1. Precision Measurements after the Higgs Discovery M.V. Chizhov Sofia University, Bulgaria and JINR, Russia

2. 09/06/20142 Why do we need the Higgs boson? S = ½ S = 1 S = 0

3. 09/06/2014 Harmonic Oscillator (Analytical Mechanics) Joseph-Louis Lagrange (Giuseppe Lodovico Lagrangia), 1788 3

4. R > 0 R < 0 09/06/2014 Harmonic Oscillator (Scalar Field) 4

5. 09/06/2014 Scalar Potential of Anharmonic Oscillator 5

6. 09/06/2014 Discrete Z 2 Symmetry of the Scalar Potential 6

7. Two Scalar Fields (or Complex Scalar Field) Potential with Broken Symmetry 7

8. 09/06/2014 Continuous U(1) Symmetry of the Potential with Complex Scalar Field J. Goldstone, Nuovo Cim. 19 (1961) 154. 8

9. 09/06/2014 Goldstone Particle (Theorem) “if there is continuous symmetry transformation under which the Lagrangian is invariant, then either the vacuum state is also invariant under the transformation, or there must exist spinless particles of zero mass.” Jeffrey Goldstone, Abdus Salam and Steven Weinberg, Phys. Rev. 127 (1962) 965 9

10. 09/06/2014 Examples of Collective Goldstone Bosons  Spin waves in a ferromagnet  Phonons in a crystal lattice  Superfluidity (Bose condensate, Боголюбов,1947)  Superconductivity (Cooper pairs, 1956; Боголюбов,1958)  Pions in the chiral limit (Nambu, 1961) 10

11. 09/06/2014 In Nature there is not a massless spinless colorless particle, which would have had an infinite radius of interaction! Only gravitational and electromagnetic forces have an infinite radius of interaction. Massless Particles in Nature 11

12. 09/06/2014 Gauge Invariance and Massless Particles AA 12

13. 09/06/201413 As Yang relates: Wolfgang Pauli (1900-1958) was spending the year in Princeton, and was deeply interested in symmetries and interactions.... Soon after my seminar began, when I had written on the blackboard, (∂  -i  B  )  Pauli asked, "What is the mass of this field B  ?" I said we did not know. Then I resumed my presentation but soon Pauli asked the same question again. I said something to the effect that it was a very complicated problem, we had worked on it and had come to no definite conclusions. I still remember his repartee: "That is not sufficient excuse". An Anecdote by C. N. Yang

14. 09/06/2014 S. L. Glashow, Nucl. Phys. 22 (1961) 579. Birth of the Standard Model of Elementary Particles SU(2) L  U(1) Y “Schwinger told me to think about unifying weak and EM. So I did it. For two years ‒ I thought about it.” 14

15. 09/06/201415 Unitarity and Z boson

16. 09/06/201416 Unitarity and Higgs boson Not yet tested experimentally… but see the following slide!

17. 09/06/201417 Evidence of electroweak W ± W ± jj production ATLAS-CONF-2014-013 (March 25, 2014), arXiv:1405.6241 Inclusive m jj QCD+EW region Enriched VBS region: m jj >500 GeV, |  y jj |>2.4

18. 09/06/2014 Gauge Invariance and Massive Particles Schwinger model (1962): two-dimentional quantum electrodynamics, where the photon becomes massive. Non-relativistic dynamics of the plasma: Philip W. Anderson (1963) – Yang  Mills fields acquire the mass due to longitudinal oscillations in plasma (Meissner  Ochsenfeld effect). AA 22 “We conclude, then, that the Goldstone zero-mass difficulty is not a serious one, because we can probably cancel it off against an equal Yang-Mills zero-mass problem.” 18

19.  F. Englert and R. Brout, Phys. Rev. Lett. 13 (1964) 321 (June 26, 1964)  P. W. Higgs, Phys. Rev. Lett. 13 (1964) 508 (August 31, 1964)  G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Phys. Rev. Lett. 13 (1964) 585 (Octomber 12, 1964) Englert-Brout-Higgs-Guralnik-Hagen- Kibble mechanism on one page 19

20. 09/06/2014 Goldstone and Higgs Particles Jeffrey Goldstone Peter W. Higgs Phys. Rev. 145 (1966) 1156 H → Z Z “it is worth noting that an essential feature of this type of theory is the prediction of incomplete multiplets of scalar and vector bosons.” Phys. Rev. Lett. 13 (1964) 508 20

21. 09/06/2014 Neither Salam and Ward, who worked at Imperial College in the same group with Guralnik, Hagen and Kibble, nor Glashow, who after Higgs seminar at Harvard on March 16, 1966 said: "that is a nice model, Peter" have realized that they could use this mechanism for generation of masses. Omitted Opportunities Glashow (1961) Salam & Ward (1964) Salam & Ward (Sept 24, 1964→ Nov 15, 1964) (On Monday, October 5, Peter Higgs gave a seminar about his mechanism at Imperial College?) GHK (Oct 12, 1964 → Nov 16, 1964) “All of us, Brout, Englert and myself, had been going in the wrong direction, looking at hadron symmetries. ” P.W. Higgs 21

22. SU(2) L U(1) Y Using of EBHGHK mechanism  S. Weinberg (1967) & A. Salam (1968) → Nobel Prize 1979 relation between the masses of intermediate bosons M W =M Z cos  W through the mechanism of spontaneous symmetry breaking 09/06/201422

23. Lagrangian of the Standard Model 09/06/201423

24. 09/06/2014 Mathematical Foundation of the Standard Model (theory)  G. ’t Hooft & M. J. G. Veltman (1972) → Nobel Prize 1999 renormalizability of non-abelian gauge theories with broken symmetry is proven a drawing of their most important discovery 24

25.  Discovery of the weak neutral interactions mediated by Z boson in experiment with bubble chamber Gargamelle at CERN (1973) Establishment of the Standard Model (experiment) sin 2  W ~ 0.3  0.5 M W =50  70 GeV M Z =75  80 GeV 09/06/201425

26. 09/06/2014 Hunt for the Higgs Boson 26 John F. Gunion, Howard E. Haber, Gordon L. Kane, Sally Dawson, The Higgs Hunter's Guide, Upton, NY: Brookhaven Nat. Lab., 1989. - 404 p.

27. 09/06/2014 began work on November 30, 1986 and stopped on September 30, 2011 TeVatron at FNAL 27

28. 09/06/201428 Tevatron Higgs Exclusion

29. 09/06/2014 Large Electron ‒ Positron (LEP) collider at CERN started in August 1989 and ended in late 2000 DELPHI L3ALEPH OPAL 29

30. 09/06/201430 Direct LEP exclusion

31. 09/06/201431 Indirect constraints on Higgs mass

32. Large Hadron Collider (LHC) 09/06/201432 10 9 interactions per second 1.5  10 11 p 2  1380 bunches

33. 09/06/2014 July 4, 2012 33

34. 09/06/201434 Is it the Higgs, or isn’t Higgs?