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December, 2004

Remarks on the History of Quantum Chromodynamics

Stephen L. Adler

Institute for Advanced Study

Princeton, NJ 08540

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Stephen L. Adler

Institute for Advanced Study

Einstein Drive, Princeton, NJ 08540

Phone 609-734-8051; FAX 609-924-8399; email [email protected] edu

ABSTRACT

I make some remarks on events leading to the final formulation of quantum chromodynamics, stimulated by the “Search and Discovery” article by Bertram Schwarzschild in the December, 2004 Physics Today. The following text with references is being submitted as a letter to the editor of Physics Today.

I read with appreciation Bertram Schwarzschild’s article about the richly deserved Nobel Prize won by David Gross, David Politzer, and Frank Wilczek for the discovery of asymptotic freedom. I am writing to point out significant inaccuracies and omissions in the historical account that Schwarzschild gives of the developments leading up to this work . Schwarzschild skips over important stages in the development of quantum chromodynamics by confusing scaling results obtained in 1969 with current algebra sum rules obtained four years earlier. Gell-Mann’s current algebra was a set of algebraic relations between currents, abstracted from a constituent quark model for hadrons, with the aim of allowing calculations of relations among the electromagnetic and weak processes coupling to these currents, without requiring details of the then unknown dynamics of the quarks. The principal sum rules testing aspects of the Gell-Mann current algebra were derived in 1965. The first, which depended only on the integrated axial-vector charge commutator, together with the PCAC (partially conserved axial current) hypothesis, was the “Adler–Weisberger” sum rule (and equivalent soft pion theorem) derived independently by Weisberger [1] and by me [2,3] in 1965. This related the nucleon axial-vector beta decay coupling to pion nucleon scattering cross sections, and was in good accord with experiment, giving great encouragement to the current algebra program. Many people entered the field, and a variety of experimentally verified current algebra/PCAC soft pion theorems were found. In my longer article about the sum rule [3], I noted that, by using my earlier observation [4] that forward neutrino reactions couple only to the divergences of the weak currents, the PCAC assumption could be eliminated. This led to relations involving cross sections for neutrino scattering with a forward-going lepton, that provided exact tests of the integrated charge commutation algebra. Soon afterwards, during a visit to CERN in the summer of 1965, Gell-Mann asked me whether I could make some comparable statement about the local current algebra. After considerable hard algebra, I discovered a sum rule [5] involving structure functions in deep inelastic neutrino scattering that directly tested the local Gell-Mann algebra. At zero momentum transfer squared , the axial-vector part of the neutrino sum rule reduced to the neutrino scattering form [3] of the Adler-Weisberger sum rule, and near , the vector part reduced to the sum rule obtained by Cabibbo and Radicatti [6] and others. My sum rule for neutrino scattering was soon afterwards converted into an inequality for deep inelastic electron scattering structure functions by Bjorken [7].

Although not directly tested until many years later [8], the neutrino sum rule had important conceptual implications that figured prominently in developments over the next few years. To begin with, it gave the first indications that deep inelastic lepton scattering could give information about the local properties of currents, a fact that at first seemed astonishing, but which turned out to have important extensions. Secondly, as noted by Chew in remarks at the 1967 Solvay Conference [9], the closure property tested in the sum rules, if verified experimentally, would suggest the presence of elementary constituents inside hadrons. In a Letter [10] published shortly after this conference, Chew argued that my sum rule, if verified, would rule out the then popular “bootstrap” models of hadrons, in which all strongly interacting particles were asserted to be equivalent (“nuclear democracy”). In his words, “such sum rules may allow confrontation between an underlying local spacetime structure for strong interactions and a true bootstrap. The pure bootstrap idea, we suggest, may be incompatible with closure.” In a similar vein, Bjorken, in his 1967 Varenna lectures [11], argued that the neutrino sum rule was strongly suggestive of the presence of hadronic constituents.

These conceptual developments still left undetermined the mechanism by which the neutrino sum rule, and Bjorken’s electron scattering inequality, could be saturated at large . In an analysis that I carried out with Gilman in 1966 of the saturation of the neutrino sum rule for small [12], we pointed out that saturation of the neutrino sum rule for large four-momentum transfer would require a new component in the deep inelastic cross section, that did not fall off with form-factor squared behavior. Bjorken became interested in the issue of how the sum rule could be saturated, and formulated several preliminary models that (in retrospect) already had hints of the dominance of a regime where the energy transfer grows proportionately to the value of . I summarized these pre-scaling proposals of Bjorken in the discussion period of the 1967 Solvay Conference [13] (which Bjorken did not attend), in response to questions from Chew and others as to how the neutrino sum rule could be saturated. The precise saturation mechanism was clarified some months later with the proposal by Bjorken [14] of scaling, and soon afterwards, with the experimental work at SLAC [15] on deep inelastic electron scattering.

The Bjorken scaling hypothesis, together with parton model ideas that were inspired by Feynman, led to powerful tools for studying deep inelastic scattering that greatly extended the scope of what could be obtained using only the Gell-Mann current algebra, precisely because more specific dynamical input was assumed. After the advent of the scaling hypothesis, Callan and Gross [16] used it to derive a proportionality relation between two of the deep inelastic structure functions, under the assumption of dominance by spin-1/2 constituents (partons in the later terminology), which was testable in electroproduction as well as neutrino experiments, without resort to the evaluation of sum rules. The Callan–Gross relation was one of a number of parton model relations that went beyond the results obtainable from current algebra. Within the parton model framework, the older current algebra results also received a new interpretation; for example, my neutrino sum rule could be recast as an integral over the partonic density of the third component of isospin, which is independent of because the proton is in an isospin 1/2 eigenstate.

Shortly after the Callan-Gross paper appeared, Tung and I [17], and independently Jackiw and Preparata [18], showed that in perturbation theory for quantum field theory there would be logarithmic deviations from the Callan-Gross relation. In other words, only free field theory would give exact scaling. In the memorable words of a seminar talk by Gell-Mann [19], in which he discussed work on light cone current algebra that he carried out with Fritzsch [20], “Nature reads the books of free field theory.” Recognition of this, together with the new renormalization group methods of Wilson, Callan, and Symanzik discussed in Schwarzschild’s article, set the stage for a search for field theories that would have almost free behavior, with the resulting discovery of asymptotic freedom of Yang-Mills theories as the only case that worked.

I also want to comment on the origins of the color hypothesis, leading up to its modern form – the tripling of the number of fractionally charged quarks – which was proposed as the solution to the wave function symmetry problem in the seminal paper of Bardeen, Gell-Mann, and Fritzsch [21]. (It was this paper that introduced the term “color” and marshaled additional experimental evidence, from neutral pion decay, and the hadron to muon production ratio at colliders, in its support.) In 1969 I gave a talk at the International Conference on High Energy Physics and Nuclear Structure, reviewing the consequences of the axial-vector anomaly [22] for decay, and as one of my closing remarks, I noted that whereas the fractionally charged quark model gave a decay amplitude a factor of 3 too small, the Han-Nambu model [23] with three triplets of integrally charged quarks supplied the missing factor of 3, giving a result in accord with experiment. At the end of my talk, a Russian physicist in the audience (I don’t remember who) came up and told me that Tavkhelidzde had also proposed tripling the quark degrees of freedom, and asked me to include the reference in the published version of my talk [24], which I did. Tavkhelidze’s paper, a published conference talk [25], dealt mainly with quark model mass and magnetic moment relations, but also noted that the -state wavefunction problem could be solved “if we introduce additional quantum numbers which antisymmetrize the total wave function. Employing these additional quantum numbers we are able to make the quark charges integer without violating the relations between the magnetic moments.” A similar observation was made in a paper of Miyamoto [26], cited in a later review by Tavkhelidze [27].

Of the papers with triplets of integrally charged quarks, only the Han-Nambu paper contemplated a possible dynamical role for octet vector gluons, and only this paper was widely known in the U. S. For example, Gell-Mann, in his plenary talk at the 1972 Fermilab (then National Accelerator Laboratory) conference [28], in which he discussed fractionally charged colored quarks as a simplification of Greenberg’s [29] parastatistics proposal, also mentions the alternative of integrally charged Han-Nambu quarks. In this same conference proceedings, as noted in a recent historical article of Wilson [30] (see also Fritzsch [31]), the first proposal of what we now know as QCD was given in the parallel session talk of Fritzsch and Gell-Mann [32]. This paper, in discussing the dynamical implications of color octet gluons, states: “If the gluons become a color octet, then we do not have to deal with a gluon field strength standing alone, only with its square, summed over the octet, and with quantities like , where the ’s are the eight 3x3 color matrices for the quark and the B’s are the eight gluon potentials.” Although the word Lagrangian is not mentioned, this is a complete description of the two terms that make up the QCD Lagrangian. Within a year after this talk, through the work of Gross, Politzer, and Wilczek, QCD was enthroned as the candidate field theory for the strong interactions.

In conclusion, I wish to acknowledge conversations with Tian-Yu Cao, and correspondence with Michela Massimi, that prompted me to look back at historical events leading up to the final formulation of quantum chromodynamics. This work was supported in part by the Department of Energy under Grant #DE–FG02–90ER40542.

REFERENCES [1] W. I. Weisberger, Phys. Rev. Lett. 14, 1047 (1965); Phys. Rev. 143, 1302 (1966). [2] S. L. Adler, Phys. Rev. Lett. 14, 1051 (1965). The various derivations of the sum rule given in refs. [1] and [2] included methods that used the infinite momentum frame limit introduced by S. Fubini and G. Furlan, Physics 1, 229 (1965). [3] S. L. Adler, Phys. Rev. 140, B736 (1965). [4] S. L. Adler, Phys. Rev. 135, B963 (1964). [5] S. L. Adler, Phys. Rev. 143, 1144 (1966). This paper presented three sum rules without addressing the issue of convergence; the convergent sum rule is the one discussed here. The other two sum rules (as I suspected at the time) were shown to be divergent, and so did not provide tests of the Gell-Mann algebra. [6] N. Cabibbo and L. Radicati, Phys. Rev. Lett. 19, 697 (1966). [7] J. D. Bjorken, Phys. Rev. Lett. 16, 408 (1966). [8] D. Allasia et al, Z. Phys. C 28, 321 (1985). [9] Fundamental Problems in Elementary Particle Physics (Proceedings of the Fourteenth Conference on Physics at the University of Brussels, October, 1967), Interscience Publishers, London, 1968. Chew’s remark, in response to my discussion of Bjorken’s models for saturation of the neutrino sum rule, is on page 212 of this proceedings. [10] G. F. Chew, Phys. Rev. Lett. 19, 1492 (1967). Chew also refers to a more general local current algebra sum rule derived by Fubini, the integrand of which is not expressible in terms of measurable structure functions. See S. Fubini, Nuovo Cimento 43 A, 475 (1966), based on methods of S. Fubini, G. Furlan, and C. Rossetti, Nuovo Cimento 40 A, 1171 (1965). [11] J. D. Bjorken, Current Algebra at Small Distances, in Proceedings of the International School of Physics ‘‘Enrico Fermi’’ Course XLI, J. Steinberger, ed., Academic Press, New York, 1968. See page 56 of this proceedings. [12] S. L. Adler and F. J. Gilman, Phys. Rev. 156, 1598 (1967). [13] S. L. Adler, untitled remarks on experimental tests of local current algebra, in the Solvay Conference proceedings of ref. [9] above, pp. 205-214. In these remarks I attributed the saturation models to Bjorken, but there is no preprint reference; I believe I learned of the models directly from Bjorken when we were both lecturers at the Varenna summer school in July, 1967 – see the remarks on page 63 of his lectures cited in ref. [11] above. [14] J. D. Bjorken, Phys. Rev. 179, 1547 (1969). [15] R. E. Taylor, Rev. Mod. Phys. 63, 573 (1991); H. W. Kendall, Rev. Mod. Phys. 63, 597 (1991); J. I. Friedman, Rev. Mod. Phys. 63, 615 (1991). [16] C. G. Callan, Jr. and D. J. Gross, Phys. Rev. Lett. 22, 156 (1969). [17] S. L. Adler and W.-K. Tung, Phys. Rev. Lett. 22, 978 (1969). [18] R. Jackiw and G. Preparata, Phys. Rev. Lett. 22, 975 (1969). [19] M. Gell-Mann, talk given at the Institute for Advanced Study, Princeton, 1971 (unpublished). See reference 10 of D. J. Gross and S. B. Treiman, Phys. Rev. D 4, 1059 (1971). [20] H. Fritzsch and M. Gell-Mann, Light Cone Current Algebra, talk at the 1971 Coral Gables Conference, extended into a preprint a few months later; reissued recently as arXiv: hep-ph/0301127. [21] W. A. Bardeen, H. Fritzsch, and M. Gell-Mann, Light-Cone Current Algebra, Decay, and Annihilation, in Scale and Conformal Symmetry in Hadron Physics, R. Gatto, ed., Wiley, New York (1973); reissued recently as arXiv: hep-ph/0212183. [22] S. L. Adler, Phys. Rev. 177, 2426 (1969; J. S. Bell and R. Jackiw, Nuovo Cimento 60 A, 47 (1969); S. L. Adler and W. A. Bardeen, Phys. Rev. 182, 1517 (1969). [23] M. Y. Han and Y. Nambu, Phys. Rev. 139, B1006 (1965). [24] S. L. Adler, Decay, in High-Energy Physics and Nuclear Structure, Proceedings of the Third International Conference on High Energy Physics and Nuclear Structure, S. Devons, ed., Plenum Press, New York (1970), pp. 647-655. See the remarks on p. 654. [25] A. Tavkhelidze, Higher Symmetries and Composite Models of Elementary Particles, in High Energy Physics and Elementary Particles, International Atomic Energy Agency, Vienna (1965), pp. 753-762. The quoted remark is on p. 758. [26] Y. Miyamoto, Three Kinds of Triplet Model, in Extra Number Supplement of Progress of Theoretical Physics: Thirtieth Anniversary of the Yukawa Meson Theory (1965), p. 187. [27] A. N. Tavkhelidze, Color, Colored Quarks, Quantum Chromodynamics, submitted to the International Seminar “Quarks-94”, Vladimir (1994); available in pdf and ps format through SPIRES. [28] M. Gell-Mann, General Status: Summary and Outlook, in Proceedings of the XVI International Conference on High Energy Physics; conference held at the University of Chicago and the National Accelerator Laboratory, Sept. 1972; see Vol. 4, p. 333 of the proceedings published by the National Accelerator Laboratory, Batavia, IL. [29] O. W. Greenberg, Phys. Rev. Lett. 13, 598 (1964). [30] K. G. Wilson, The Origins of Lattice Gauge Theory, hep-lat/0412043. [31] H. Fritzsch, A Time Dependence of QCD, hep-ph/0411391. [32] H. Fritzsch and M. Gell-Mann, Current Algebra: Quarks and What Else?, in Proceedings of the XVI International Conference on High Energy Physics; conference held at the University of Chicago and the National Accelerator Laboratory, Sept. 1972; see Vol. 2, p. 135 of the proceedings published by the National Accelerator Laboratory, Batavia, IL. The quoted remark is on p. 140.