The Discovery of Color A Personal Perspective

1. The Discovery of ColorA Personal Perspective O. W. Greenberg Miami 2007 December 13, 2007

2. Outline • Developments in particle physics prior to the work on color. • Discovery of color as a quantum number. • Introduction of gauged SU(3) color. Greenberg_Color

3. Particle physics prior to color • The muon and pion had been discovered. • Strange particles were found in cosmic rays. • Lambda and Sigma hyperons. • Kaon and antikaon, both charged and neutral. • Xi, the cascade; the Omega minus. • Tau-theta puzzle. Greenberg_Color

4. Accelerators come online • About 1½ V events per day in a bubble chamber on a medium-height mountain. • Separated beams of ~106 K’s every 3 sec. at the AGS • New problem: to avoid swamping the detectors. • Major problem at the LHC. Greenberg_Color

5. Paradox: copious production, slow decay. • Attempt to understand using known dynamics • Potential barriers, possibly connected with spin could inhibit decays—did not work. Greenberg_Color

6. Paradox: copious production, slow decay, (continued). • A. Pais, associated production. • Strangeness is conserved for rapid production by strong and electromagnetic interactions • Violated for slow decay by weak interactions. Greenberg_Color

7. Gell-Mann, Nakano and Nishijima—displaced charge multiplets. Nishijima, Gell-Mann formula, Q=I3+Y/2. Weak interaction selection rules. Strangeness Greenberg_Color

8. K-zero, K-zero bar complex • K1, K2 with different decay modes, lifetimes. • Particle mixing effects, regeneration. • Beautiful illustration of superposition principle of quantum theory. Greenberg_Color

9. Tau-theta puzzle • Tau→3 pi • Theta→2 pi • Same lifetimes • Bruno Rossi—probably one particle Greenberg_Color

10. Tau-theta puzzle, (continued) • Dalitz analysis→different parities • Parity was considered sacred • The plot thickens • The unexpected stimulates thought Greenberg_Color

11. Tau-theta puzzle (continued) • Suggestions by Lee and Yang • Possible Interference Phenomena between Parity Doublets • Question of Parity Conservation in Weak Interactions, 22 June 1956 Greenberg_Color

12. Tau-theta puzzle, (continued) • Lee and Yang proposed parity doublets to explain this puzzle. • Lee and Yang examined the data for conservation of parity, and found there was no evidence for parity conservation in weak interactions. • Two solutions for one problem—can’t both be correct. Greenberg_Color

13. Wigner’s comment • Why should parity be violated before the rest of the Lorentz group? • Why is that surprising? • Discrete transformations are independent of the connected component of the Lorentz group. Greenberg_Color

14. Parity violation was found earlier? • Double scattering of beta decay electrons, R.T. Cox, et al., PNAS 14, 544 (1928). Redone with electrons from an electron gun with much higher statistics. No effect seen, C.J. Davisson and L.H. Germer, Phys. Rev. 33, 760 (1929). Greenberg_Color

15. Wightman, Axiomatic Quantum Field Theory • Asymptotic condition in quantum field theory—formalization of LSZ scattering theory. Purely theoretical—no numbers, except to label pages and equations. • Operator-valued distributions, relative mathematical rigor. Greenberg_Color

16. Divergent influences • Very simple ideas used to classify newly discovered particles. • Sophisticated techniques based on quantum field theory. Greenberg_Color

17. Interest in identical particles • Why only bosons or fermions? • Are there other possibilities? • H.S. Green’s parastatistics (1953) as a generalization of each type.— • Boson—paraboson, order p, • Fermion—parafermion, order p; • p=1 is Bose or Fermi. Greenberg_Color

18. 1962: Naples, Istanbul, SACLAY • Axiomatic version of parastatistics with Dell’Antonio and Sudarshan in Naples. • Presented at NATO summer school in Bebek, near Istanbul. • Starting a collaboration with Messiah after giving a talk at SACLAY. Greenberg_Color

19. Istanbul • NATO summer school organized by Feza Gursey at the Robert College in Bebek • Eduardo Caianiello, Sidney Coleman, David Fairlie, Shelly Glashow, Arthur Jaffe, Bruria Kauffman, Louis Michel, Giulio Racah, Eugene Wigner Greenberg_Color

20. SACLAY with Messiah • Albert Messiah, who fought with the Free French army of General Leclerc, was at SACLAY • Entering SACLAY with guards on either side. Greenberg_Color

21. Generalized statistics • First quantized theory that allows all representations of the symmetric group. • Theorems that show the generality of parastatistics—Green’s ansatz is not necessary. Greenberg_Color

22. 1964 • Crucial year for the discovery of quarks and color. Greenberg_Color

23. The crucial year, 1964 • Gell-Mann—”quarks”—current quarks. • Zweig—”aces”—constituent quarks. • Why only qqq and q-qbar? • No reason in the original models. Greenberg_Color

24. Background, Princeton, Fall 1964 • Relativistic SU(6), Gursey and Radicati • Generalization of Wigner’s nonrelativistic nuclear physics idea to combine SU(2)I with SU(2)S to get an SU(4) to classify nuclear states. • Gursey and Radicati combined SU(3)f with SU(2)S to get an SU(6) to classify particle states. Greenberg_Color

25. SU(6) classifications Greenberg_Color

26. Mesons Greenberg_Color

27. Baryons Greenberg_Color

28. Statistics paradox • 56 • 70 • 20 Greenberg_Color

29. Attempts to make a higher dimensional relativistic theory • U(6,6) • U(12) • GL(12,C) • Pais, Salam, et al, Freund, et al. • Pais, Rev. Mod. Physics 38, 215 (1966). Greenberg_Color

30. Magnetic moment ratio • Beg, Lee, and Pais Greenberg_Color

31. Greenberg_Color

32. Previous calculations of magnetic moments • Complicated calculations using pion clouds failed. • Nobody even realized that the ratio was so simple. Greenberg_Color

33. Significance of the magnetic moment calculation • A simple one-line calculation gave the ratio accurate to 3%. • Very convincing additional argument for the quark model. • Quarks have concrete reality. Greenberg_Color

34. The spin-statistics theorem • Particles that have integer spin must obey Bose statistics • Particles that have odd-half-integer spin must obey Fermi statistics. Greenberg_Color

35. Generalized spin-statistics theorem • Not part of general knowledge: • Particles that have integer spin must obey parabose statistics and particles that have odd-half-integer spin must obey parafermi statistics. • Each family is labeled by an integer p; p=1 is ordinary Bose or Fermi statistics. Greenberg_Color

36. Parafermi quark model, 1964 • Suggested a model in which quarks carry order-3 parafermi statistics. • This allows up to three quarks in the same space-spin-flavor state without violating the Pauli principle, so the statistics paradox is resolved. • This leads to a model for baryons that is now accepted. Greenberg_Color

37. Resolution of the statistics paradox • Exhilarated—resolving the statistics problem seemed of lasting value. • Not interested in higher relativistic groups; from O’Raifeartaigh’s and my own work I knew that combining internal and spacetime symmetries is difficult or impossible.. Greenberg_Color

38. No-go theorems • Later work of Coleman and Mandula and of Haag, Lopuszanski and Sohnius showed that the only way to combine internal and spacetime symmetries in a larger group is supersymmetry. Greenberg_Color

39. Baryon spectroscopy • Hidden parafermi (color) degree of freedom takes care of the required antisymmetry of the Pauli principle. • Quarks can be treated as Bosons in the visible space, spin and flavor degrees of freedom. Greenberg_Color

40. Table of excited baryons • Developed a simple bound state model with s and p state quarks in the 56, L=0 and 70, L=1 supermultiplets. Greenberg_Color

41. Greenberg_Color

42. Later developments of baryon spectroscopy • OWG, Resnikoff • Dalitz, and collaborators • Isgur and Karl • Riska and collaborators Greenberg_Color

43. How did the physics community react? • J. Robert Oppenheimer • Steven Weinberg Greenberg_Color

44. Gave Oppenheimer a preprint in Princeton • Met him at a conference in Maryland • “Greenberg, it’s beautiful!” Greenberg_Color

45. Oppenheimer’s response, (continued) • “but I don’t believe a word of it.” Greenberg_Color

46. Weinberg, ”The making of the standard model” • ”At that time I did not have any faith in the existence of quarks.” (1967) Greenberg_Color

47. Sources of skepticism • Quarks had just been suggested. • Fractional electric charges had never been seen. • Gell-Mann himself was ambiguous. Greenberg_Color

48. Gell-Mann’s comments • ”It is fun to speculate …if they were physical particles of finite mass (instead of purely mathematical entities as they would be in the limit of infinite mass)….A search … would help to reassure us of the non-existence of real quarks.” Greenberg_Color

49. Skepticism, continued • Assuming a hidden degree of freedom on top of the fractionally charged unseen quarks seemed to stretch credibility to the breaking point. • Some felt that parastatistics was inconsistent. Greenberg_Color

50. Other solutions to the statistics paradox • Explicit color SU(3), Han-Nambu, 1965 • Complicated antisymmetric ground state • Quarks are not real anyway • Other models Greenberg_Color