Chapter 6: Elementary Particle Physics and The Unification of The Forces - PDF

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Chapter 6: Elementary Particle Physics and The Unification of The Forces Three quarks for Muster Mark! Sure he hasn t got much of a bark and sure any he has it s all beside the mark James Joyce, Finnegan
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Chapter 6: Elementary Particle Physics and The Unification of The Forces Three quarks for Muster Mark! Sure he hasn t got much of a bark and sure any he has it s all beside the mark James Joyce, Finnegan s Wake 6.1 Introduction Man has always searched for simplicity in nature. Recall that the ancient Greeks tried to describe the entire physical world in terms of the four quantities of earth, air, fire, and water. These, of course, have been replaced with the fundamental quantities of length, mass, charge, and time in order to describe the physical world of space, matter, and time. We have seen that space and time are not independent quantities, but rather are a manifestation of the single quantity spacetime and that mass and energy are interchangeable, so that energy could even be treated as one of the fundamental quantities. We also found that energy is quantized and therefore, matter should also be quantized. What is the smallest quantum of matter? That is, what are the fundamental or elementary building blocks of matter? What are the forces that act on these fundamental particles? Is it possible to combine these forces of nature into one unified force that is responsible for all the observed interactions? We shall attempt to answer these questions in this chapter. 6.2 Particles and Antiparticles As mentioned in chapter 20, the Greek philosophers Leucippus and Democritus suggested that matter is composed of fundamental or elementary particles called atoms. The idea was placed on a scientific foundation with the publication, by John Dalton, of A New System of Chemical Philosophy in 1808, in which he listed about 20 chemical elements, each made up of an atom. By 1896 there were about 60 known elements. It became obvious that there must be a way to arrange these different atoms in an orderly way in order to make sense of what was quickly becoming chaos. In 1869 the Russian chemist, Dimitri Mendeleev, developed the periodic table of the elements based on the chemical properties of the elements. Order was brought to the chaos of the large diversity of elements. In fact, new chemical elements were predicted on the basis of the blank spaces found in the periodic table. Later with the discovery of the internal structure of the atom, the atom could no longer be considered as elementary By 1932, only four elementary particles were known; the electron, the proton, the neutron, and the photon. Things looked simple again. But this simplicity was not to last. Other particles were soon discovered in cosmic rays. Cosmic rays are particles from outer space that impinge on the top of the atmosphere. Some of them make it to the surface of the earth, whereas others decay into still other particles before they reach the surface. Other new particles were found in the large 6-1 accelerating machines made by man. Today, there are hundreds of such particles. Except for the electron, proton, and neutron, most of these elementary particles decay very quickly. We are again in the position of trying to make order out of the chaos of so many particles. The first attempt at order is the classification of particles according to the scheme shown in figure 6.1. All the elementary particles can be grouped into particles called hadrons or leptons. Figure 6.1 First classification of the elementary particles. Leptons The Leptons are particles that are not affected by the strong nuclear force. They are very small in terms of size, in that they are less than m in diameter. They all have spin ½ in units of. There are a total of six leptons: the electron, e, the muon, and the tauon,, each with an associated neutrino. They can be grouped in the form ( e ) ( ) ( ) (e ) ( ) ( ) (6.1) There are thus three neutrinos: the neutrino associated with the electron, e; the neutrino associated with the muon, ; and the neutrino associated with the tauon,. The muon is very much like an electron but it is much heavier. It has a mass about 200 times greater than the electron. It is not stable like the electron but decays in about 10 6 s. Originally the word lepton, which comes from the Greek word leptos meaning small or light in weight, signified that these particles were light. However, in 1975 the lepton was discovered and it has twice the mass of the proton. That is, the lepton is a heavy lepton, certainly a misnomer. Leptons are truly elementary in that they apparently have no structure. That is, they are not composed of something still smaller. Leptons participate in the weak nuclear force, while the charged leptons, e,,, also participate in the electromagnetic interaction. The muon was originally thought to be Yukawa s meson that mediated the strong nuclear force, and hence it was called a meson. This is now known to be a misnomer, since the muon is not a meson but a lepton. 6-2 Hadrons Hadrons are particles that are affected by the strong nuclear force. There are hundreds of known hadrons. Hadrons have an internal structure, composed of what appears to be truly elementary particles called quarks. The hadrons can be further broken down into two subgroups, the baryons and the mesons. 1. Baryons. Baryons are heavy particles that, when they decay, contain at least one proton or neutron in the decay products. The baryons have half-integral spin, that is, 1/2, 3/2, and so on. We will see in a moment that all baryons are particles that are composed of three quarks. 2. Mesons. Originally, mesons were particles of intermediate-sized mass between the electron and the proton. However many massive mesons have since been found, so the original definition is no longer appropriate. A meson is now defined as any particle whose decay products do not include a baryon. We will see that mesons are particles that are composed of a quark-antiquark pair. All mesons have integral spin, that is, 0, 1, 2, 3, and so on. The mass of the meson increases with its spin. A list of some of the elementary particles is shown in table 6.1. Table 6.1 List of Some of the Elementary Particles Leptons Hadrons Baryons Mesons electron, muon, tauon, neutrinos, proton, neutron, delta, lambda, Sigma, Hyperon, Omega pi, eta, rho, omega, delta, phi e e p n In 1928, Paul Dirac merged special relativity with the quantum theory to give a relativistic theory of the electron. A surprising result of that merger was that his equations predicted two energy states for each electron. One is associated with 6-3 the electron, whereas the other is associated with a particle, like the electron in every way, except that it carries a positive charge. This new particle was called the antielectron or the positron. This was the first prediction of the existence of antimatter. The positron was found in For every particle in nature there is associated an antiparticle. The antiparticle of the proton is the antiproton. It has all the characteristics of the proton except that it carries a negative charge. Some purely neutral particles such as the photon and the 0 meson are their own antiparticles. Antiparticles are written with a bar over the symbol for the particle. Hence, p is an antiproton and n is an antineutron. Matter consists of electrons, protons and neutrons, whereas antimatter consists of antielectrons (positrons), antiprotons, and antineutrons. Figure 6.2 shows atoms of matter and antimatter. The same electric forces that hold matter Figure 6.2 Matter and antimatter. together, hold antimatter together. (Note that the positive and negative signs are changed in antimatter.) The antihelium nucleus has already been made in highenergy accelerators. Whenever particles and antiparticles come together they annihilate each other and only energy is left. For example, when an electron comes in contact with a positron they annihilate according to the reaction e e 2 (6.2) where the 2 s are photons of electromagnetic energy. (Two gamma rays are necessary in order to conserve energy and momentum.) This energy can also be used to create other particles. Conversely, particles can be created by converting the energy in the photon to a particle-antiparticle pair such as e e (6.3) 6-4 Creation or annihilation can be shown on a spacetime diagram, called a Feynman diagram, after the American physicist Richard Feynman ( ), such as in figure 6.3. Figure 6.3(a) shows the creation of an electron-positron pair. A Figure 6.3 Creation and annihilation of particles. photon moves through spacetime until it reaches the spacetime point A, where the energy of the photon is converted into the electron-positron pair. Figure 6.3(b) shows an electron and positron colliding at the spacetime point B where they annihilate each other and only the photon now moves through spacetime. (In order to conserve momentum and energy in the creation process, the presence of a relatively heavy nucleus is required.) 6.3 The Four Forces of Nature In the study of nature, four forces that act on the particles of matter are known. They are: 1. The Gravitational Force. The gravitational force is the oldest known force. It holds us to the surface of the earth and holds the entire universe together. It is a long-range force, varying as 1/r 2. Compared to the other forces of nature it is by far the weakest force of all. 2. The Electromagnetic Force. The electromagnetic force was the second force known. In fact, it was originally two forces, the electric force and the magnetic force, until the first unification of the forces tied them together as a single electromagnetic force. The electromagnetic force holds atoms, molecules, solids, and liquids together. Like gravity, it is a long-range force varying as 1/r The Weak Nuclear Force. The weak nuclear force manifests itself not so much in holding matter together, but in allowing it to disintegrate, such as in the decay of the neutron and the proton. The weak force is responsible for the fusion process occurring in the sun by allowing a proton to decay into a neutron such as given in equation The proton-proton cycle then continues until helium is formed and large quantities of energy are given off. The nucleosynthesis of the chemical elements also occurred because of the weak force. Unlike the gravitational and electromagnetic force, the weak nuclear force is a very short range force. 4. The Strong Nuclear Force. The strong nuclear force is responsible for holding the nucleus together. It is the strongest of all the forces but is a very short range force. 6-5 That is, its effects occur within a distance of about m, the diameter of the nucleus. At distances greater than this, there is no evidence whatsoever for its very existence. The strong nuclear force acts only on the hadrons. Why should there be four forces in nature? Einstein, after unifying space and time into spacetime, tried to unify the gravitational force and the electromagnetic force into a single force. Although he spent a lifetime trying, he did not succeed. The hope of a unification of the forces has not died, however. In fact, we will see shortly that the electromagnetic force and the weak nuclear force have already been unified theoretically into the electroweak force by Glashow, Weinberg, and Salam, and experimentally confirmed by Rubbia. A grand unification between the electroweak and the strong force has been proposed. Finally an attempt to unify all the four forces into one superforce is presently underway. 6.4 Quarks In the attempt to make order out of the very large number of elementary particles, Murray Gell-Mann and George Zweig in 1964, independently proposed that the hadrons were not elementary particles but rather were made of still more elementary particles. Gell-Mann called these particles, quarks. He initially assumed there were only three such quarks, but with time the number has increased to six. The six quarks are shown in table 6.2. The names of the quarks are: up, down, strange, charmed, bottom, and top. One of the characteristics of these Table 6.2 The Quarks Name (Flavor) Symbol Charge Spin up u 2/3 1/2 down d 1/3 1/2 strange s 1/3 1/2 charmed c 2/3 1/2 bottom b 1/3 1/2 top t 2/3 1/2 quarks is that they have fractional electric charges. That is, the up, charmed, and top quark has 2/3 of the charge found on the proton, whereas the down, strange, and bottom quark has 1/3 of the charge found on the electron. They all have spin 1/2, in units of. Each quark has an antiquark, which is the same as the original quark except it has an opposite charge. The antiquark is written with a bar over the letter, that is q. We will now see that all of the hadrons are made up of quarks. The baryons are made up of three quarks: Baryon = qqq (6.4) 6-6 While the mesons are made up of a quark-antiquark pair: Meson = qq (6.5) As an example of the formation of a baryon from quarks, consider the proton. The proton consists of two up quarks and one down quark, as shown in figure 6.4(a). Figure 6.4 Some quark configurations of baryons and mesons. The electric charge of the proton is found by adding the charges of the constitutive quarks. That is, since the u quark has a charge of 2/3, and the d quark has a charge of 1/3, the charge of the proton is 2/3 + 2/3 1/3 = 1 which is exactly as expected. Now the proton should have a spin of 1/2 in units of. In figure 6.4(a), we see the two up quarks as having their spin up by the direction of the arrow on the quark. The down quark has its arrow pointing down to signify that its spin is down. Because each quark has spin 1/2, the spin of the proton is found by adding the spins of the quarks as 1/2 + 1/2 1/2 = 1/2 We should note that the names up and down for the quarks are just that, a name, and have nothing to do with the direction of the spin of the quark. For example, the delta plus + baryon is made from the same three quarks as the proton, but their spins are all aligned in the same direction, as shown in figure 6.4(b). Thus, the spin of the + particle is 1/2 + 1/2+ 1/2 = 3/2 6-7 That is, the + particle has a spin of 3/2. Since it takes more energy to align the spins in the same direction, when quark spins are aligned, they have more energy. This manifests itself as an increased mass by Einstein s equivalence of mass and energy (E = mc 2 ). Thus, we see that the mass of the + particle has a larger mass than the proton. Hence, in the formation of particles from quarks, we not only have to know the types of quarks making up the particle but we must also know the direction of their spin. Figure 6.4(c) shows that a neutron is made up of one up quark and two down quarks. The total electric charge is While its spin is 2/3 1/3 1/3 = 0 1/2 + 1/2 1/2 = 1/2 Again note that the delta zero 0 particle is made up of the same three quarks, figure 6.4(d), but their spins are all aligned. As an example of the formation of a meson from quarks, consider the pi plus + meson in figure 6.4(e). It consists of an up quark and an antidown quark. Its charge is found as 2/3 + [ ( 1/3)] = 2/3 + 1/3 = 1 That is, the d quark has a charge of 1/3, so its antiquark d has the same charge but of opposite sign +1/3. The spin of the + is 1/2 1/2 = 0 Thus, the + meson has a charge of +1 and a spin of zero. If the spins of these same two quarks are aligned, as in figure 6.4(f), the meson is the positive rho-meson +, with electric charge of +1 and spin of 1. The quark structure of some of the baryons is shown in table 6.3, whereas table 6.4 shows the quark structure for some mesons. Particles that contain the strange quark are called strange particles. The reason for this name is because these particles took so much longer to decay than the other elementary particles, that it was considered strange. If a proton or neutron consists of quarks, we would like to see them. Just as Rutherford saw inside the atom by bombarding it with alpha particles, we can see inside a proton by bombarding it with electrons or neutrinos. In 1969, at the Stanford Linear Accelerator Center (SLAC), protons were bombarded by highenergy electrons. It was found that some of these electrons were scattered at very large angles, just as in Rutherford scattering, indicating that there are small constituents within the proton. Figure 6.5 shows the picture of a proton as 6-8 Table 6.3 Quark Structure of Some of the Baryons Name Symbol Structure Charge Spin Mass (units of e) (units of (GeV) Proton p u u d 1 1/ Neutron n u d d 0 1/ Delta plus plus ++ u u u 2 3/ Delta plus + u u d 1 3/2 Delta zero 0 u d d 0 3/2 Delta minus d d d 1 3/2 Lambda zero 0 u d s 0 1/ Positive sigma + u u s 1 3/ Positive sigma + u u s 1 1/ Neutral sigma *0 u d s 0 3/ Neutral sigma 0 u d s 0 1/ Negative sigma * d d s 1 3/ Negative sigma d d s 1 1/ Negative xi s d s 1 1/ Neutral xi o s u s 0 1/ Omega minus s s s 1 3/ Charmed lambda + c u d c 1 1/ Table 6.4 Quark Structure of Some Mesons Name Symbol Structure Charge (units of e) Spin (units of Positive pion + d u Positive rho + d u Negative pion u d Negative rho u d Mass (GeV) Pi zero 50%(u u) %d d) Positive kaon + u s Neutral kaon s d Negative kaon u s J/Psi (charmonium) J/ c d Charmed eta c c c Neutral D D 0 u c Neutral D D *0 u c 0 1 Positive D D + d c Zero B-meson B 0 d b Negative B-meson B u b Upsilon b b Phi-meson s s F-meson F + c s observed by scattering experiments. The scattering appears to come from particles with charges of +2/3 and 1/3 of the electronic charge. (Recall that the up quark has a charge of +2/3, whereas the down quark has a charge of 1/3.) There is thus, experimental evidence for the quark structure of the proton. Similar experiments have also been performed on neutrons with the same success. The scattering also confirmed the existence of some quark-antiquark pairs within the proton. Recall that quark-antiquark pairs are the constituents of mesons. The experiments also showed the existence of other particles within the nucleons, called gluons. The gluons are the exchange particles between the quarks that act to hold the quarks together. They are the nuclear glue. The one difficulty with the quark model at this point is that there seems to be a violation of the Pauli exclusion principle. Recall that the Pauli exclusion principle stated that no two electrons can have the same quantum numbers at the same time. The Pauli exclusion principle is actually more general than that, in that it applies not only to electrons, but to any particles that have half-integral spin, such as 1/2, 3/2, 5/2, and so on. Particles that have half-integral spin are called fermions. Because quarks have spin 1/2, they also must obey the Pauli exclusion principle. But the ++ particle is composed of three up quarks all with the same spin, and the particle has three strange quarks all with the same spin. Thus, there must be an additional characteristic of each quark, that is different for each quark, so that the Pauli exclusion principle will not be violated. This new attribute of the quark is called color. Figure 6.5 Structure of the proton. (From D. H. Perkins, Inside the Proton in The Nature of Matter, Clarendon Press, Oxford. 1981) Quarks come in three colors: red, green, and blue. We should note that these colors are just names and have no relation to the real colors that we see everyday with our eyes. The words are arbitrary. As an example, they could just as easily have been called A, B, and C. We can think of color in the same way as electric charges. Electric charges come in two varieties, positive and negative. Color charges come in three varieties: red, green, and blue. Thus, there are three types of up 6-10 quarks; a red-up quark ur, a green-up quark ug, and a blue-up quark ub. Hence the delta plus-plus particle ++ can be represented as in figure 6.6(a). In this way there is no violation of the Pauli exclusion principle since each up quark is different. Figure 6.6 Colored quarks. All baryons are composed of red, green, and blue quarks. Just as the primary colors red, green, and blue add up to white, the combination of a red, green, and blue quark is said to make up the color white.
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