1. From an obscure term in an equation to a headline discovery – and beyond John Ellis King’s College London (& CERN) Different Scales for Higgs Physics

2. The (G)AEBHGHKMP’tH Mechanism The only one who mentioned a massive scalar boson

3. Why a Higgs Boson is Needed Trouble with WW scattering: M ~ E 2  uncontrollable infinities in loop diagrams can be cancelled by scalar exchange with HWW couplings Need new physics @ TeV scale

4. 2011: Combining Information from Previous Direct Searches and Indirect Data m H = 125 ± 10 GeV Gfitter collaboration

5. CMS γγ and ZZ* measurements consistent Higgs Mass Measurements

6. Tension in ATLAS γγ and ZZ* measurements Higgs Mass Measurements

7. Quite consistent: Δχ 2 ~ 1.5 Comparison with Electroweak Fit

8. 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 Vacuum could be stabilized by Supersymmetry Degrassi, Di Vita, Elias-Miro, Giudice, Isodori & Strumia, arXiv:1205.6497 Instability @ 10 10 – 10 13 GeV

9. Vacuum Instability in the Standard Model Very sensitive to m t as well as M H Present vacuum probably metastable with lifetime >> age of the Universe Degrassi, Di Vita, Elias-Miro, Giudice, Isodori & Strumia, arXiv:1205.6497

10. What is it? –Higgs or …? What else is there? –Supersymmetry …? What next? –A Higgs factory or …? Some Questions Supersymmetric model fits

11. Elementary Higgs or Composite? Higgs field: ≠ 0 Quantum loop problems Fermion-antifermion condensate Just like QCD, BCS superconductivity Top-antitop condensate? needed m t > 200 GeV New technicolour force? -Heavy scalar resonance? -Inconsistent with precision electroweak data? Cut-off Λ ~ 1 TeV with Supersymmetry? e.g., cutoff Λ = 10 TeV

12. Higgs as a Pseudo-Goldstone Boson Loop cancellation mechanism SupersymmetryLittle Higgs ‘Little Higgs’ models (breakdown of larger symmetry)

13. Assume custodial symmetry: Parameterize gauge bosons by 2 × 2 matrix Σ: Coefficients a = c = 1 in Standard Model Phenomenological Framework

14. Global Analysis of Higgs-like Models Rescale couplings: to bosons by a, to fermions by c Standard Model: a = c = 1 JE & Tevong You, arXiv:1303.3879 b bbarτ γ W Z Global No evidence for deviation from SM

15. It Walks and Quacks like a Higgs Do couplings scale ~ mass? With scale = v? Red line = SM, dashed line = best fit JE & Tevong You, arXiv:1303.3879 Global fit

16. Loop Corrections ? ATLAS sees excess in γγ, CMS sees deficit Loop diagrams ~ Standard Model? JE & Tevong You, arXiv:1303.3879

17. What else is there? Higher-dimensional operators as relics of higher- energy physics? Operators constrained by SU(2) × U(1) symmetry: Constrain using LHC + Tevatron Higgs measurements Corbett, Eboli & Gonzalez 2

18. What else is there? Combine Higgs coupling measurements with constraints on anomalous triple-gauge boson couplings Corbett, Eboli & Gonzalez 2

19. What else is there? Constraints from energy dependence of Higgs production cross section on JE, Sanz & You, arXiv:1303.0208 Λ > ~ 250 GeV

20. What else is there? Supersymmetry Successful prediction for Higgs mass –Should be < 130 GeV in simple models Successful predictions for Higgs couplings –Should be within few % of SM values Could explain the dark matter Naturalness, GUTs, string, … (???)

21. MSSM Higgs Masses & Couplings Lightest Higgs mass up to ~ 130 GeV Heavy Higgs masses quite close Consistent With LHC

22. “Classic” missing-energy search Searches ~ 5/fb @ 8 TeVSearches with 8 TeV Data Multiple searches including b, leptons

23. 5 p-value of simple models < 10% 2 Scan of CMSSM Impacts of searches with full 2012 data Update of Buchmueller et al: arXiv:1207.3715

24. 5 1 Favoured values of gluino mass significantly above pre-LHC, > 1.5 TeV Gluino mass Update of Buchmueller, JE et al: arXiv:1207.3715 CMSSM

25. Favoured values of dark matter scattering cross section significantly below XENON100 5 --- 1/fb ___ 5/fb Buchmueller, JE et al: arXiv:1207.3715 Spin-independent Dark matter scattering Excluded by XENON100 Excluded by LHC 2

26. What Next: A Higgs Factory? To study the ‘Higgs’ in detail: The LHC –Rethink LHC upgrades in this perspective? A linear collider? –ILC up to 500 GeV –CLIC up to 3 TeV (Larger cross section at higher energies) A circular e + e - collider: LEP3, TLEP –A photon-photon collider: SAPPHiRE A muon collider

27. What Higgs Factory? New large tunnel could also be used for pp collisions E CM up to 100 TeV TLEP Steering Group, arXiv:1208.0504, 1305.6498, 1306.5981

28. Possible Layouts for TLEP

29. Comparison of Possible Higgs Factory Measurements

30. Predictions of current best fits in simple SUSY models Current uncertainties in SM calculations [LHC Higgs WG] Comparisons with –LHC –HL-LHC –ILC –TLEP Don’t decide before LHC 13/4 Impact of Higgs Factory? Supersymmetric model fits

31. Part of a Vision for the Future A large circular tunnel –Circumference ~ 80 to 100 km Could accommodate TLEP and VHE-LHC –E CM up to 100 TeV with 15 Tesla magnets Could be sited around Geneva –Interest in China, US TLEP Study Group under way Timely to study VHE-LHC

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