“Three Quarks for Muster Mark!” – James Joyce, Finnigan’s Wake

Fifty years ago today, the journal Physics Letters received a paper from Murray Gell-Mann entitled “A Schematic Model of Baryons and Mesons”.¹ The brief two page paper introduced the concept of “quarks” as the constituent particles of hadrons. As is generally the case with new discoveries, this one did not emerge all at once overnight.

The Particle Zoo and Strangeness

[Note: Much of this section summarizes portions of the first chapter of David Griffiths’ Introduction to Elementary Particles.]

In the decades following World War 2, spurred by the Cold War’s nuclear arms race, particle physicists had been building more and more powerful particle accelerators, as well as more sensitive particle detection technology to use in conjunction with those accelerators, as well as for use in the study of cosmic rays and the radiation from nuclear reactors. In this booming period of research, something unexpected happened. New particles were being discovered at a rapid pace. The simple pre-war world of just electrons, protons, and neutrons had exploded into a particle zoo of exotic, short-lived particles that existing physical models simply could not account for.

This proliferation began in 1947 with the first detection of mesons, specifically charged pions, in cosmic rays by Cecil Powell, César Lattes, Giuseppe Occhialini, et al.² Later that same year, Rochester and Butler observed the production by cosmic rays of neutral mesons which then decayed into two oppositely-charged pions via the interaction $K^{0}\rightarrow\pi^{+} + \pi^{-}$ . This became known as the neutral kaon.³ In 1949, Powell identified a charged kaon, decaying as $K^{+}\rightarrow\pi^{+} + \pi^{+} + \pi^{-}$ .⁴

In 1950, another odd particle joined the particle zoo. Discovered by Hopper and Biswas, the $\Lambda$ particle (decaying as $\Lambda \rightarrow p^{+} + \pi^{-}$ ) appeared to be heavier than the proton, and was thus classified as a baryon rather than a meson.⁵ This classification was also necessary to preserve the conservation of baryon number that had been proposed by Stueckelberg in 1938 to explain the stability of protons.

And so it went, with even more mesons ( $\eta$ , $\phi$ , $\omega$ , $\rho$ ) and heavy baryons (the $\Sigma$ ‘s, the $\Xi$ ‘s, the $\Delta$ ‘s, and so forth) being discovered in the ensuing years, with the rate of discovery being ramped up by Brookhaven’s Cosmotron accelerator coming online in 1952, followed by others.

One interesting property exhibited by these “strange” new particles (as they were referred to by particle physicists) is that, while they appear to be formed via rather quick interactions (on the scale of 10^-23 seconds), the decays are relatively slow (on the order of 10^-10 seconds). Pais⁶ and others proposed that this could be due to the creation and decay of these particles being mediated by different mechanisms, and that strange particles have to be produced in pairs. In modern parlance, the creation of these particles is mediated by the strong nuclear force, while their decay is mediated by the weak nuclear force. In 1953, Gell-Mann^7,8 and Nishijima^9,10 expanded upon this idea, assigning to each particle a new quantum number which Gell-Mann dubbed “strangeness.” In this new scheme, strangeness is a conserved quantity in strong interactions, but not in weak interactions.

The Eightfold Way

The next step on the road to the quark model involved corralling this particle zoo into some semblance of order. In 1961, Gell-Mann¹¹ and Yuval Ne’eman^12,13 concurrently applied the principles of group theory to analyze the relationships between these particles in terms of the SU(3) special unitary symmetry group. Gell-Mann famously referred to his scheme as the “Eightfold Way,” in reference to the Noble Eightfold Path of Buddhism.

Rather than diving into the rather esoteric mathematics of group theory, let us take a look at the symmetries involved using a graphical format, plotting the particles in various groupings (by particle family and spin) in terms of strangeness vs. charge. (Actually, we are graphing strangeness vs. a projection of the third component of isospin, with the charges lining up on diagonals.) This is the most common method of presenting the Eightfold Way, although these graphs never appeared in Gell-Mann’s original paper. Instead, he represented these relationships in a matrix format.

The spin 0 pseudoscalar meson nonet. (Illustration by the author.)

The spin 1/2 baryon octet. (Illustration by the author.)

The spin 3/2 baryon decuplet. (Illustration by the author.)

Note the particle at the bottom of the baryon decuplet. At the time that Gell-Mann wrote his paper on the Eightfold Way, that particle had not yet been detected. At a 1962 meeting at CERN where the discovery of the cascade or $\Xi$ baryons was announced, Gell-Mann predicted that a baryon with a strangeness of -3 and charge of -1 would be discovered, as well as predicting what its mass would be. Sure enough, the $\Omega^-$ particle was subsequently observed in 1964 at Brookhaven, with precisely the properties predicted by Gell-Mann.¹⁴

I feel somewhat obligated to point out here that papers from this time period frequently make reference to a value called “hypercharge,” which originally referred to the sum of strangeness and baryon number. This value is generally considered obsolete.

Quarks, Aces, & Partons

With a framework in place for organizing and mathematically analyzing the particle zoo, it did not take much longer for Gell-Mann to construct his quark model, which brings us to his 1964 paper. He postulated the existence of three new fundamental particles, the up quark (S=0, Q=2/3), the down quark (S=0, Q=-1/3), and the strange quark (S=-1, Q=-1/3), as well as corresponding anti-quarks with opposite strangeness and charge values. (The word “quark” was taken from the James Joyce line quoted at the top of this article.) He further postulated that baryons all consist of triplets of quarks or anti-quarks, and that mesons all consist of quark/anti-quark pairs. (In modern quark theory, it is understood that these particles all consist of a large number of quarks, with virtual quark/anti-quark pairs constantly being created and annihilated, but always with an excess of either two or three “valence quarks.”)

Let us take another look at our Eightfold Way diagrams with the constituent quarks for each particle labelled (u=up, d=down, s=strange). Note that the degenerate states at the center of the meson nonet consist of superpositions of quark states.

The spin 0 pseudoscalar meson nonet, with quark composition. (Illustration by the author.)

The spin 1/2 baryon octet, with quark composition. (Illustration by the author.)

The spin 3/2 baryon decuplet, with quark composition. (Illustration by the author.)

At about the same time, George Zweig, a researcher at CERN who had previously been a student of Richard Feynman, had independently constructed an almost identical model for the composition of hadrons. However, due to CERN policies in place at the time regarding the approval of papers submitted for publication, he was unable to get his paper published in a timely manner. Fortunately, his work survives in the form of internal CERN preprints.¹⁵ In Zweig’s model, the constituent particles of hadrons were called “aces.”

In the late 60’s, in an effort to explain experimental data related to deep inelastic scattering experiments, Richard Feynman developed what he called his “parton” model of hadrons. Eventually, it came to be realized that Feynman’s partons were simply quarks travelling at relativistic velocities. What Gell-Mann had arrived at through studying symmetry, Feynman had arrived at by studying hadron cross sections.

It is worth noting that Gell-Mann didn’t consider quarks to be actual particles. For him, they were a convenient mathematical abstraction. However, Feyman’s parton work made it quite clear that quarks were actual “things.”

Next Time

In Part II, we’ll dig into the experimental confirmation of the existence of quarks, gluons, color charge, the charm, top, and bottom quarks, and the development of quantum chromodynamics. Stay tuned.

References

1. M. Gell-Mann, “A Schematic Model of Baryons and Mesons”, Phys. Lett.8:214 (1964).

2. Occhialini, G.P.S. and Powell, C.F., “Nuclear Disintegrations Produced by Slow Charged Particles of Small Mass“, Nature 159, 186-190 (1947)

3. Rochester, G.D. and Butler, C.C., “Evidence for the existence of new unstable elementary particles“, Nature, 160, 855 (1947)

4. F. Powell et al., “Observations with Electron-Sensitive Plates Exposed to Cosmic Radiation“, Nature 163, 82-87 (1949)

5. Hopper, V.D. and Biswas, S., “Evidence Concerning the Existence of the New Unstable Elementary Neutral Particle“. Phys. Rev. 80: 1099. (1950)

6. Pais, A., “Some Remarks on the V-Particles“, Phys. Rev., 86, 663-672 (1952). DOI: 10.1103/PhysRev.86.663

7. Gell-Mann, M., “Isotopic Spin and New Unstable Particles“, Phys. Rev. 92, 833 (1953). Bibcode:1953PhRv…92..833G. doi: 10.1103/PhysRev.92.833

8. Gell-Mann, M., “The Interpretation of the New Particles as Displaced Charged Multiplets“, Il Nuovo Cimento, 4 (Supplement 2), 848 (1956). DOI: 10.1007/BF02748000

9. Nakano, T. and Nishijima, N., “Charge Independence for V-particles“. Progress of Theoretical Physics 10 (5): 581 (1953). Bibcode:1953PThPh..10..581N. doi: 10.1143/PTP.10.581.

10. Nishijima, K., “Charge Independence Theory of V Particles“. Progress of Theoretical Physics 13 (3): 285 (1955). Bibcode:1955PThPh..13..285N.doi:10.1143/PTP.13.285

11. Gell-Mann, M. , “The Eightfold Way: A Theory of Strong Interaction Symmetry“, DOE Technical Report, March 15, 1961

12. Ne’eman, Y., “Derivation of Strong Interactions from a Gauge Invariance,” Nucl Phys, 26, 222-229 (1961). DOI: 10.1016/0029-5582(61)90134-1

13. Ne’eman, Y., “Gauges, Groups And An Invariant Theory Of The Strong Interactions” Tel-Aviv : Israel At. Energy Comm. (Aug. 1961) 213 pages

14. Barnes, V. E. et al., “Observation of a Hyperon with Strangeness Minus Three”. Physical Review Letters 12 (8): 204 (1964). Bibcode: 1964PhRvL..12..204B. doi:10.1103/PhysRevLett.12.204.

15. Zweig, G., “An SU3 model for strong interaction symmetry and its breaking“, internal CERN pre-prints, 1964.