50 Years of Quarks

The following sections are included:

• Preface
• Contents

If we assume that the strong interactions of baryons and mesons are correctly described in terms of the broken “eightfold way”, we are tempted to look for some fundamental explanation of the situation. A highly promised approach is the purely dynamical “boot trap” model for all the strongly interacting particles within which one may try to derive isotopic spin and strangeness conservation and broken eighfold symmetry from self-consistency alone. Of course, with only strong interactions, the orientation of the asymmetry in the unitary space cannot be specified; one hopes that in some way the selection of specific components of the F-spin by electromagnetism and the weak interactions determines the choice of isotopic spin and hyper-charge directions.…

In these lectures I want to speak about at least two interpretations of the concept of quarks for hadrons and the possible relations between them…

A short history of the physics of strongly interacting particles is presented. Events leading to the discovery, and eventual acceptance, of concrete quarks are described. (Other aspects of quark history are given in Refs. 1 and 2.)

This is my contribution to “50 Years of Quarks” written on the invitation from Prof. K. K. Phua and Prof. Harald Fritzsch to the 50th Jubilee of the discovery of quarks. It consists of two parts. In the first part I describe chronologically personal recollections from the years 1956–1980. The second part contains excerpts from my book “Particle Physics: The Quest for the Substance of Substance” published in 1985.

This is a personal, anecdotal and autobiographical account of my early endeavors in particle physics, emphasizing how they interwove with the conception and eventual acceptance of the quark hypothesis. I focus on the years from 1958, when my doctoral work at Harvard was completed, to 1970, when John Iliopoulos, Luciano Maiani and I introduced the GIM mechanism, thereby extending the electroweak model to include all known particles, and some that were not then known. I have not described the profound advances in quantum field theory and the many difficult and ingenious experimental efforts that undergird my story which is not intended to be an inclusive record of this exciting decade of my discipline. My tale begins almost two years before I met Murray and over five years before the invention of quarks…

The quark model emerged from the Gell-Mann–Ne'eman flavor SU(3) symmetry. Its development, in the context of strong interactions, took place in a heuristic theoretical framework, referred to as the Bootstrap Era. Setting the background for the dominant ideas in strong interaction of the early 1960s, we outline some aspects of the constituent quark model. An independent theoretical development was the emergence of hadron duality in 1967, leading to a realization of the Bootstrap idea by relating hadron resonances (in the s-channel) with Regge pole trajectories (in t- and u-channels). The synthesis of duality with the quark-model has been achieved by duality diagrams, serving as a conceptual framework for discussing many aspects of hadron dynamics toward the end of the 1960s.

Attempts to understand the plethora of meson baryon and meson resonances by the introduction of symmetries, which led to the invention of quarks and the quark model, and finally to the formulation of QCD, are described.

In the period 1968–1974 I was a graduate student and then a postdoc at Caltech and was involved with the developments of the quark and parton models. Most of this time I worked in close contact with Richard Feynman and thus was present from the parton model was proposed until QCD was formulated. A personal account is presented how the collaboration took place and how the various stages of this development looked like from the inside until QCD was established as a theory for strong interactions with the partons being quarks and gluons.

We are used to thinking of quarks as fundamental particles in the same way we think of the electron, or gauge bosons, neutrinos, leptons. In strong theory, these objects are unified with gravitation and the physics of spacetime into what is hoped to be an ultimate theory, string/M theory. The string/M theory paradigm completely changes the way we think of the socalled elementary particles in quantum field theory.

I briefly review the conceptual developments that led to the Standard Model and discuss some of its remarkable qualitative features. On the way, I draw attention to several puzzling aspects that are beyond the reach of our present understanding of the basic laws of physics.

In the decade after 1950 many new particles were discovered, in particular the four Δ resonances, the six hyperons and the four K mesons. The Δ resonances were observed in pion–nucleon collisions at the Radiation Laboratory in Berkeley. The hyperons and K mesons were discovered in cosmic-ray experiments. They were called “strange particles.”…

Soon after the postulation of quarks, it was suggested that they interact via gluons, but direct experimental evidence was lacking for over a decade. In 1976, Mary Gaillard, Graham Ross and the author suggested searching for the gluon via 3-jet events due to gluon bremsstrahlung in e⁺e⁻ collisions. Following our suggestion, the gluon was discovered at DESY in 1979 by TASSO and the other experiments at the PETRA collider.

This article “Discovery of the Gluon” is dedicated to Professor Chen Ning Yang. The Gluon is the first Yang Mills non-Abelian gauge particle discovered experimentally. The Yang Mills non-Abelian gauge field theory was proposed by Yang and Mills in 1954, sixty years ago.

The experimental discovery of the first Yang–Mills non-Abelian gauge particle — the gluon — in the spring of 1979 is summarized, together with some of the subsequent developments, including the role of the gluon in the recent discovery of the Higgs particle…

This is a review of the program we started in 1968 to understand and generalize Bjorken scaling and Feynman's parton model in a canonical quantum field theory. It is shown that the parton model proposed for deep inelastic electron scatterings can be derived if a transverse momentum cutoff is imposed on all particles in the theory so that the impulse approximation holds. The deep inelastic electron–positron annihilation into a nucleon plus anything else is related by the crossing symmetry of quantum field theory to the deep inelastic electron–nucleon scattering. We have investigated the implication of crossing symmetry and found that the structure functions satisfy a scaling behavior analogous to the Bjorken limit for deep inelastic electron scattering. We then find that massive lepton pair production in collisions of two high energy hadrons can be treated by the parton model with an interesting scaling behavior for the differential cross-sections. This turns out to be the first example of a class of hard processes involving two initial hadrons.

The Baryon–Lepton difference (B–L) is increasingly emerging as a possible new symmetry of the weak interactions of quarks and leptons as a way to understand the small neutrino masses. There is the possibility that current and future searches at colliders and in low energy rare processesmay provide evidence for this symmetry. This paper provides a brief overview of the early developments that led to B–L as a possible symmetry beyond the standard model, and also discusses some recent developments.

The fact that quarks of the same electric charge possess a mass hierarchy is a big puzzle in particle physics, and it must be highly correlated with the hierarchy of quark flavor mixing. This chapter is intended to provide a brief description of some important issues regarding quark masses, flavor mixing and CP-violation. A comparison between the salient features of quark and lepton flavor mixing structures is also made.

The current status of determinations of the QCD running quark masses is reviewed. Emphasis is on recent progress on analytical precision determinations based on finite energy QCD sum rules. A critical discussion of the merits of this approach over other alternative QCD sum rules is provided. Systematic uncertainties from both the hadronic and the QCD sector have been recently identified and dealt with successfully, thus leading to values of the quark masses with unprecedented accuracy. Results currently rival in precision with lattice QCD determinations.

After a short review of the activities of Shoichi Sakata and his group, how the six-quark model explains CP violation is described. Experimental verification of the model at the B-factories is also briefly discussed.

The present performance of the constituent-quark model as an effective tool to describe low-energy hadrons on the basis of quantum chromodynamics is exemplified along the relativistic constituent-quark model with quark dynamics relying on a realistic confinement and a Goldstone-boson-exchange hyperfine interaction. In particular, the spectroscopy of all known baryons is covered within a universal model in good agreement with phenomenology. The structure of the nucleons as probed under electromagnetic, weak, and gravitational interactions is produced in a correct manner. Likewise, the electroweak form factors of the baryons with u, d, and s flavor contents, calculated so far, result reasonably. Shortcomings still remain with regard to hadronic resonance decays.

I discuss accurate theoretical predictions for masses of baryons containing the b quark. I point out an approximate effective supersymmetry between heavy quark baryons and mesons and provide predictions for the magnetic moments of Λ_c and Λ_b. Proper treatment of the color-magnetic hyperfine interaction in QCD is crucial for obtaining these results. Closely related methods are then applied to doubly-heavy hadrons: the recently observed exotic mesons and QQq baryons. Predictions are given for the masses and decay modes of additional mesons and of QQq baryons: Ξ_cc(ccq), Ξ_bb(bbq) and Ξ_bc(bcq), which might soon be seen experimentally, as indicated by the large number of B_c mesons observed by LHCb.

From 7 GeV/c pions to 600 GeV/c jets, the wonderful journey from the “old days” of Feynman–Field collider phenomenology to the Tevatron and the LHC…

I review the historical development of QCD predictions for exclusive hadronic processes, beginning with constituent counting rules and the quark interchange mechanism, phenomena which gave early validation for the quark structure of hadrons. The subsequent development of pQCD factorization theorems for hard exclusive amplitudes and the development of evolution equations for the hadron distribution amplitudes provided a rigorous framework for calculating hadronic form factors and hard scattering exclusive scattering processes at high momentum transfer. I also give a brief introduction to the field of “light-front holography” and the insights it brings to quark confinement, the behavior of the QCD coupling in the nonperturbative domain, as well as hadron spectroscopy and the dynamics of exclusive processes.

At temperatures above about 150 MeV and energy densities exceeding 500 MeV/fm³, quarks and gluons exist in the form of a plasma of free color charges that is about 1000 times hotter and a billion times denser than any other plasma ever created in the laboratory. This quark–gluon plasma (QGP) turns out to be strongly coupled, flowing like a liquid. About 35 years ago, the nuclear physics community started a program of relativistic heavy-ion collisions with the goal of producing and studying QGP under controlled laboratory conditions. This article recounts the story of its successful creation in collider experiments at Brookhaven National Laboratory and CERN and the subsequent discovery of its almost perfectly liquid nature, and reports on the recent quantitatively precise determination of its thermodynamic and transport properties.

A nonperturbative understanding of neutral pion decay was an essential step towards the idea that strong interactions are governed by a color gauge theory for quarks. Some aspects of this work and related problems are still important.

We review physical scenarios in different vacua of 𝒩 = 2 supersymmetric QCD deformed by the mass term μ for the adjoint matter. This deformation breaks supersymmetry down to 𝒩 = 1 and, at large μ, the theory flows to 𝒩 = 1 QCD. We focus on dynamical scenarios which can serve as prototypes of what we observe in real-world QCD. The so-called r = N vacuum is especially promising in this perspective. In this vacuum an “instead-of-confinement” phase was identified previously, which is qualitatively close to the conventional QCD confinement: the quarks and gauge bosons screened at weak coupling, at strong coupling evolve into monopole–antimonopole pairs confined by non-Abelian strings. We review genesis of this picture.

Quarks were introduced 50 years ago opening the road towards our understanding of the elementary constituents of matter and their fundamental interactions. Since then, a spectacular progress has been made with important discoveries that led to the establishment of the Standard Theory that describes accurately the basic constituents of the observable matter, namely quarks and leptons, interacting with the exchange of three fundamental forces, the weak, electromagnetic and strong force. Particle physics is now entering a new era driven by the quest of understanding of the composition of our Universe such as the unobservable (dark) matter, the hierarchy of masses and forces, the unification of all fundamental interactions with gravity in a consistent quantum framework, and several other important questions. A candidate theory providing answers to many of these questions is string theory that replaces the notion of point particles by extended objects, such as closed and open strings. In this short note, I will give a brief overview of string unification, describe in particular how quarks and leptons can emerge and discuss what are possible predictions for particle physics and cosmology that could test these ideas.

We formulate an SU(8) family unification model motivated by requiring that the theory should incorporate the graviton, gravitinos, and the fermions and gauge fields of the standard model, with boson.fermion balance. Gauge field SU(8) anomalies cancel between the gravitinos and spin ½ fermions. The 56 of scalars breaks SU(8) to SU(3)_family×SU(5)×U(1)/Z₅, with the fermion representation content needed for “flipped” SU(5) with three families, and with residual scalars in the 10 and representations that break flipped SU(5) to the standard model. Dynamical symmetry breaking can account for the generation of 5 representation scalars needed to break the electroweak group. Yukawa couplings of the 56 scalars to the fermions are forbidden by chiral and gauge symmetries, so in the first stage of SU(8) breaking fermions remain massless. In the limit of vanishing gauge coupling, there are N = 1 and N = 8 supersymmetries relating the scalars to the fermions, which restrict the form of scalar self-couplings and should improve the convergence of perturbation theory, if not making the theory finite and “calculable.” In an Appendix we give an analysis of symmetry breaking by a Higgs component, such as the (1, 1)(−15) of the SU(8) 56 under SU(8) ⊃ SU(3) × SU(5) × U(1), which has nonzero U(1) generator.