The Physics of Energy, page 58
Electrons are attracted to nuclei by forces that are transmitted by electric and magnetic fields. Together, electrons and nuclei formed from protons and neutrons form atoms; atoms form molecules; and molecules form complex systems like us.
Photons – the quanta of the electromagnetic field – are emitted and absorbed when electrons or protons make transitions from one quantum state to another.
Electromagnetic fields play a dual role: as classical waves that can be broadcast and absorbed, and as quantized photons as already mentioned.
Antineutrinos A neutron can decay into a proton, an electron, and an electron antineutrino. This is a weak interaction known as β-decay. Sometimes, when protons and neutrons are bound into nuclei, this reaction is forbidden by energy conservation and instead the opposite reaction can occur: effectively a proton can decay into a neutron, a positron, and an electron neutrino ().
The Standard Model “Lite”
Only five particles – the proton, neutron, electron, photon, and the electron antineutrino – are needed to provide a fairly good description of almost all phenomena in our world. Electromagnetism and gravity are the principal macroscopic forces of consequence. Weak and strong interactions operate within nuclei, which are held together by the strong nuclear interaction between nucleons (protons and neutrons).
Gravity acts on all these particles, even photons which are massless but carry energy.
For a short period of time – roughly the period between 1935 and 1950 – the five particles in the Standard Model lite were thought to be the only elementary particles in nature. In fact, this relatively complacent era in fundamental physics was over almost before it began, since the first additional particle, the muon, had already been detected in a cloud chamber photograph in 1937. Trying to understand the muon and the plethora of strongly interacting particles related to protons and neutrons that were made in accelerators in the 1950s led eventually to the Standard Model.
The remainder of this section provides a brief introduction to the other particles in the Standard Model.
14.2.2 Leptons
Charged leptons All six known leptons experience the weak, but not the strong interactions. Three of these leptons also carry electromagnetic charge. The electron is the lightest and most familiar of the (electromagnetically) charged leptons. We know of two other charged leptons: the muon (μ) with a mass of approximately 207 times the mass of the electron, and the tauon (τ) with a mass about 3478 times the mass of the electron. As far as we can tell, the μ and the τ are almost identical copies of the electron, except for their masses. They have the same charges, and the same kinds of interactions; they are just heavier. They are short-lived and decay into electrons, neutrinos and, occasionally, other stuff. There is good reason to believe that the electron, muon, and tauon are the only charged leptons.
Neutral leptons Each charged lepton is associated with a neutral lepton, called a neutrino. For the e there is the , for the μ, the , and for the τ, the . What is meant by “associated with” is explained in more detail in §14.3. Neutrinos feel only the weak force and gravity. They are very light – for many years they were thought to be massless like photons, but late last century it was discovered that they have small but nonzero masses. Their interactions are so weak that they pass through matter almost like it isn't there. To make that statement quantitative: the mean free path (the typical distance traveled before an interaction takes place, §20) of a 1 MeV neutrino moving through lead is roughly 1 light-year ( m)!
Lepton interactions An important tool in analyzing systems of elementary particles is the existence of additional exactly or approximately conserved charges like the total electric charge, which remain unchanged under all, or almost all, physical processes. Each of the three lepton pairs, , , and is associated with a discrete approximately conserved quantity.6 This quantity is called lepton number (L) generically: electron number, muon number, and tauon number () refer to the approximately conserved quantities associated with each of the three lepton types. The charged leptons and their associated neutrinos have lepton number , their antiparticles have lepton number . An example of an interaction that conserves both muon number and electron number is muon decay,
(14.7)
The muon () decays into a muon neutrino (), an electron (), and an electron antineutrino (). Thus the muon number is one on both sides of the equation and the total electron number is zero.
Muons are not particularly exotic. They are made by cosmic rays in the upper atmosphere and travel down well into the ground (on average), before decaying or interacting. The lifetime of the muon is about 2.2 μs, and the flux at sea level is about 200 m s. So hundreds have passed through you in the time it has taken you to read these words.
14.2.3 Quarks and their Interactions
Quarks are massive particles that feel the chromodynamic force. While they are similar in some respects to leptons at a fundamental level, the role they play in nature is quite different. Whether or not a particle feels the chromodynamic force is determined by a “charge” – not electric charge, but similar in that particles with this charge feel the force and particles without it do not. This charge is called color, but it has nothing to do with visible color, which is, of course, a characteristic of electromagnetic radiation. Electric charge comes in two types, which we call positive and negative, with the property that combining positive and negative charges of equal strengths results in a system that is electrically neutral. Similarly, each type of quark comes in three versions which differ by their “color.” If three quarks, one of each version, are combined, the result is neutral under chromodynamic forces. Because this resembles the rule for addition of the primary colors of light – when red, green, and blue light are combined, they yield white, or neutral light – physicists chose, somewhat whimsically, to call the chromodynamic charge color. The proton and the neutron are both examples of color-neutral three-quark systems. Another successful feature of the analogy is that combining a quark and antiquark also can yield a color-neutral system, in much the same way that combining a visual color with its complement gives color-neutral, i.e. white, light.
The chromodynamic forces are very strong. Furthermore, as discussed further below, gluons themselves carry color charge (unlike photons, which are electrically neutral). These effects combine in such a way that quarks can never escape from the color-neutral bound states that they form. Thus, individual quarks are never seen. Color-neutral states of three quarks are called baryons and bound color-neutral states of a quark and an antiquark are called mesons. Together, these color-neutral composite particles are known as hadrons.7 Protons and neutrons are the lightest baryons. Almost all the known particles that feel the strong force fit into these two categories: baryons (or antibaryons, like the antiproton) or mesons. The exception being a handful of recently discovered and/or very short-lived states that appear to be essentially composed of two quarks and two antiquarks, or four quarks and one antiquark.
Quark Properties
Baryon number There are literally hundreds of different types of baryons, but all are unstable except for protons (and neutrons when they are bound within certain nuclei). Eventually, if you follow its life, any baryon decays into a proton or neutron plus a lot of other stuff that may include mesons, leptons, antileptons, and photons. Protons, however, do not seem to decay – ever. Searches for proton decay have come up empty, and the proton lifetime is now known to be greater than yr [69]. To account for this, physicists endow baryons with a type of “charge” called baryon number, which is +1 for baryons and for antibaryons. So, for example, the proton and neutron have baryon number +1 and the antiproton and antineutron have baryon number –1. The stability of the proton can then be expressed as conservation of baryon number.8 A baryon can decay, but among its decay products one must always find another baryon, and if you wait long enough only protons and/or neutrons will be left. Mesons, leptons, photons, and the rest have baryon number zero. A proton and an antiproton can annihilate into a cloud of mesons and photons because this conserves baryon number: .
Baryon Number (Atomic Mass)
An atomic nucleus can be labeled by the number of nucleons it contains. That number is called the baryon number or atomic mass, and is usually denoted by A. A nucleus of atomic mass A contains quarks. Baryon number is conserved in all observed processes.
The concept of baryon number can be attributed at a more fundamental level to quarks. Since there are three quarks in a baryon, each quark is assigned baryon number . While quark number conservation implies conservation of baryon number, the name “baryon number” was invented long before quarks were discovered, and the name stuck. Nuclei are bound states of protons and neutrons, so they can be labeled by their baryon number. Carbon, for example, with six protons and six neutrons, has baryon number 12. The baryon number of a nucleus is thus the same thing as its atomic mass number in the language of chemistry. We use the terms interchangeably.
Quark charges and colors, gluons Aside from the fact that they are never seen in isolation, perhaps at first sight the most bizarre property of quarks is that their electric charges are either or , where is the electron’s charge. When quarks were originally proposed in 1964 by American physicists Murray Gell-Mann and George Zweig, the idea that a particle could have fractional electric charge was considered strange if not silly. Now there is plenty of evidence for these charge assignments, and the only oddity is that fractional charges are not observed directly because the allowed, color neutral, combinations of quarks and antiquarks always have charges that are integer multiples of e.
Given that they are never seen in isolation, how can we be certain that quarks have fractional charge, or indeed, that quarks exist at all? The reason is that when electrons or other particles that do not feel the strong force are scattered from protons or other nuclei, the pattern of scattering depends on the nature and distribution of the constituents of the baryon(s). In the late 1960s American physicists Jerome Friedman, Henry Kendall, and Richard Taylor scattered electrons from protons and observed scattering patterns that could only be accounted for if protons were made of pointlike spin-1/2 particles with electric charges that are third integral fractions of the electron’s charge. Physicists now agree that quarks are just as “real” as electrons, even though the nature of chromodynamic force sequesters them permanently inside protons and neutrons.
The gluons that mediate the chromodynamic force couple to color charges in much the same way that a photon couples to electric charge, but in addition, gluons themselves are colored. Two beams of light pass through one another because photons do not scatter significantly from one another.9 Gluons not only do not pass through one another, they interact with one another strongly by emitting and absorbing more gluons, and those interact by emitting and absorbing more gluons, ad infinitum. This is why chromodynamic forces are so complicated.
Flavor On top of all the previous complications, quarks come in six distinct types, more or less in parallel to the six types of leptons (remember , , and ). The six types are called up (u), down (d), charm (c), strange (s), top (t), and bottom (b). They differ in electric charge: three () have charge and three () have charge . The properties of the quarks, to the extent they are known, are listed in Table 14.2. Note that they all have electric charge, so they feel electromagnetic forces. They all feel the weak force as well.
These six different types of quarks are known as different flavors of quarks. The name “flavor” is even more fanciful than “color.” It has no content except to allow physicists to discuss an abstract concept in simple words. Note that the six flavors of quarks can be divided into the three generations of matter as discussed above, with up and down quarks in the first generation, charm and strange in the second generation, and top and bottom in the third generation, with each generation progressively more massive than the previous.
The chromodynamic interactions of quarks conserve flavor. The number of u quarks (minus the number of u antiquarks), for example, does not change in a chromodynamic interaction. In contrast, the weak interactions allow quarks to change their flavors. Thus, for example, a weak interaction can enable a d quark to emit an electron and an electron antineutrino and turn into a u quark – a transformation not otherwise possible. These transformations are important in nuclear energy processes, and are described in §14.3.
The quark structure of protons and neutrons Protons and neutrons are the lightest baryons. The proton is a bound state of two u quarks and one d quark. The sum of the electric charges is . The neutron is a bound state of two d quarks and one u quark, with electric charge . This structure is illustrated in Figure 14.5. The proton is lighter than the neutron because the u quark is slightly lighter than the d quark. The masses of the u and d quarks are tiny, which at first sight may seem very strange: how can objects of mass be made of only three particles with masses of –5 MeV/c each? Where does all the mass come from? The answer lies in quantum mechanics and the concept of zero-point energy, which was briefly mentioned in §9.2.1. Recall that in each of the potentials that was studied (square-well and harmonic oscillator) in §7, the lowest energy state has energy greater than zero. The smaller the region to which a particle is confined, the greater its energy. For a region as small as 1 fm, the zero-point energy of a massless particle is ~300 MeV (Problem 14.5). The proton contains three such particles, each with a zero-point energy of about 300 MeV, so the energy of a proton at rest is ~900 MeV; by Einstein’s , that energy contributes 900 MeV/c2 to its mass.
Figure 14.5 A cartoon of a proton and neutron showing the dominant quarks: uud in the proton and ddu in the neutron. The quarks are colored to remind us that all three colors must be present to make a color-neutral hadron. In actuality, protons and neutrons are described by quantum states that include fluctuating gluon fields and quark–antiquark pairs, though this complexity does not affect the nuclear reactions relevant to nuclear energy processes.
The visible matter in the universe consists of nuclei and electrons. The nuclei in turn consist of protons and neutrons. The mass of an electron is that of a proton or neutron. So we conclude that most of the mass of the visible universe is due to the quantum zero-point energy of bound quarks!
Mass in the Visible Universe
Almost all of the visible mass in the universe is found in the rest masses of protons (hydrogen nuclei), neutrons, and the nuclei they compose. This mass, in turn, is a manifestation of the quantum zero-point energy of almost-massless quarks confined to the interior of nucleons.
Although protons and neutrons have excited states, the energies emitted and absorbed in the nuclear reactions of interest to us here are not great enough to excite the quarks in protons or neutrons. Protons and neutrons can therefore, to a good approximation, be regarded as persistent, unstructured objects whose identity does not change inside a nucleus. The internal quark substructure of protons and neutrons is manifested in the complicated structure of the strong nuclear interactions.
14.2.4 Force Carriers
As summarized earlier, the chromodynamic, weak, and electromagnetic forces each are mediated by spin one vector bosons. Each of the vector bosons has its own features and character. The photon is most visible because it is massless and carries no charge, so that it propagates freely through space mediating the long-range electromagnetic force. The gluon, while also massless, is itself charged under the chromodynamic interactions, so that it cannot propagate freely. Even in the absence of quarks or leptons, gluons can in principle bind together into color-free massive states known as glueballs. Up to now, however, no glueball has been convincingly identified experimentally. The and vector bosons that mediate the weak interactions are massive, and thus weak interactions are intrinsically short-range forces.
14.2.5 The Higgs Boson
The final particle in the standard model is the Higgs boson, or Higgs particle. Originally predicted in 1964, this particle was found experimentally in 2013. Though this particle does not play a direct role in any energy-related processes, it is a central component of the Standard Model. It is responsible for electroweak symmetry breaking, the mechanism that gives rise to masses for the and Z bosons and differentiates the weak interactions from the closely related electromagnetic interaction. The Higgs particle is also associated with the phenomenon that gives rise to quark and lepton masses.
14.3The Weak Interactions and β-decay
We have alluded several times to the crucial role that the weak interactions play in the universe. Their fundamental practical importance is that they allow protons to turn into neutrons and vice versa. In this section we take a more careful look at this and related processes.
14.3.1 Discovery of β-decay
In the early twentieth century physicists observed that some nuclei emit electrons and change their chemical identity. A simple, illustrative, and important example is the decay of a rare form of potassium into calcium or argon. Potassium is an atom with 19 electrons bound to a nucleus with 19 protons and usually 20 neutrons. This nucleus is stable. About one in ten thousand potassium nuclei contains 21 neutrons rather than 20, giving the nucleus a baryon number (atomic mass number) of 40. An atom with this nucleus at its core has all the chemical properties of ordinary potassium, but it weighs about 2.5% more due to the extra neutron. What is special about potassium-40 ( in standard notation, §17.1.2) is that it is unstable. It decays with a lifetime of greater than a billion years.
