The experimentalists appreciated that Bjorken had made an important discovery, but a fuller understanding of the experimental results came about only when Richard Feynman visited SLAC in 1968 and invented what he called the “parton model” of strong interactions.6 The partons were hard objects being hit by the electrons inside the proton, and Feynman was able to explain Bjorken’s scaling result using this model. I discuss the parton model in more detail later in this chapter. Eventually, Feynman’s partons were identified with Gell-Mann’s quarks. Further experiments at SLAC, Brookhaven National Laboratory, and CERN were able to reveal the need for the quarks to have fractional electric charge.
In light of all this experimental evidence, there was a growing impetus for particle physicists to accept that the quarks were real particles and not some fictitious mathematical notion. Gell-Mann was also eventually convinced that his quarks were real. However, why were the fractionally charged quarks not seen as independent particles experimentally? Why were they only able to be detected indirectly inside the protons and neutrons, when electrons bounced off them? In fact, how were they confined inside the protons and neutrons? Answering these questions led to an important turning point in the development of particle physics, and eventually the quark model and the parton model were subsumed in quantum field theory based on the gauge principle.
The strange physical contradiction between the quarks and gluons of quantum chromodynamics (QCD)7 and the old particles of nuclear physics, such as protons, neutrons, and electrons, is that the latter particles can be detected directly either by ionization of nuclei producing electrons or by high-energy accelerators. The fact that one cannot detect quarks and gluons directly as free particles outside the proton was initially considered a failure of the QCD theory. It has not yet been possible to derive a theory of quark and gluon confinement from first principles in QCD. That is, it has not been possible to provide a convincing explanation about why the quarks and gluons appear to be trapped within the nucleus and invisible to detection. Instead of obtaining an explanation of confinement from the basic mathematical formulas of QCD, physicists have been forced to come up with a somewhat ad hoc phenomenological explanation added in by hand. However, in the current particle physics community, this problem is simply ignored, and the hidden quarks and gluons are detected indirectly through hadronizing jets appearing as events after the collisions of protons with protons or with antiprotons. These jets consist of streams of hadrons (the particles that contain quarks and gluons), which, when analyzed, tell you which jet is associated with which quark in the detection process. Although the mystery of confinement has been, to some extent, set aside by the theoretical and experimental particle physics community, it still remains a problem that has to be resolved eventually to make QCD a convincing theory.
TRYING TO MAKE SENSE OF QUARKS
Along with the mystery of “quark confinement,” there was another serious problem in understanding the nature of quarks. The proton and neutron were made of different combinations of three up quarks and down quarks. However, these up and down quarks looked identical as far as the quantum spin ½ is concerned. According to Pauli’s exclusion principle, which he discovered during the development of quantum mechanics during the 1920s, three fermions of spin ½ (such as quarks) cannot occupy the same quantum state to make up the proton. Something was wrong. It’s like attempting to put three unruly identical triplets into a playpen, but each one refuses to be in the same space with the other two. If you try to put three of these up and down quarks into the same quantum state inside the proton and neutron, this would violate quantum statistics and Pauli’s exclusion principle. Theoretical physicist Walter Greenberg proposed a way of solving this conundrum. He changed the nature of the quantum statistics for the quarks, calling the new statistics “parastatistics,” which allowed one to get around the problem with the Pauli exclusion principle for the quarks. To follow through with the analogy of the triplets, Greenberg proposed to put them in a newly constructed playpen in which they were comfortable with one another. By changing the quantum statistics, he managed to get the three quarks in the same quantum state. However, this was a somewhat radical solution to the problem.
Then, Yoichiro Nambu and Moo Young Han proposed yet another radical idea. They invented a new kind of charge associated specifically with quarks in order to bypass the problem of the Pauli exclusion principle. Murray Gell-Mann and Harald Fritzsch proposed that this new charge be called “color charge.” Now, each up and down quark could have one of three “colors”—red, blue, or green. These colors are, of course, not real colors, but are simply used as labels for the new charge. This proposal provided, in effect, three times more quarks for nature to choose from when building particles. The observed hadrons such as baryons and mesons were termed colorless or white, indicating that their color charges always combined to make the observed hadrons color-neutral.
In collaboration with Swiss physicist Heinrich Leutwyler, Gell-Mann and Fritzsch discovered the mathematical theory underlying the colored quarks. They bound the three colored quarks in the proton by massless force carriers that they called gluons, which in turn had their own colors. The mathematical symmetry group describing these colored quarks and gluons was SU(3), but this was a different kind of SU(3) from Gell-Mann’s original Eightfold Way SU(3). The different kinds of quarks and leptons are named by their “flavors.” The three flavors of quarks known during the late 1960s—up, down, and strange—constituted the fundamental triplet of SU(3), whereas the gluon force carriers were represented by the octet of SU(3). In contrast to the colorless photon of electromagnetism, each gluon is a combination of two colors of the three possible colors, to produce eight colored gluons.
In keeping with the fashion among particle physicists of giving fancy titles to particles and theories, Gell-Mann christened the new theory of colored quarks and gluons quantum chromodynamics, using the Greek word chromo, which means “color.” To accommodate the fact that quarks were always confined and never seen experimentally in high-energy collisions, the hadrons, which are the particles that undergo strong interactions such as protons and neutrons, were colorless and were described as color singlets in QCD. In other words, the colored quarks were always combined to produce a colorless hadron. For example, in the mesons, which are composed of a quark and an antiquark, a red quark combines with an anti-red quark to produce a colorless meson. And in the proton, a red, green, and blue quark combine to produce a colorless proton. This means that the hadrons we observe in accelerators do not reveal the colored quarks, which are confined inside them. This, of course, does not explain the dynamics of confinement, and how they came to be that way, but simply indicates the fact that we cannot observe free quarks. The dynamic mechanism of confinement is still a controversial issue in particle physics. (See Figure 1.5 for a summary of the elementary particles of the standard model, and Figure 1.6 for a description of the quark colors.)
FOUR, FIVE, AND SIX QUARKS FOR MUSTER MARK!
James Bjorken and Sheldon Glashow published a paper in 1964 predicting the existence of a fourth quark, which they called the “charm” quark.8 The four quarks were represented by the fundamental quartet representation of SU(4), which replaced the triplet representation of SU(3). I also came up with the prediction that a fourth quark should exist, and published a paper in Physical Review in 1965,9 with a fractionally charged fourth quark and fractional baryon number. Bjorken and Glashow’s fourth quark had integer charge and baryon number because it was still early days for physicists to accept the idea that quarks were fractionally charged. I called my additional fractionally charged quark simply the “fourth quark,” not nearly as flashy as “charm.”
Figure 1.5 The elementary particles of the standard model of particle physics. The quarks and leptons are named by their “flavor,” with six quark flavors and six lepton flavors. The scalar Higgs boson is not a gauge boson, so it is not included in the fourth column of gauge bosons.
SOURCE: PBS NOVA/
Fermilab/Office of Science/US Dept of Energy.
The three quarks—up, down, and strange—constituted three so-called flavors of quarks. The high-energy experiments showed two kinds of currents associated with the weak force to create radioactive decay. One is an electrically charged current in which quarks are coupled to the charged intermediate vector boson W, and the other is a neutral current that is coupled to the neutral vector boson Z. In weak decays of particles, the charged W boson associated with the charged current can change the charge and flavor of quarks, while the neutral Z boson cannot change the quark charge and flavor. During these neutral Z interactions, no decays of hadrons have been observed that change the quark flavor through the decay.
Figure 1.6 The quark color combinations of mesons and baryons.
SOURCE: Wikipedia.
This restriction of neutral current decays in the flavors of quarks is known as the anomaly problem. In 1970, Sheldon Glashow, John Iliopoulos, and Luciano Maiani used the idea of a fourth quark to solve this anomaly problem in the quark model. They found a way to explain the experimental fact that, in neutral current decays, there was no change of flavor going from the decaying quark to its decay products containing quarks. The GIM mechanism (with GIM standing for Glashow, Iliopoulos, and Maiani) explained the lack of flavor-changing neutral currents in weak interactions. This observational fact called for the existence of a fourth quark, which had been predicted in 1964 and 1965.
The quark revolution began to culminate in 1974, when one group at Stanford, headed by Burton Richter, and another at Brookhaven, headed by Samuel Ting, discovered a narrow resonance that was identified immediately as being composed of a charm and an anticharm quark. Ting called the new charm resonance “the J particle,” whereas Richter called it “the psi particle,” and it eventually became known as the J/psi particle. The narrowness of the new resonance was caused by it being a tightly bound composite of a charm and an anticharm quark, which was later called a quarkonium system.
We now had four quarks confirmed experimentally: up, down, strange, and charm. In 1977, Leon Lederman and his collaborators at Fermilab discovered a fifth quark, which was called the bottom (or beauty) quark. It was known theoretically from the properties of QCD that there had to be a sixth quark and, of course, it would be called the top (or truth) quark. Indeed, it was discovered in 1995, also at Fermilab. The names top and bottom had been introduced by Israeli physicist Haim Harari in 1975, two years before the discovery of the bottom quark, to replicate at higher masses the up and down quarks.
The story of these last two quarks, or the third generation of quarks, is worth telling in more detail. In 1973, Japanese physicists Makoto Kobayashi and Toshihide Maskawa had predicted the existence of a third generation or family of quarks to explain the violation of charge conjugation and parity in the decay of K mesons. Charge conjugation is a mathematical transformation of a positively charged particle to a negatively charged one, and vice versa. This transformation turns a particle into its antiparticle. Parity is left–right symmetry in particle physics. This third generation of quarks was required to implement the GIM mechanism. The 1978 discovery by Martin Perl at SLAC of the tau lepton strengthened the need for the introduction of a fifth and sixth quark to implement the GIM mechanism fully, which explained why flavor-changing neutral currents were not detected.
It was not easy to discover these fifth and sixth quarks. Early searches for the top quark at SLAC and at the German accelerator, the Deutsches Elektronen Synchrotron (DESY) in Hamburg, came up with nothing. In 1983, when the super proton synchrotron (SPS) at CERN detected the W and Z bosons, experimentalists at CERN felt that the discovery of the top quark was imminent. A race soon ensued between the Tevatron in the United States, with an energy of 2 TeV, and the SPS collider at CERN to discover the top quark. However the SPS machine reached its energy limit without finding the top quark, which was expected, at the time, to have a mass of about 40 GeV, whereas the energy limit of the SPS was 77 GeV.
At this stage, only the Tevatron accelerator at Fermilab had enough energy to detect the top quark, with a mass that was now expected to be greater than 77 GeV. The two detectors, the Collider Detector at Fermilab (CDF) and the D0 detector also at Fermilab, were actually built to discover the top quark. Indeed, in 1992, the two groups associated with these two detectors saw the first hint of a top quark. It was a tempting clue that the top quark discovery was imminent. By 1995, there were enough events to establish the existence of the top quark at an energy of about 175 GeV.
We now have six quarks discovered in the lineup of elementary particles. In the standard model, however, there also had to be six leptons to match them. Indeed, new leptons were discovered eventually. In addition to the electron and the muon, there was the tau and also a neutrino associated with each of these leptons: the electron neutrino, the muon neutrino, and the tau neutrino. These quarks and leptons are the basic building blocks of the standard model (Figure 1.5).
THE FORCES OR INTERACTIONS IN NATURE
There are four basic forces in nature that have been confirmed experimentally: strong, electromagnetic, weak, and gravity. The weakest force is gravity. Isaac Newton published in his Principia in 1687 the first universal gravity theory based on his mechanics. Newton hypothesized that the inverse square law of gravity held true everywhere in the universe. The strength of this gravitational force was proportional to Newton’s gravitational constant, and his calculations agreed with the observed 28-day period of the moon with remarkable accuracy. In 1916, Einstein published his seminal paper on generalizing his special theory of relativity to include gravity and named it the “general theory of relativity.”10 He postulated that gravity was not a “force” between two masses, as it had been under Newton, but was a warping of spacetime geometry by matter. A key prediction of his new theory was accounting for an unusual feature of the planet Mercury’s orbit. The perihelion, or closest approach of the planet to the sun, was “precessing,” or moving in a rosette shape. Astronomical observations over a century showed that Mercury’s orbit was precessing by a tiny anomalous amount that did not fit Newton’s theory. Einstein calculated correctly the anomalous precession of Mercury to be approximately 43 seconds of arc per century, which did fit the astronomical data. A second key prediction, of the bending of light by the eclipsing sun, was verified in 1919 by astronomers, including Arthur Eddington. Today we interpret the gravitational force between massive objects as being caused not only by the warping of spacetime in the presence of matter, but also, in the quantized version of Einstein’s gravity theory, by the force carrier called the graviton. In contrast to the photon, the carrier of the electromagnetic force, the graviton has never been detected experimentally. In quantum gravity, Einstein’s geometrical theory of gravity is interpreted as a particle physics force, with the graviton as the carrier of the force.
The second weakest force is the one responsible for the radioactive decay of matter, discovered by Henri Becquerel in 1896, following the discovery of X-rays by Wilhelm Röntgen. Becquerel and his followers, including Pierre and Marie Curie, were interested in radioactive elements such as uranium, which emitted gamma rays (photons) to become other elements or isotopes, such as plutonium. In the language of the standard model of particle physics, we interpret radioactive decay as the weak decay of hadrons, such as neutrons, into leptons, such as electrons, muons, and neutrinos. For example, the neutron can decay into a proton plus an electron and an antineutrino. The carriers of the weak force have been identified as the massive W and Z bosons, discovered at CERN in 1983. Because the W and Z have masses, the weak force is a short-range force, unlike gravity or electromagnetism, which are long-range forces.
The next strongest force is electromagnetism, which is the force that we are most aware of in everyday life. It was originally thought to be two separate forces—electricity and magnetism—but, in 1873, James Clerk Maxwell unified them within his famous electromagnetic field equations. Electricity manifests itself in an
inverse square law such as gravity between two electrically charged particles, either positively charged or negatively charged. Magnetism displays itself as two magnetic poles that always come in pairs, a north and south pair. Danivsh physicist Hans Christian Ørsted in 1820 had discovered that electricity moving in a wire induced a magnetic field that deflected the north and south poles of a compass. Following this, Michael Faraday, during the 1830s, discovered magnetic induction—the fact that electric fields produce magnetic fields and vice versa. This discovery paved the way for Maxwell’s electromagnetic field equations. The modern interpretation of electromagnetism finds expression in the theory of quantum electrodynamics (QED), in which the electromagnetic force between charged particles is carried by the photon.
The fourth force in nature is the strong force, which is responsible for binding protons and neutrons in nuclei. It is about 200 times stronger than the electromagnetic force, which in turn is about 1038 times stronger than gravity. In the standard model of particle physics, the strong force is carried by the massless gluons, which bind quarks together in hadrons such as protons and neutrons, and thereby bind protons and neutrons together in atomic nuclei.
During the past four decades, theoretical physicists have devoted much effort to attempting to unify the four forces of nature in a grand design. A successful unification would mean that there is ultimately only one force in nature, carried by a massive boson often named the X particle, which would reveal itself at very high energies. The electroweak theory represents a partial unification of weak interactions and electromagnetism. The modern attempts at unification have not been as successful as Maxwell’s unification of electricity and magnetism. In particular, there has not yet been a successful unification of gravity with the other three forces. During the 1970s and 1980s, there were three main attempts to unify all the forces: grand unified theories (GUTs), supergravity, and string theory.
Cracking the Particle Code of the Universe Page 3
