Chapter 33 Particle Physics
33.4 Particles, Patterns, and Conservation Laws
Summary
- Define matter and antimatter.
- Outline the differences between hadrons and leptons.
- State the differences between mesons and baryons.
In the early 1930s only a small number of subatomic particles were known to exist—the proton, neutron, electron, photon and, indirectly, the neutrino. Nature seemed relatively simple in some ways, but mysterious in others. Why, for example, should the particle that carries positive charge be almost 2000 times as massive as the one carrying negative charge? Why does a neutral particle like the neutron have a magnetic moment? Does this imply an internal structure with a distribution of moving charges? Why is it that the electron seems to have no size other than its wavelength, while the proton and neutron are about 1 fermi in size? So, while the number of known particles was small and they explained a great deal of atomic and nuclear phenomena, there were many unexplained phenomena and hints of further substructures.
Things soon became more complicated, both in theory and in the prediction and discovery of new particles. In 1928, the British physicist P.A.M. Dirac (see Figure 1) developed a highly successful relativistic quantum theory that laid the foundations of quantum electrodynamics (QED). His theory, for example, explained electron spin and magnetic moment in a natural way. But Dirac’s theory also predicted negative energy states for free electrons. By 1931, Dirac, along with Oppenheimer, realized this was a prediction of positively charged electrons (or positrons). In 1932, American physicist Carl Anderson discovered the positron in cosmic ray studies. The positron, or

Matter and Antimatter
The positron was only the first example of antimatter. Every particle in nature has an antimatter counterpart, although some particles, like the photon, are their own antiparticles. Antimatter has charge opposite to that of matter (for example, the positron is positive while the electron is negative) but is nearly identical otherwise, having the same mass, intrinsic spin, half-life, and so on. When a particle and its antimatter counterpart interact, they annihilate one another, usually totally converting their masses to pure energy in the form of photons as seen in Figure 2. Neutral particles, such as neutrons, have neutral antimatter counterparts, which also annihilate when they interact. Certain neutral particles are their own antiparticle and live correspondingly short lives. For example, the neutral pion
Hadrons and Leptons
Particles can also be revealingly grouped according to what forces they feel between them. All particles (even those that are massless) are affected by gravity, since gravity affects the space and time in which particles exist. All charged particles are affected by the electromagnetic force, as are neutral particles that have an internal distribution of charge (such as the neutron with its magnetic moment). Special names are given to particles that feel the strong and weak nuclear forces. Hadrons are particles that feel the strong nuclear force, whereas leptons are particles that do not. The proton, neutron, and the pions are examples of hadrons. The electron, positron, muons, and neutrinos are examples of leptons, the name meaning low mass. Leptons feel the weak nuclear force. In fact, all particles feel the weak nuclear force. This means that hadrons are distinguished by being able to feel both the strong and weak nuclear forces.
Table 2 lists the characteristics of some of the most important subatomic particles, including the directly observed carrier particles for the electromagnetic and weak nuclear forces, all leptons, and some hadrons. Several hints related to an underlying substructure emerge from an examination of these particle characteristics. Note that the carrier particles are called gauge bosons. First mentioned in Chapter 30.7 Patterns in Spectra Reveal More Quantization, a boson is a particle with zero or an integer value of intrinsic spin (such as

Category | Particle name | Symbol | Antiparticle | Rest mass ( |
Lifetime2 (s) | |||||
---|---|---|---|---|---|---|---|---|---|---|
Gauge | Photon | Self | 0 | 0 | 0 | 0 | 0 | 0 | Stable | |
Bosons | 0 | 0 | 0 | 0 | 0 | |||||
Self | 0 | 0 | 0 | 0 | 0 | |||||
Leptons | Electron | 0.511 | 0 | 0 | 0 | 0 | Stable | |||
Neutrino (e) | 0 | 0 | 0 | 0 | Stable | |||||
Muon | 105.7 | 0 | 0 | 0 | 0 | |||||
Neutrino |
0 | 0 | 0 | 0 | Stable | |||||
Tau | 1777 | 0 | 0 | 0 | 0 | |||||
Neutrino |
0 | 0 | 0 | 0 | Stable | |||||
Hadrons (selected) | ||||||||||
Mesons | Pion | 139.6 | 0 | 0 | 0 | 0 | 0 | |||
Self | 135.0 | 0 | 0 | 0 | 0 | 0 | ||||
Kaon | 493.7 | 0 | 0 | 0 | 0 | |||||
497.6 | 0 | 0 | 0 | 0 | ||||||
Eta | Self | 547.9 | 0 | 0 | 0 | 0 | 0 | |||
(many other mesons known) | ||||||||||
Baryons | Proton | 938.3 | ± 1 | 0 | 0 | 0 | 0 | Stable4 | ||
Neutron | 939.6 | ± 1 | 0 | 0 | 0 | 0 | 882 | |||
Lambda | 1115.7 | ± 1 | 0 | 0 | 0 | |||||
Sigma | 1189.4 | ± 1 | 0 | 0 | 0 | |||||
1192.6 | ± 1 | 0 | 0 | 0 | ||||||
1197.4 | ± 1 | 0 | 0 | 0 | ||||||
Xi | 1314.9 | ± 1 | 0 | 0 | 0 | |||||
1321.7 | ± 1 | 0 | 0 | 0 | ||||||
Omega | 1672.5 | ± 1 | 0 | 0 | 0 | |||||
(many other baryons known) | ||||||||||
Table 2: Selected Particle Characteristics1 |
All known leptons are listed in the table given above. There are only six leptons (and their antiparticles), and they seem to be fundamental in that they have no apparent underlying structure. Leptons have no discernible size other than their wavelength, so that we know they are pointlike down to about
Once the muon was discovered in cosmic rays, its decay mode was found to be
which implied another “family” and associated conservation principle. The particle
More recently, a third lepton family was discovered when
Conservation of total
Mesons and Baryons
Now, note that the hadrons in the table given above are divided into two subgroups, called mesons (originally for medium mass) and baryons (the name originally meaning large mass). The division between mesons and baryons is actually based on their observed decay modes and is not strictly associated with their masses. Mesons are hadrons that can decay to leptons and leave no hadrons, which implies that mesons are not conserved in number. Baryons are hadrons that always decay to another baryon. A new physical quantity called baryon number
Forces, Reactions, and Reaction Rates
The forces that act between particles regulate how they interact with other particles. For example, pions feel the strong force and do not penetrate as far in matter as do muons, which do not feel the strong force. (This was the way those who discovered the muon knew it could not be the particle that carries the strong force—its penetration or range was too great for it to be feeling the strong force.) Similarly, reactions that create other particles, like cosmic rays interacting with nuclei in the atmosphere, have greater probability if they are caused by the strong force than if they are caused by the weak force. Such knowledge has been useful to physicists while analyzing the particles produced by various accelerators.
The forces experienced by particles also govern how particles interact with themselves if they are unstable and decay. For example, the stronger the force, the faster they decay and the shorter is their lifetime. An example of a nuclear decay via the strong force is
Yet another quantum number emerges from decay lifetimes and patterns. Note that the particles
Example 1: Calculating Quantum Numbers in Two Decays
(a) The most common decay mode of the
(b) Is the decay
Strategy
In part (a), the conservation laws can be examined by adding the quantum numbers of the decay products and comparing them with the parent particle. In part (b), the same procedure can reveal if a conservation law is broken or not.
Solution for (a)
Before the decay, the
Discussion for (a)
The
Solution for (b)
The decay
Discussion for (b)
This decay is not only allowed by our reckoning, it is, in fact, the primary decay mode of the
There are hundreds of particles, all hadrons, not listed in Table 2, most of which have shorter lifetimes. The systematics of those particle lifetimes, their production probabilities, and decay products are completely consistent with the conservation laws noted for lepton families, baryon number, and strangeness, but they also imply other quantum numbers and conservation laws. There are a finite, and in fact relatively small, number of these conserved quantities, however, implying a finite set of substructures. Additionally, some of these short-lived particles resemble the excited states of other particles, implying an internal structure. All of this jigsaw puzzle can be tied together and explained relatively simply by the existence of fundamental substructures. Leptons seem to be fundamental structures. Hadrons seem to have a substructure called quarks. Chapter 33.5 Quarks: Is That All There Is? explores the basics of the underlying quark building blocks.

Summary
- All particles of matter have an antimatter counterpart that has the opposite charge and certain other quantum numbers as seen in Table 2. These matter-antimatter pairs are otherwise very similar but will annihilate when brought together. Known particles can be divided into three major groups—leptons, hadrons, and carrier particles (gauge bosons).
- Leptons do not feel the strong nuclear force and are further divided into three groups—electron family designated by electron family number
; muon family designated by muon family number ; and tau family designated by tau family number . The family numbers are not universally conserved due to neutrino oscillations. - Hadrons are particles that feel the strong nuclear force and are divided into baryons, with the baryon family number
being conserved, and mesons.
Conceptual Questions
1: Large quantities of antimatter isolated from normal matter should behave exactly like normal matter. An antiatom, for example, composed of positrons, antiprotons, and antineutrons should have the same atomic spectrum as its matter counterpart. Would you be able to tell it is antimatter by its emission of antiphotons? Explain briefly.
2: Massless particles are not only neutral, they are chargeless (unlike the neutron). Why is this so?
3: Massless particles must travel at the speed of light, while others cannot reach this speed. Why are all massless particles stable? If evidence is found that neutrinos spontaneously decay into other particles, would this imply they have mass?
4: When a star erupts in a supernova explosion, huge numbers of electron neutrinos are formed in nuclear reactions. Such neutrinos from the 1987A supernova in the relatively nearby Magellanic Cloud were observed within hours of the initial brightening, indicating they traveled to earth at approximately the speed of light. Explain how this data can be used to set an upper limit on the mass of the neutrino, noting that if the mass is small the neutrinos could travel very close to the speed of light and have a reasonable energy (on the order of MeV).
5: Theorists have had spectacular success in predicting previously unknown particles. Considering past theoretical triumphs, why should we bother to perform experiments?
6: What lifetime do you expect for an antineutron isolated from normal matter?
7: Why does the
8: (a) Is a hadron always a baryon?
(b) Is a baryon always a hadron?
(c) Can an unstable baryon decay into a meson, leaving no other baryon?
9: Explain how conservation of baryon number is responsible for conservation of total atomic mass (total number of nucleons) in nuclear decay and reactions.
Problems & Exercises
1: The
2: The primary decay mode for the negative pion is
3: The mass of a theoretical particle that may be associated with the unification of the electroweak and strong forces is
(a) How many proton masses is this?
(b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity
4: The decay mode of the negative muon is
(a) Find the energy released in MeV.
(b) Verify that charge and lepton family numbers are conserved.
5: The decay mode of the positive tau is
(a) What energy is released?
(b) Verify that charge and lepton family numbers are conserved.
(c) The
6: The principal decay mode of the sigma zero is
(a) What energy is released?
(b) Considering the quark structure of the two baryons, does it appear that the
(c) Verify that strangeness, charge, and baryon number are conserved in the decay.
(d) Considering the preceding and the short lifetime, can the weak force be responsible? State why or why not.
7: (a) What is the uncertainty in the energy released in the decay of a
(b) What fraction of the decay energy is this, noting that the decay mode is
8: (a) What is the uncertainty in the energy released in the decay of a
(b) Is the uncertainty in this energy greater than or less than the uncertainty in the mass of the tau neutrino? Discuss the source of the uncertainty.
Footnotes
Glossary
- boson
- particle with zero or an integer value of intrinsic spin
- baryons
- hadrons that always decay to another baryon
- baryon number
- a conserved physical quantity that is zero for mesons and leptons and
for baryons and antibaryons, respectively
- conservation of total baryon number
- a general rule based on the observation that the total number of nucleons was always conserved in nuclear reactions and decays
- conservation of total electron family number
- a general rule stating that the total electron family number stays the same through an interaction
- conservation of total muon family number
- a general rule stating that the total muon family number stays the same through an interaction
- electron family number
- the number
that is assigned to all members of the electron family, or the number 0 that is assigned to all particles not in the electron family
- fermion
- particle with a half-integer value of intrinsic spin
- gauge boson
- particle that carries one of the four forces
- hadrons
- particles that feel the strong nuclear force
- leptons
- particles that do not feel the strong nuclear force
- meson
- hadrons that can decay to leptons and leave no hadrons
- muon family number
- the number
that is assigned to all members of the muon family, or the number 0 that is assigned to all particles not in the muon family
- strangeness
- a physical quantity assigned to various particles based on decay systematics
- tau family number
- the number
that is assigned to all members of the tau family, or the number 0 that is assigned to all particles not in the tau family
Solutions
Problems & Exercises
1: 67.5 MeV
3: (a)
(b)
5: (a) 1671 MeV 1671 MeV
(b)
(c)
7: (a) 3.9 eV
(b)