Particles, Patterns, and Conservation Laws

OpenStaxCollege; Saul Beceiro-Novo

Particle Physics and Frontiers of Physics

134 Particles, Patterns, and Conservation Laws

Learning Objectives

Define matter and antimatter and describe how particles differ from their antiparticles.
Explain what happens when a particle and its antiparticle interact.
Distinguish between hadrons and leptons.
Distinguish between mesons and baryons.
Use particle properties and conservation laws to analyze simple particle reactions and decays.

In the early 1930s, only a small number of subatomic particles were known: the electron, proton, neutron, and photon, along with indirect evidence for the neutrino. This relatively short list explained much of atomic and nuclear physics, but it also raised important questions.

For example, why is the positively charged proton almost 2000 times more massive than the negatively charged electron? Why does the electrically neutral neutron have a magnetic moment? Why do protons and neutrons have measurable sizes, while the electron appears pointlike down to the smallest distances yet tested?

These observations suggested that protons and neutrons might contain internal structure, while electrons might be fundamentally different. During the following decades, the discovery of many additional particles revealed that matter is organized into several distinct families.

One of the most important theoretical developments came from British physicist P. A. M. Dirac. In 1928, Dirac developed a relativistic quantum theory of the electron that successfully incorporated both quantum mechanics and special relativity. His theory explained properties such as electron spin and the electron’s magnetic behavior, but it also produced unexpected mathematical solutions corresponding to particles with the same mass as the electron and the opposite electric charge.

These solutions were eventually interpreted as predicting the existence of the positron, the electron’s antiparticle. The positron, represented by [latex]e^+[/latex], has the same mass and intrinsic spin as the electron but carries positive rather than negative electric charge.

In 1932, Carl Anderson discovered positrons while studying tracks produced by cosmic rays. This was the first experimental observation of antimatter and one of the most dramatic confirmations of a theoretical prediction in modern physics.

The discovery of the positron was followed by many others. The muon was observed in cosmic-ray experiments in 1936, pions were discovered in 1947, and increasingly powerful particle accelerators produced dozens and eventually hundreds of short-lived particles.

At first, this growing collection was sometimes called the particle zoo. The apparent complexity eventually led physicists to search for underlying patterns. Those patterns revealed that many particles once thought to be elementary are actually composite structures made from smaller particles called quarks.

This chapter introduces the major categories used to organize known particles, including matter and antimatter, leptons and hadrons, and the two principal groups of hadrons: mesons and baryons.

Portrait of physicist P. A. M. Dirac as a young man. — **Figure 134.1** P. A. M. Dirac developed a relativistic quantum theory of the electron that helped establish quantum electrodynamics and predicted the existence of antimatter. The positron, the electron’s antiparticle, was discovered experimentally several years later. (Credit: Cambridge University, Cavendish Laboratory)

Matter and Antimatter

The discovery of the positron demonstrated that every known particle has a corresponding antiparticle. An antiparticle has the same mass, intrinsic spin, and lifetime as its corresponding particle but differs in certain quantum numbers, most notably electric charge. For example, the electron carries a charge of [latex]-e[/latex], whereas the positron carries a charge of [latex]+e[/latex]. Similarly, the proton has a positively charged antiparticle called the antiproton, and the neutron has an electrically neutral antiparticle called the antineutron.

Some particles are their own antiparticles. The photon, which carries the electromagnetic force, is one example. Another is the neutral pion, [latex]\pi^0[/latex], which has an extremely short lifetime because it rapidly decays into photons.

When a particle encounters its antiparticle, the pair can undergo annihilation, converting their rest mass and kinetic energy into other particles while conserving energy, momentum, electric charge, and all other relevant quantum numbers. Electron-positron annihilation commonly produces two high-energy gamma-ray photons traveling in opposite directions, as illustrated in Figure 134.2.

Diagram showing an electron and a positron colliding and annihilating to produce two gamma-ray photons that travel in opposite directions. — **Figure 134.2** When a particle meets its antiparticle, they may annihilate, converting their mass into other particles. In this example, an electron and a positron annihilate to produce two gamma-ray photons that travel in opposite directions, conserving both energy and momentum.

Antimatter is routinely produced in particle accelerators and certain radioactive decays. For example, antiprotons were first created experimentally in 1955, and antihydrogen atoms, consisting of an antiproton bound to a positron, were first produced at CERN in the 1990s. Although individual antiparticles and small numbers of anti-atoms can be confined using electric and magnetic fields, storing large amounts of antimatter remains extremely difficult because any contact with ordinary matter results in immediate annihilation.

One of the greatest unanswered questions in modern physics is why the observable universe contains far more matter than antimatter. According to current cosmological models, the Big Bang should have produced nearly equal amounts of both. Understanding how this imbalance developed remains an active area of research in particle physics and cosmology.

Healthcare Connection: Positron Emission Tomography (PET)

Antimatter has an important medical application in positron emission tomography (PET). During a PET scan, a radioactive tracer emits positrons as it decays. Each positron quickly encounters an electron in nearby tissue, and the two particles annihilate to produce a pair of gamma-ray photons traveling in opposite directions. Detectors surrounding the patient record these photons simultaneously, allowing a computer to reconstruct detailed three-dimensional images of metabolic activity within the body. PET imaging is widely used in oncology, cardiology, and neurology.

Hadrons and Leptons

Particles can also be classified according to the fundamental forces they experience. Gravity acts on every particle because all particles possess energy. Charged particles experience the electromagnetic force, while neutral particles with internal charge distributions, such as the neutron, can also interact electromagnetically through their magnetic moments.

The most important distinction in particle physics is whether a particle experiences the strong nuclear force.

Hadrons are particles that experience the strong nuclear force.
Leptons are particles that do not experience the strong nuclear force.

Protons, neutrons, and pions are examples of hadrons. Electrons, positrons, muons, tau particles, and neutrinos are examples of leptons. Both hadrons and leptons participate in the weak nuclear interaction, and charged particles from either group also experience the electromagnetic force.

Today we understand that hadrons are composite particles made of quarks, whereas leptons appear to be fundamental particles with no measurable internal structure. Experiments have shown that leptons behave as pointlike particles down to distances smaller than approximately [latex]10^{-18}\,\text{m}[/latex].

Another useful classification depends on a particle's intrinsic spin. Particles with integer spin ([latex]0,1,2,\ldots[/latex]) are called bosons, while particles with half-integer spin ([latex]\frac12,\frac32,\ldots[/latex]) are called fermions.

Fermions obey the Pauli exclusion principle and make up ordinary matter. Bosons act as force carriers or, in some cases, composite particles made from quarks. The particles that transmit the fundamental forces—including the photon and the [latex]W^{\pm}[/latex] and [latex]Z^0[/latex] bosons—are collectively known as gauge bosons.

Table 134.1 summarizes the properties of many of the most important elementary particles and hadrons. Examining these properties reveals patterns that eventually led physicists to the quark model and, ultimately, to the modern Standard Model of particle physics.

**Table 134.1** Selected Particle Characteristics
Category	Particle	Symbol	Antiparticle	Rest mass [latex]\left(\text{MeV}/c^2\right)[/latex]	[latex]B[/latex]	[latex]L_e[/latex]	[latex]L_\mu[/latex]	[latex]L_\tau[/latex]	[latex]S[/latex]	Lifetime (s)
Gauge bosons	Photon	[latex]\gamma[/latex]	Self	0	0	0	0	0	0	Stable
	[latex]W[/latex] boson	[latex]W^+[/latex]	[latex]W^-[/latex]	[latex]80.39\times10^3[/latex]	0	0	0	0	0	[latex]1.6\times10^{-25}[/latex]
	[latex]Z[/latex] boson	[latex]Z^0[/latex]	Self	[latex]91.19\times10^3[/latex]	0	0	0	0	0	[latex]1.32\times10^{-25}[/latex]
Leptons	Electron	[latex]e^-[/latex]	[latex]e^+[/latex]	0.511	0	[latex]\pm1[/latex]	0	0	0	Stable
	Electron neutrino	[latex]\nu_e[/latex]	[latex]\overline{\nu}_e[/latex]	[latex]0\;(\lt 7.0\ \text{eV})[/latex]	0	[latex]\pm1[/latex]	0	0	0	Stable
	Muon	[latex]\mu^-[/latex]	[latex]\mu^+[/latex]	105.7	0	0	[latex]\pm1[/latex]	0	0	[latex]2.20\times10^{-6}[/latex]
	Muon neutrino	[latex]\nu_\mu[/latex]	[latex]\overline{\nu}_\mu[/latex]	[latex]0\;(\lt 0.27)[/latex]	0	0	[latex]\pm1[/latex]	0	0	Stable
	Tau	[latex]\tau^-[/latex]	[latex]\tau^+[/latex]	1777	0	0	0	[latex]\pm1[/latex]	0	[latex]2.91\times10^{-13}[/latex]
	Tau neutrino	[latex]\nu_\tau[/latex]	[latex]\overline{\nu}_\tau[/latex]	[latex]0\;(\lt 31)[/latex]	0	0	0	[latex]\pm1[/latex]	0	Stable
Mesons	Charged pion	[latex]\pi^+[/latex]	[latex]\pi^-[/latex]	139.6	0	0	0	0	0	[latex]2.60\times10^{-8}[/latex]
	Neutral pion	[latex]\pi^0[/latex]	Self	135.0	0	0	0	0	0	[latex]8.4\times10^{-17}[/latex]
	Charged kaon	[latex]K^+[/latex]	[latex]K^-[/latex]	493.7	0	0	0	0	[latex]\pm1[/latex]	[latex]1.24\times10^{-8}[/latex]
	Neutral kaon	[latex]K^0[/latex]	[latex]\overline{K}^0[/latex]	497.6	0	0	0	0	[latex]\pm1[/latex]	[latex]0.90\times10^{-10}[/latex]
	Eta	[latex]\eta^0[/latex]	Self	547.9	0	0	0	0	0	[latex]2.53\times10^{-19}[/latex]
Baryons	Proton	[latex]p[/latex]	[latex]\overline{p}[/latex]	938.3	[latex]\pm1[/latex]	0	0	0	0	Stable
	Neutron	[latex]n[/latex]	[latex]\overline{n}[/latex]	939.6	[latex]\pm1[/latex]	0	0	0	0	882
	Lambda	[latex]\Lambda^0[/latex]	[latex]\overline{\Lambda}^0[/latex]	1115.7	[latex]\pm1[/latex]	0	0	0	[latex]\mp1[/latex]	[latex]2.63\times10^{-10}[/latex]
	Positive sigma	[latex]\Sigma^+[/latex]	[latex]\overline{\Sigma}^-[/latex]	1189.4	[latex]\pm1[/latex]	0	0	0	[latex]\mp1[/latex]	[latex]0.80\times10^{-10}[/latex]
	Neutral sigma	[latex]\Sigma^0[/latex]	[latex]\overline{\Sigma}^0[/latex]	1192.6	[latex]\pm1[/latex]	0	0	0	[latex]\mp1[/latex]	[latex]7.4\times10^{-20}[/latex]
	Negative sigma	[latex]\Sigma^-[/latex]	[latex]\overline{\Sigma}^+[/latex]	1197.4	[latex]\pm1[/latex]	0	0	0	[latex]\mp1[/latex]	[latex]1.48\times10^{-10}[/latex]
	Neutral xi	[latex]\Xi^0[/latex]	[latex]\overline{\Xi}^0[/latex]	1314.9	[latex]\pm1[/latex]	0	0	0	[latex]\mp2[/latex]	[latex]2.90\times10^{-10}[/latex]
	Negative xi	[latex]\Xi^-[/latex]	[latex]\overline{\Xi}^+[/latex]	1321.7	[latex]\pm1[/latex]	0	0	0	[latex]\mp2[/latex]	[latex]1.64\times10^{-10}[/latex]
	Omega	[latex]\Omega^-[/latex]	[latex]\overline{\Omega}^+[/latex]	1672.5	[latex]\pm1[/latex]	0	0	0	[latex]\mp3[/latex]	[latex]0.82\times10^{-10}[/latex]

Note:

When a table entry contains [latex]\pm[/latex] or [latex]\mp[/latex], the upper sign applies to the particle and the lower sign applies to its antiparticle. Only selected hadrons are shown; many additional mesons and baryons have been observed.

The Three Lepton Families

The six known leptons are organized into three families, or generations. Each family contains one charged lepton and one electrically neutral neutrino:

the electron and electron neutrino,
the muon and muon neutrino, and
the tau and tau neutrino.

Each charged lepton has an antiparticle with the same mass and opposite charge. Each neutrino also has a corresponding antineutrino. Leptons appear to have no internal structure and behave as pointlike particles down to distances of approximately [latex]10^{-18}\,\text{m}[/latex].

A quantum number can be assigned to each lepton family. The electron family number is represented by [latex]L_e[/latex], the muon family number by [latex]L_\mu[/latex], and the tau family number by [latex]L_\tau[/latex].

A lepton is assigned a family number of [latex]+1[/latex] for its own family, while its antiparticle is assigned [latex]-1[/latex]. Particles belonging to other families are assigned zero.

For example:

an electron has [latex]L_e=+1[/latex],
a positron has [latex]L_e=-1[/latex],
an electron neutrino has [latex]L_e=+1[/latex], and
an electron antineutrino has [latex]L_e=-1[/latex].

These assignments help physicists analyze whether a proposed reaction or decay is allowed. In beta decay, for example, the creation of an electron is accompanied by the creation of an electron antineutrino. Their electron family numbers add to zero:

[latex]L_e=(+1)+(-1)=0.[/latex]

The muon’s most common decay illustrates the involvement of two lepton families:

[latex]\mu^-\rightarrow e^-+\overline{\nu}_e+\nu_\mu.[/latex]

Before the decay, the muon has

[latex]L_\mu=+1 \qquad\text{and}\qquad L_e=0.[/latex]

After the decay, the muon neutrino carries [latex]L_\mu=+1[/latex]. The electron and electron antineutrino have electron family numbers [latex]+1[/latex] and [latex]-1[/latex], so their total electron family number remains zero:

[latex]L_e=(+1)+(-1)=0.[/latex]

The tau lepton decays in a similar way. One possible decay is

[latex]\tau^-\rightarrow \mu^-+\overline{\nu}_\mu+\nu_\tau.[/latex]

The tau neutrino carries the original tau family number, while the muon and muon antineutrino have opposite muon family numbers. Consequently, the total values of [latex]L_\tau[/latex] and [latex]L_\mu[/latex] are unchanged during the decay.

Lepton family numbers are useful conservation rules for many particle reactions. However, neutrino oscillations show that neutrinos can transform from one family type into another as they travel. Individual electron, muon, and tau family numbers are therefore not universally conserved, although the total lepton number remains an important organizing principle in the reactions considered here.

Mesons and Baryons

Hadrons are divided into two major groups: mesons and baryons. Although the names originally referred to particles of intermediate and large mass, respectively, the modern distinction is based on their internal structure and conservation laws rather than their masses.

According to the quark model, mesons consist of one quark and one antiquark, whereas baryons consist of three quarks. Although the details of quarks are introduced in the next chapter, this simple classification explains many of the observed properties of hadrons.

Mesons include particles such as the pions ([latex]\pi[/latex]), kaons ([latex]K[/latex]), and eta mesons ([latex]\eta[/latex]). They are generally unstable and eventually decay into lighter particles. Because mesons have a baryon number of zero, they may decay entirely into leptons, photons, or other mesons.

Baryons include the familiar proton and neutron as well as heavier particles such as the lambda ([latex]\Lambda[/latex]), sigma ([latex]\Sigma[/latex]), xi ([latex]\Xi[/latex]), and omega ([latex]\Omega[/latex]) particles. Every baryon eventually decays into another baryon unless it is already the lightest member of the family. For example, the proton is stable, while the neutron decays into a proton through the weak interaction.

A useful quantity for describing these particles is the baryon number, represented by the symbol [latex]B[/latex].

Leptons and mesons have [latex]B=0[/latex].
Baryons have [latex]B=+1[/latex].
Antibaryons have [latex]B=-1[/latex].

Experiments have shown that the total baryon number is conserved in all observed particle reactions. This conservation law extends the familiar observation from nuclear physics that the total number of nucleons remains constant in ordinary nuclear reactions. In modern particle physics, nucleon conservation is understood as a consequence of the more general conservation of baryon number.

Forces, Reactions, and Reaction Rates

The fundamental forces determine not only how particles interact with one another but also how rapidly unstable particles decay. In general, stronger interactions produce more probable reactions and shorter particle lifetimes.

For example, pions interact through the strong nuclear force and therefore lose energy rapidly when passing through matter. Muons, on the other hand, do not experience the strong interaction and can penetrate much farther into materials. This difference in penetration depth helped physicists recognize that the muon could not be the particle responsible for carrying the strong nuclear force.

The interaction responsible for a particle's decay can often be identified by measuring its lifetime. Decays governed by the strong interaction occur extremely rapidly, whereas weak-interaction decays are much slower.

For example, the unstable nucleus beryllium-8 decays through the strong interaction:

[latex]{}^{8}\mathrm{Be}\rightarrow \alpha+\alpha .[/latex]

Its lifetime is only about

[latex]10^{-16}\ \text{s}.[/latex]

By contrast, the neutron decays through the weak interaction:

[latex]n\rightarrow p+e^-+\overline{\nu}_e,[/latex]

with a mean lifetime of approximately

[latex]882\ \text{s}.[/latex]

One clue that the neutron decays through the weak interaction is the appearance of leptons among the decay products. The strong interaction does not produce isolated leptons in this way.

More generally,

strong-interaction decays typically have lifetimes between approximately [latex]10^{-23}[/latex] and [latex]10^{-16}\ \text{s}[/latex],
weak-interaction decays usually have lifetimes between about [latex]10^{-16}[/latex] and [latex]10^{-6}\ \text{s}[/latex], although some particles live considerably longer.

Consequently, measuring a particle's lifetime often provides evidence for which fundamental interaction is responsible for its decay.

Strangeness

As more particles were discovered during the 1950s and 1960s, physicists noticed another intriguing pattern. Particles such as the lambda ([latex]\Lambda[/latex]), sigma ([latex]\Sigma[/latex]), xi ([latex]\Xi[/latex]), and omega ([latex]\Omega[/latex]) baryons were readily produced in strong-interaction collisions but decayed much more slowly than expected. Their comparatively long lifetimes indicated that their decays occurred through the weak interaction instead.

To describe this behavior, physicists introduced a new quantum number called strangeness, represented by the symbol [latex]S[/latex]. Values of strangeness were assigned so that experimental observations followed a simple rule:

Strangeness is conserved in strong interactions.
Strangeness is not conserved in weak interactions.

This rule successfully explained why certain particles could be produced easily in accelerator experiments yet decay only through relatively slow weak-interaction processes.

Today we understand that strangeness is directly related to the presence of strange quarks inside hadrons. Although the quark model had not yet been developed when strangeness was first proposed, the conservation of strangeness provided one of the strongest clues that hadrons possessed an internal structure.

Together with the conservation of electric charge, baryon number, lepton numbers, and energy, strangeness became one of the key organizing principles that allowed physicists to classify hundreds of newly discovered particles. These conservation laws ultimately led to the development of the quark model, which is the subject of the next chapter.

Worked Example: Applying Conservation Laws to Particle Decays

Conservation laws provide a powerful way to determine whether a particle decay is possible. In this example, we use the quantum numbers listed in Table 134.1 to analyze two common particle decays.

Problem

(a) The most common decay mode of the [latex]\Xi^-[/latex] particle is

[latex]\Xi^- \rightarrow \Lambda^0+\pi^-.[/latex]

Using the quantum numbers in Table 134.1, show that strangeness changes by one unit while baryon number, electric charge, and lepton family numbers are conserved.

(b) Determine whether the decay

[latex]K^+\rightarrow\mu^++\nu_\mu[/latex]

is allowed.

Strategy

For each decay, compare the quantum numbers of the initial particle with the sum of the quantum numbers of the decay products. A decay is allowed only if all applicable conservation laws are satisfied.

Solution

(a) Before the decay, the [latex]\Xi^-[/latex] has

Strangeness: [latex]S=-2[/latex]
Baryon number: [latex]B=+1[/latex]
Charge: [latex]Q=-1[/latex]
Lepton family numbers: all zero

After the decay, the products have the following quantum numbers:

[latex]\Lambda^0[/latex]: [latex]S=-1,\;B=+1,\;Q=0[/latex]
[latex]\pi^-[/latex]: [latex]S=0,\;B=0,\;Q=-1[/latex]

Therefore,

Strangeness changes from [latex]-2[/latex] to [latex]-1[/latex] (a change of +1).
Total baryon number remains [latex]+1[/latex].
Total electric charge remains [latex]-1[/latex].
All lepton family numbers remain zero.

(b) Consider the decay

[latex]K^+\rightarrow\mu^++\nu_\mu.[/latex]

Checking each conservation law:

Electric charge: [latex]+1\rightarrow(+1)+0[/latex] ✓
Baryon number: [latex]0\rightarrow0+0[/latex] ✓
Muon family number: [latex]0\rightarrow(-1)+(+1)=0[/latex] ✓
Electron and tau family numbers remain zero ✓
Mass-energy is conserved because the kaon is more massive than the decay products ✓
Strangeness changes from [latex]+1[/latex] to [latex]0[/latex], which is allowed for a weak interaction ✓

Since every relevant conservation law is satisfied, this decay is allowed.

Discussion

In part (a), the change in strangeness immediately indicates that the decay proceeds through the weak interaction, consistent with the relatively long lifetime of the [latex]\Xi^-[/latex] particle.

The decay in part (b) is the dominant decay mode of the charged kaon. Its lifetime of approximately [latex]1.24\times10^{-8}\,\text{s}[/latex] is also characteristic of a weak-interaction decay.

Only a small fraction of the known hadrons are listed in Table 134.1. Hundreds of additional particles have been discovered, many with extremely short lifetimes. Despite this apparent complexity, their production and decay follow a relatively small set of conservation laws involving electric charge, baryon number, lepton numbers, strangeness, energy, and momentum.

As physicists accumulated experimental data, they recognized patterns in particle masses, lifetimes, and decay modes that suggested hadrons were not elementary particles. Instead, these observations pointed to an underlying internal structure. Today we understand that leptons are fundamental particles, while hadrons are composite particles built from quarks.

The next chapter introduces the quark model and shows how combinations of just a few types of quarks can explain the remarkable variety of mesons and baryons observed in nature.

Portrait of physicist Murray Gell-Mann, who proposed the quark model to explain the internal structure of hadrons. — **Figure 134.3** Murray Gell-Mann proposed the quark model in 1964, providing a simple explanation for the growing number of observed hadrons and the conservation laws that govern their interactions. His work earned the 1969 Nobel Prize in Physics. (Credit: Luboš Motl)

Section Summary

Every known particle has a corresponding antiparticle with the same mass and intrinsic spin but opposite values of electric charge and certain other quantum numbers. When a particle and its antiparticle meet, they may annihilate and convert their energy into other particles, often photons.
Known particles can be organized into matter particles and force-carrier particles. Matter particles include leptons and hadrons, while gauge bosons carry the fundamental interactions.
Leptons do not experience the strong nuclear force. The six known leptons form three families: the electron family, the muon family, and the tau family.
Lepton family numbers are useful conservation quantities in many reactions, although neutrino oscillations show that individual family numbers are not universally conserved.
Hadrons experience the strong nuclear force and are composed of quarks. They are divided into mesons and baryons.
Mesons contain a quark-antiquark pair and have baryon number [latex]B=0[/latex]. Baryons contain three quarks and have baryon number [latex]B=+1[/latex], while antibaryons have [latex]B=-1[/latex].
Total baryon number is conserved in all observed particle reactions. Conservation of nucleon number in ordinary nuclear reactions is a special case of this broader conservation law.
The interaction responsible for a particle decay can often be inferred from its lifetime. Strong-interaction decays are generally much faster than weak-interaction decays.
Strangeness is conserved in strong interactions but may change in weak interactions. This pattern helped reveal the quark structure of hadrons.

Conceptual Questions

Suppose a large quantity of antimatter could be isolated from ordinary matter. An anti-atom made from positrons, antiprotons, and antineutrons should have the same atomic spectrum as the corresponding ordinary atom. Could you identify it as antimatter by detecting “antiphotons” in its emission spectrum? Explain.
Why can a massless particle not carry electric charge?
Massless particles must travel at the speed of light in a vacuum. Why does this make a spontaneous decay into slower particles impossible unless other conservation requirements are satisfied?
Suppose evidence showed that a neutrino could spontaneously decay into lighter particles. What would this imply about the neutrino’s mass?
Neutrinos from supernova 1987A arrived on Earth within a few hours of the first observed light from the explosion. Explain how the small difference in arrival times can be used to place an upper limit on neutrino mass.
Theoretical physics has successfully predicted several particles before they were observed experimentally. Why are experiments still necessary?
What lifetime would you expect for an antineutron isolated from ordinary matter? Explain your reasoning.
Why does the [latex]\eta^0[/latex] meson have a much shorter lifetime than many particles that decay through the weak interaction?
1. Is every hadron a baryon?
2. Is every baryon a hadron?
3. Can a baryon decay entirely into mesons and leptons, leaving no baryon among the products? Explain.
Explain how conservation of baryon number leads to conservation of the total number of nucleons in ordinary nuclear reactions and decays.
A particle is produced readily in strong-interaction collisions but has a comparatively long lifetime. What might this suggest about the interaction responsible for its decay?
Why does a change in strangeness indicate that a decay cannot be caused entirely by the strong interaction?

Problems & Exercises

The neutral pion is its own antiparticle and decays according to
[latex]\pi^0\rightarrow\gamma+\gamma.[/latex]

What is the energy of each gamma-ray photon if the [latex]\pi^0[/latex] is initially at rest?
The principal decay mode of the negative pion is
[latex]\pi^-\rightarrow\mu^-+\overline{\nu}_\mu.[/latex]

Calculate the energy released in this decay in MeV. Treat the neutrino mass as negligible.
A theoretical particle associated with unification of the strong and electroweak interactions is predicted to have a rest mass of
[latex]10^{14}\ \text{GeV}/c^2.[/latex]
1. How many proton masses is this?
2. How many electron masses is this?
3. Why would producing such a particle require an accelerator operating at an energy far beyond that needed to create ordinary hadrons?
The negative muon decays according to
[latex]\mu^-\rightarrow e^-+\overline{\nu}_e+\nu_\mu.[/latex]
1. Find the total energy released in MeV, treating the neutrino masses as negligible.
2. Verify that electric charge is conserved.
3. Verify that the electron and muon family numbers are conserved.
The positive tau can decay according to
[latex]\tau^+\rightarrow\mu^++\nu_\mu+\overline{\nu}_\tau.[/latex]
1. Calculate the energy released, treating the neutrino masses as negligible.
2. Verify that electric charge is conserved.
3. Verify that the muon and tau family numbers are conserved.
4. Show that each decay product is the antiparticle of the corresponding product in the decay of a [latex]\tau^-[/latex].
The principal decay mode of the neutral sigma particle is
[latex]\Sigma^0\rightarrow\Lambda^0+\gamma.[/latex]
1. Calculate the energy released in the decay.
2. Does the small difference in mass suggest that the [latex]\Sigma^0[/latex] may be an excited state related to the [latex]\Lambda^0[/latex]? Explain.
3. Verify that strangeness, electric charge, and baryon number are conserved.
4. Given the very short lifetime of the [latex]\Sigma^0[/latex], is the weak interaction likely to be responsible for this decay? Explain.
The neutral pion has a very short lifetime and decays according to
[latex]\pi^0\rightarrow\gamma+\gamma.[/latex]
1. Use the energy-time uncertainty relation to estimate the uncertainty in the energy released by the decay.
2. What fraction of the total decay energy does this uncertainty represent?
1. Use the energy-time uncertainty relation to estimate the uncertainty in the rest energy of the [latex]\tau^-[/latex] due to its short lifetime.
2. Compare this uncertainty with the experimental uncertainty in the tau-neutrino mass.
3. Explain why the uncertainty associated with the tau lifetime and the uncertainty in the neutrino mass arise from different physical sources.
Consider the hypothetical decay
[latex]p\rightarrow\pi^0+e^+.[/latex]
1. Determine the total baryon number before and after the decay.
2. Would this decay be allowed under baryon-number conservation?
3. Explain why searches for proton decay provide tests of theories that extend beyond the Standard Model.
Consider the proposed decay
[latex]K^0\rightarrow\pi^++\pi^-.[/latex]
1. Verify that electric charge and baryon number are conserved.
2. Determine the strangeness before and after the decay.
3. Which fundamental interaction must be responsible for the decay?

Glossary

antimatter: Matter composed of antiparticles, which have the same masses and intrinsic spins as corresponding ordinary particles but opposite values of certain quantum numbers, such as electric charge.
antiparticle: A particle with the same mass and intrinsic spin as another particle but opposite electric charge and other opposite quantum numbers.
annihilation: A process in which a particle and its antiparticle interact and convert their energy into other particles, often photons.
baryon: A hadron composed of three quarks. Protons and neutrons are baryons.
baryon number: A conserved quantum number represented by [latex]B[/latex]. Baryons have [latex]B=+1[/latex], antibaryons have [latex]B=-1[/latex], and leptons and mesons have [latex]B=0[/latex].
boson: A particle with integer intrinsic spin. Bosons do not obey the Pauli exclusion principle.
fermion: A particle with half-integer intrinsic spin. Fermions obey the Pauli exclusion principle.
gauge boson: A boson that carries one of the fundamental interactions, such as the photon or the [latex]W[/latex] and [latex]Z[/latex] bosons.
hadron: A composite particle made of quarks that participates in the strong nuclear interaction.
lepton: A fundamental particle that does not participate in the strong nuclear interaction. Electrons, muons, tau particles, and neutrinos are leptons.
lepton family number: A quantum number associated with the electron, muon, or tau family and represented by [latex]L_e[/latex], [latex]L_\mu[/latex], or [latex]L_\tau[/latex].
meson: A hadron composed of one quark and one antiquark. Mesons have baryon number zero.
neutrino oscillation: The transformation of a neutrino from one family type into another as it travels.
strangeness: A quantum number represented by [latex]S[/latex] and associated with the presence of strange quarks in a hadron. Strangeness is conserved in strong interactions but may change in weak interactions.

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