gμ - 2 LHC Excluded because stau LSP Excluded by b  s gamma WMAP constraint on CDM density Preferred (?) by latest g - 2 JE, Olive & Spanos

  23. Supersymmetric Models to Study • Gravity-mediated: • NUHM2 • as below, mhu ≠ mhd • NUHM1 • as below, common mh ≠ m0 • CMSSM • m0, m1/2, tan β (B0), A0 • VCMSSM • as above, & A0 = B0 + m0 • mSUGRA • as above, & m3/2 = m0 • RPV CMSSM • Other SUSY ✕ models: • Gauge-mediated • Anomaly-mediated • Mixed modulus-anomaly-mediated • Phenomenological 19-parameter MSSM • NMSSM • …. Also studied in global fits Most studied in global fits Less studied in global fits Some Global fits If model has N parameters, sample 100 values/parameter: 102N points, e.g., 108 in CMSSM

  24. Data • Electroweak precision observables • Flavour physics observables • gμ - 2 • Higgs mass • Dark matter • LHC MasterCode: O.Buchmueller, JE et al.

  25. Electroweak Precision Observables • Inclusion essential for fair comparison with Standard Model • Some observables may be significantly different • E.g., mW, Afb(b) • Advantage for SUSY? • Some may not be changed significantly • Should be counted against/for all models

  26. To gμ – 2 or not to gμ – 2 ? CMSSM NUHM1 Pre-LHC fits: Mild preference for small masses even without gμ – 2 ? MasterCode: O.Buchmueller, JE et al.

  27. XENON100 Experiment Aprile et al: arXiv:1104.2549

  28. Supersymmetry Searches in CMS Jets + missing energy (+ lepton(s))

  29. Supersymmetry Searches in ATLAS Jets + missing energy + 0 lepton

  30. Limits on Heavy MSSM Higgses

  31. Higgs mass χ2 price to pay if Mh = 125 GeV is < 2 Buchmueller, JE et al: arXiv:1112.3564 Favoured values of Mh ~ 119 GeV: Range consistent with evidence from LHC !

  32. 68% & 95% CL contours ….. pre-Higgs ___ Higgs @ 125 Buchmueller, JE et al: arXiv:1112.3564

  33. Gluino mass --- pre-Higgs ___ Higgs @ 125 … H@125, no g-2 Buchmueller, JE et al: arXiv:1112.3564 Favoured values of gluino mass significantly above pre-LHC, > 2 TeV

  34. Squark mass --- pre-Higgs ___ Higgs @ 125 … H@125, no g-2 Buchmueller, JE et al: arXiv:1112.3564 Favoured values of squark mass significantly above pre-LHC, > 2 TeV

  35. Bsμ+μ- --- pre-Higgs ___ Higgs @ 125 … H@125, no g-2 Buchmueller, JE et al: arXiv:1112.3564 Favoured values of Bs μ+μ- above Standard Model

  36. Spin-independent Dark matter scattering --- pre-Higgs ___ Higgs @ 125 Buchmueller, JE et al: arXiv:1112.3564 Favoured dark matter scattering rate well below XENON100 limit

  37. The Stakes in the Higgs Search • How is gauge symmetry broken? • Is there any elementary scalar field? • Would have caused phase transition in the Universe when it was about 10-12 seconds old • May have generated then the matter in the Universe: electroweak baryogenesis • A related inflaton might have expanded the Universe when it was about 10-35 seconds old • Contributes to today’s dark energy: 1060 too much!

  38. Conversation with Mrs Thatcher: 1982 Wouldn’t it be better if they found what you predicted? Think of things for the experiments to look for, and hope they find something different What do you do? Then we would not learn anything!

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