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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

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.

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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.

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Paradox: copious production, slow decay.

- Attempt to understand using known dynamics
- Potential barriers, possibly connected with spin could inhibit decays—did not work.

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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.

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Gell-Mann, Nakano and Nishijima—displaced charge multiplets.

Nishijima, Gell-Mann formula, Q=I3+Y/2.

Weak interaction selection rules.

StrangenessGreenberg_Color

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.

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Tau-theta puzzle, (continued)

- Dalitz analysis→different parities
- Parity was considered sacred
- The plot thickens
- The unexpected stimulates thought

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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

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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.

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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.

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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).

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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.

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Divergent influences

- Very simple ideas used to classify newly discovered particles.
- Sophisticated techniques based on quantum field theory.

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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.

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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.

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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

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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.

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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.

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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.

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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.

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SU(6) classifications

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Mesons

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Baryons

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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).

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Previous calculations of magnetic moments

- Complicated calculations using pion clouds failed.
- Nobody even realized that the ratio was so simple.

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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.

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The spin-statistics theorem

- Particles that have integer spin

must obey Bose statistics

- Particles that have odd-half-integer spin must obey Fermi statistics.

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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.

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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.

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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..

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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.

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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.

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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.

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Later developments of baryon spectroscopy

- OWG, Resnikoff
- Dalitz, and collaborators
- Isgur and Karl
- Riska and collaborators

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Gave Oppenheimer a preprint in Princeton

- Met him at a conference in Maryland
- “Greenberg, it’s beautiful!”

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Weinberg, ”The making of the standard model”

- ”At that time I did not have any faith in the existence of quarks.” (1967)

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Sources of skepticism

- Quarks had just been suggested.
- Fractional electric charges had never been seen.
- Gell-Mann himself was ambiguous.

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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.”

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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.

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Other solutions to the statistics paradox

- Explicit color SU(3), Han-Nambu, 1965
- Complicated antisymmetric ground state
- Quarks are not real anyway
- Other models

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Other solutions

- Explicit color SU(3)—Han-Nambu, 1965;
- Used three dissimilar triplets in order to have integer charges.
- “Introduce now eight gauge vector fields which behave as (1,8), namely as an octet in SU(3)''.”

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Color & electromagnetism commute

- Identical fractional electric charges allow color & electromagnetism to commute.
- Allows color to be an exact, unbroken, symmetry.
- Crucial part of understanding of quantum chromodynamics, QCD.

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Attempt to avoid a new degree of freedom

- Dalitz preferred a complicated ground state that would avoid the statistics problem.
- As rapporteur Dalitz always put a model with Fermi quarks first.
- The first rapporteur who preferred the parastatistics model was Harari, Vienna, 1968.

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Arguments for a simple ground state

- General theorems lead to an s-wave ground state.
- The simplest antisymmetric polynomial in the quark coordinates is

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Arguments for a simple ground state (continued)

Then not clear what to choose for excited states.

- The polynomial

vanishes because the coordinates are linearly dependent.

Adding pairs leads to unseen “exploding SU(3) states” that are not seen.

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Arguments for a simple ground state (continued)

- Zeroes in the ground state wave function would lead to
- zeroes in the proton electric and magnetic form factors, which are not seen.

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If quarks are not “real?”

- If quarks are just mathematical constructs, then their statistics is irrelevant.

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Other models

- Baryonettes, in which 9 objects (baryonettes) compose a hadron.
- Many other models.

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Work with Zwanziger, 1966

- We surveyed existing models and constructed new models to account for saturation.
- The only models that worked were the parafermi model, order 3, and the equivalent three-triplet or color SU(3) models.

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Equivalence as a classification symmetry

States that are bosons or fermions in the parafermi model, order 3,

are in

one-to-one correspondence with the states that are color singlets in the SU(3) color model.

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Relations and differences between the models

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Properties that require gauge theory

- Confinement
- S. Weinberg, 1973
- D.J. Gross and F. Wilczek, 1973
- H. Fritzsch, M. Gell-Mann and H. Leutwyler, 1973

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Properties that require gauge theory (continued)

- Asymptotic freedom, Gross, Wilczek, 1973

Politzer, 1973

- Reconciles quasi-free quarks of the parton model with confined quarks of low-energy hadrons

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Properties that require gauge theory (continued)

- Running of coupling constants and precision tests of QCD.
- Jets in high-energy collisions.

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Two facets of strong interaction

- Color as a classification symmetry and a global quantum number
- parafermi model (1964)
- was the first introduction of color as a global quantum number.
- SU(3) color as a local gauge theory
- Han-Nambu model (1965) was the first introduction of gauged SU(3) color.

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Outstanding puzzles of the standard model

- The reason for three generations of quarks and leptons,
- Origin of quark masses and the CKM matrix,
- Does the Higgs exist, if not what replaces it?

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Conclusion

- I reviewed the discovery of color, one of the properties of the “standard model.”
- Not clear where the next advances will come from—simple physical ideas or deep mathematically motivated concepts. Time, and new experimental data, will tell.

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