Elementary Particles


I have already mentioned that quarks have some bizarre characteristics. It is now time to review them.

Particle physics was in a state of confusion during the 1960s. With the advent of new high energy particle accelerators and particle detectors, a large number of hadrons were discovered by the 1960, and it was unclear how these various particles were related to each other.

In 1961 a classification scheme called the Eightfold way was developed by Murry Gell-Mann for these newly discovered particles. We will talk about the Eightfold way, later, when we discuss the role of symmetry in physics. The Eightfold way, much like the periodic table of the elements, not only provided a semblance of order for these newly discovered particles, but it also predicted the existence of particles that not had yet been discovered (all of those predicted particles were discovered later). But the question was: Why is this classification scheme so successful?

In 1964, Gell-Mann and George Zweig independently proposed quarks as the building blocks of hadrons, because they realized that quarks could be the basis of this classification scheme. Initially, the quark model had three types of quarks: the up, down, and the strange. The up quark has a charge +2/3, the down quark has -1/3 and the strange quark has -1/3. While the quark model was very successful in accounting for all the known hadrons, it raised more questions than answers, particularly during the early days of its introduction. Fractional charges were really strange and unacceptable to many because no particle in nature was ever found with a fractional charge. So the general point of view in 1966 was that quarks were most likely just mathematical devices, useful but not real.

All that changed in 1968, when the results from the electron-proton scattering experiments conducted at the Stanford Linear Accelerator Center (SLAC) by Jerome Friedman, Henry Kendall, and Richard Taylor showed a pattern of rare large angle scattering of the electrons. The incoming electron passed through the proton without much deviation. But occasionally an electron scattered with a large angle from one of the “constituents”. The physicists inferred that the protons are indeed made up of three compact constituents called quarks. The experimentalists were originally not able to determine if these “point-like constituents” had the correct fractional charges. Determining the fractional charge proved to be a much more difficult problem and the answer came when the results were compared with the neutrino scattering measurements conducted at CERN which demonstrated without a doubt that the quark model was correct. Physicists who strongly doubted the existence of quarks finally had to accept them as real.

Friedman, Kendall, and Taylor were jointly awarded the 1990 Nobel Prize in physics “for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics”.


Physicists were slow in accepting the quark model mainly because quarks were never seen as isolated particles outside of the nucleus. In addition, accelerator experiments revealed the existence of short-lived particles such as \Delta^{++} and \Delta^- made up only of up quarks (uuu) and down quarks (ddd), respectively. Their existence seemed to violate the Pauli Exclusion Principle according to which no two identical spin-half particles can have the same set of quantum numbers in the same state. But the quarks are indeed spin-half particles having the same set of quantum numbers in the uuu and ddd combinations.

In 1965, Moo-Young Han of Duke University, Yoichiro Nambu of the University of Chicago and Oscar Greenberg of the University of Maryland at College Park found a way out of this predicament. Their proposal was to introduce a new quantum number that made the quarks distinguishable. The new quantum number was called color charge. Quarks come in three different “colors” and only mix in such ways as to form colorless objects. For example, a proton is made up of two up quarks and a down quark (see Figure 3-1). One of those quarks will be red, one will be blue, and the other will be green; together they will make white, which is colorless. In case of the \Delta^{++}, each quark type could exist in three color states, e.g. u-red, u-green and u-blue, so that the combination no longer violated the Pauli principle. The requirement that only color-neutral objects can exist as free particles explained the occurrence of bosons (three quarks). Antiparticles would carry anticolor so that the quark–antiquark combination in mesons could also be color-neutral.


So we see all observed particles in nature are color neutral. But why are quarks never found in free state? The simple answer is, if one tries to pull apart a color neutral hadron, a spray of new hadrons are produced which are color neutral themselves.


Let’s explore this idea in details. We know the gluons are the carrier particles of the strong force. The color-force field inside the hadrons consists of gluons holding the quarks together. The quarks can move freely inside hadrons and exchange gluons continuously. If one of the quarks in a given hadron is pulled apart, as is done in high energy accelerators, the color-force field “stretches” between that quark and its neighbors. More and more energy is pumped into the color-force field as the quark is pulled with greater force. At some point, it is energetically advantageous for the color-force field to break into a new quark-antiquark pair. The energy is conserved because the energy of the color-force field is converted into the mass of the new quarks, and the color-force field can revert back to the normal state.


On the other hand, the SLAC deep-inelastic scattering experiments were still puzzling. It was as if the quarks inside a proton are nearly free and not subject to any force. The higher the energy of the electron beam, the more the electrons “reacted” as if they were encountering particles moving freely inside the proton. But when the distance between two quarks increased, the force became greater—an effect analogous to the stretching of a rubber band. Physicists coined the term “asymptotic freedom” to describe the way quarks seemed to interact more and more feebly at higher energies. In 1969 Richard Feynman proposed his “parton” model to describe the dynamics, in which a nucleon is composed of a number of point-like constituents called partons. Feynman’s partons were later identified as quarks and gluons. Interestingly, Feynman’s arrived at his parton picture while trying to interpret the SLAC data, while Gell-Mann’s quark idea came from the notions of symmetry.

But there seemed to be a contradiction between asymptotic freedom and quark confinement. How could nuclear forces be both strong enough to account for the permanent confinement of quarks and weak enough to be asymptotically free inside the hadrons?

David Gross, then at Princeton University, and his graduate student Frank Wilczek, and independently, David Politzer, then a graduate student at Harvard University, discovered why quarks behave almost as free particles only at high energies and why on the other hand, is it so difficult to dislodge a free quark from its hadron casing. At the beginning, Gross and Wilczek did not expect asymptotic freedom could be a feature of any legitimate quantum theory of particle interactions. Surprisingly, they found the exact opposite to be true. They discovered a class of theories in which the strength of the interaction becomes steadily smaller at shorter distances. David Politzer independently came to the same conclusion. Their papers appeared back-to-back in Physical Review Letters (PRL).


The strength of an interaction depends on a factor called the “coupling constant”, denoted by \alpha_s. Figure 6-2 shows a compilation of \alpha_s obtained from many different experiments, versus the energy μ of the exchanged gluons, plotted on a logarithmic scale (gluon energy is measured in GeV). Notice that at lower energies, or longer distances, the value of \alpha_s gets progressively higher. At very low energies or at very large distances, \alpha_s essentially is infinite (not shown in this diagram), while at very high energies when the quarks are squeezed very close together, \alpha_s, or the strength of their interaction becomes progressively weaker. This quintessentially is asymptotic freedom as theorized by Gross, Politzer, and Wilczek. Quarks are confined inside hadrons and cannot be liberated as free particles. At high enough energies a struck quark will “hadronize” by combining as a quark triplet or a quark-antiquark pair.

Although a complete theoretical proof for absolute quark confinement does not exist even today, most physicists find Gross, Politzer, and Wilczek’s theoretical arguments convincing. The discovery laid the foundation for theory of the color interaction (or Quantum Chromo Dynamics, QCD) and the 2004 Nobel Prize in physics was awarded jointly to David J. Gross, H. David Politzer and Frank Wilczek “for the discovery of asymptotic freedom in the theory of the strong interaction”.

It turns out that QCD is mathematically remarkably similar to QED. In QED, the force between two electrically charged particles is mediated by the exchange of a photon between the two charged particles while in QCD, the quarks carry a different kind of charge, the color charge, and the force between two colored particles is mediated by the exchange of a gluon. The crucial difference is that while the photons of QED carry no charge, the gluons of QCD carry the color charge. A quark is surrounded by a sea of “virtual” gluons arising due to quantum fluctuations. In QED, the quantity α = e²/4π is called the fine structure constant, a dimensionless number whose value is ≈ 1/137. In QCD α is not a constant—it decreases with increasing momentum and its distribution demonstrates the main characteristics of strong interaction.

QCD also explained another odd aspect of hadrons. If you tally the masses of constituent quarks, you will find only a very small part of the mass of a hadron is actually due to the individual quarks. QCD indicated that proton’s mass, for example, arises because of the energy tied up in the strong binding of the three quarks.

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