Contents

Particles, Patterns, and Conservation Laws

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 33.12) 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 $e^{+} e^{+} size 12{e rSup { size 8{+{}} } } {}$ , is the same particle as emitted in $β^{+} β^{+} size 12{e rSup { size 8{+{}} } } {}$ decay and was the first antimatter that was discovered. In 1935, Yukawa predicted pions as the carriers of the strong nuclear force, and they were eventually discovered. Muons were discovered in cosmic ray experiments in 1937, and they seemed to be heavy, unstable versions of electrons and positrons. After World War II, accelerators energetic enough to create these particles were built. Not only were predicted and known particles created, but many unexpected particles were observed. Initially called elementary particles, their numbers proliferated to dozens and then hundreds, and the term “particle zoo” became the physicist’s lament at the lack of simplicity. But patterns were observed in the particle zoo that led to simplifying ideas such as quarks, as we shall soon see.

Figure 33.12 P.A.M. Dirac’s theory of relativistic quantum mechanics not only explained a great deal of what was known, it also predicted antimatter. (credit: Cambridge University, Cavendish Laboratory)

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 33.13. 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 $π^{0} π^{0} size 12{π rSup { size 8{0} } } {}$ is its own antiparticle and has a half-life about $10^{- 8} 10^{- 8} size 12{"10" rSup { size 8{ - 8} } } {}$ shorter than $π^{+} π^{+} size 12{π rSup { size 8{+{}} } } {}$ and $π^{-} π^{-} size 12{π rSup { size 8{ - {}} } } {}$ , which are each other’s antiparticles. Without exception, nature is symmetric—all particles have antimatter counterparts. For example, antiprotons and antineutrons were first created in accelerator experiments in 1956 and the antiproton is negative. Antihydrogen atoms, consisting of an antiproton and antielectron, were observed in 1995 at CERN, too. It is possible to contain large-scale antimatter particles such as antiprotons by using electromagnetic traps that confine the particles within a magnetic field so that they don't annihilate with other particles. However, particles of the same charge repel each other, so the more particles that are contained in a trap, the more energy is needed to power the magnetic field that contains them. It is not currently possible to store a significant quantity of antiprotons. At any rate, we now see that negative charge is associated with both low-mass (electrons) and high-mass particles (antiprotons) and the apparent asymmetry is not there. But this knowledge does raise another question—why is there such a predominance of matter and so little antimatter? Possible explanations emerge later in this and the next chapter.

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 33.2 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 Patterns in Spectra Reveal More Quantization, a boson is a particle with zero or an integer value of intrinsic spin (such as $s = 0, 1, 2, ... s = 0, 1, 2, ... size 12{s=0,`1,`2,` "." "." "." } {}$ ), whereas a fermion is a particle with a half-integer value of intrinsic spin ( $s = 1 / 2, 3 / 2, . . . s = 1 / 2, size 12{s=1/2,`3/2,` "." "." "." } {}$ ). Fermions obey the Pauli exclusion principle whereas bosons do not. All the known and conjectured carrier particles are bosons.

The upper image shows an electron and positron colliding head-on. The lower image shows a starburst image from which two photons are emerging in opposite directions.

Figure 33.13 When a particle encounters its antiparticle, they annihilate, often producing pure energy in the form of photons. In this case, an electron and a positron convert all their mass into two identical energy rays, which move away in opposite directions to keep total momentum zero as it was before. Similar annihilations occur for other combinations of a particle with its antiparticle, sometimes producing more particles while obeying all conservation laws.

Category	Particle name	Symbol	Antiparticle	Rest mass $(MeV / c^{2}) (MeV / c^{2})$	$B B$	$L_{e} L_{e}$	$L_{μ} L_{μ}$	$L_{τ} L_{τ} size 12{L rSub { size 8{τ} } } {}$	$S S size 12{S} {}$	Lifetime4 (s) 4 Lifetimes are traditionally given as $t_{1 / 2} / 0 . 693 t_{1 / 2} / 0 . 693$ (which is $1 / λ 1 / λ size 12{ {1} slash {λ} } {}$ , the inverse of the decay constant).
Gauge	Photon	$γ γ size 12{γ} {}$	Self	0	0	0	0	0	0	Stable
Bosons	$W W size 12{W} {}$	$W^{+} W^{+} size 12{W rSup { size 8{+{}} } } {}$	$W^{-} W^{-} size 12{W rSup { size 8{ - {}} } } {}$	$80 . 39 \times 10^{3} 80 . 39 \times 10^{3} size 12{"80" "." "22" times "10" rSup { size 8{3} } } {}$	0	0	0	0	0	$1.6 \times 10^{- 25} 1.6 \times 10^{- 25} size 12{3 times "10" rSup { size 8{ - "25"} } } {}$
Bosons	$Z Z size 12{Z} {}$	$Z^{0} Z^{0} size 12{Z rSup { size 8{0} } } {}$	Self	$91 . 19 \times 10^{3} 91 . 19 \times 10^{3} size 12{"91" "." "19" times "10" rSup { size 8{3} } } {}$	0	0	0	0	0	$1.32 \times 10^{- 25} 1.32 \times 10^{- 25} size 12{3 times "10" rSup { size 8{ - "25"} } } {}$
Leptons	Electron	$e^{-} e^{-} size 12{e rSup { size 8{ - {}} } } {}$	$e^{+} e^{+} size 12{e rSup { size 8{ - {}} } } {}$	0.511	0	$\pm 1 \pm 1 size 12{ +- 1} {}$	0	0	0	Stable
	Neutrino (e)	$ν_{e} ν_{e} size 12{e rSup { size 8{ - {}} } } {}$	${\bar{v}}_{e} {\bar{v}}_{e} size 12{ { bar {v}} rSub { size 8{e} } } {}$	$0 (7.0 eV) 0 (7.0 eV) size 12{0` left (<7 "." 0`"eV" right )} {}$ 5 5 Neutrino masses may be zero. Experimental upper limits are given in parentheses.	0	$\pm 1 \pm 1 size 12{ +- 1} {}$	0	0	0	Stable
	Muon	$μ^{-} μ^{-} size 12{μ rSup { size 8{ - {}} } } {}$	$μ^{+} μ^{+} size 12{μ rSup { size 8{+{}} } } {}$	105.7	0	0	$\pm 1 \pm 1 size 12{ +- 1} {}$	0	0	$2 . 20 \times 10^{- 6} 2 . 20 \times 10^{- 6} size 12{2 "." "20" times "10" rSup { size 8{ - 6} } } {}$
	Neutrino $(μ) (μ size 12{μ} {})$	$v_{μ} v_{μ} size 12{v rSub { size 8{μ} } } {}$	${\bar{v}}_{μ} {\bar{v}}_{μ} size 12{v rSub { size 8{μ} } } {}$	$0 (< 0.27) 0 (< 0.27)$	0	0	$\pm 1 \pm 1 size 12{ +- 1} {}$	0	0	Stable
	Tau	$τ^{-} τ^{-} size 12{τ rSup { size 8{ - {}} } } {}$	$τ^{+} τ^{+} size 12{τ rSup { size 8{+{}} } } {}$	1777	0	0	0	$\pm 1 \pm 1 size 12{ +- 1} {}$	0	$2 . 91 \times 10^{- 13} 2 . 91 \times 10^{- 13} size 12{2 "." "29" times "10" rSup { size 8{ - "13"} } } {}$
	Neutrino $(τ) (τ size 12{τ} {})$	$v_{τ} v_{τ} size 12{v rSub { size 8{τ} } } {}$	${\bar{v}}_{τ} {\bar{v}}_{τ} size 12{ { bar {v}} rSub { size 8{τ} } } {}$	$0 (< 31) 0 (< 31)$	0	0	0	$\pm 1 \pm 1 size 12{ +- 1} {}$	0	Stable
Hadrons (selected)
Mesons	Pion	$π^{+} π^{+} size 12{π rSup { size 8{+{}} } } {}$	$π^{-} π^{-} size 12{π rSup { size 8{ - {}} } } {}$	139.6	0	0	0	0	0	2.60 × 10 ⁻⁸
	Pion	$π^{0} π^{0} size 12{π rSup { size 8{0} } } {}$	Self	135.0	0	0	0	0	0	8.4 × 10 ⁻¹⁷
	Kaon	$K^{+} K^{+} size 12{K rSup { size 8{+{}} } } {}$	$K^{-} K^{-} size 12{K rSup { size 8{ - {}} } } {}$	493.7	0	0	0	0	$\pm 1 \pm 1 size 12{ +- 1} {}$	1.24 × 10 ⁻⁸
	Kaon	$K^{0} K^{0} size 12{K rSup { size 8{0} } } {}$	${\bar{K}}^{0} {\bar{K}}^{0} size 12{ { bar {K}} rSup { size 8{0} } } {}$	497.6	0	0	0	0	$\pm 1 \pm 1 size 12{ +- 1} {}$	0.90 × 10 ⁻¹⁰
	Eta	$η^{0} η^{0} size 12{η rSup { size 8{0} } } {}$	Self	547.9	0	0	0	0	0	2.53 × 10 ⁻¹⁹
(many other mesons known)
Baryons	Proton	$p p size 12{p} {}$	$\bar{p} \bar{p} size 12{ { bar {p}}} {}$	938.3	± 1	0	0	0	0	Stable6 6 Experimental lower limit is $>5 \times 10^{32} >5 \times 10^{32} size 12{>5 times "10" rSup { size 8{"32"} } } {}$ for proposed mode of decay.
	Neutron	$n n size 12{n} {}$	$\bar{n} \bar{n} size 12{ { bar {n}}} {}$	939.6	± 1	0	0	0	0	882
	Lambda	$Λ^{0} Λ^{0} size 12{Λ rSup { size 8{0} } } {}$	${\bar{Λ}}^{0} {\bar{Λ}}^{0} size 12{ { bar {Λ}} rSup { size 8{0} } } {}$	1115.7	± 1	0	0	0	$\mp 1 \mp 1 size 12{ -+ 1} {}$	2.63 × 10 ⁻¹⁰
	Sigma	$Σ^{+} Σ^{+} size 12{Σ rSup { size 8{+{}} } } {}$	${\bar{Σ}}^{-} {\bar{Σ}}^{-} size 12{ { bar {Σ}} rSup { size 8{ - {}} } } {}$	1189.4	± 1	0	0	0	$\mp 1 \mp 1 size 12{ -+ 1} {}$	0.80 × 10 ⁻¹⁰
		$Σ^{0} Σ^{0} size 12{Σ rSup { size 8{0} } } {}$	${\bar{Σ}}^{0} {\bar{Σ}}^{0} size 12{ { bar {Σ}} rSup { size 8{0} } } {}$	1192.6	± 1	0	0	0	$\mp 1 \mp 1 size 12{ -+ 1} {}$	7.4 × 10 ⁻²⁰
		$Σ^{-} Σ^{-} size 12{Σ rSup { size 8{ - {}} } } {}$	${\bar{Σ}}^{+} {\bar{Σ}}^{+} size 12{ { bar {Σ}} rSup { size 8{+{}} } } {}$	1197.4	± 1	0	0	0	$\mp 1 \mp 1 size 12{ -+ 1} {}$	1.48 × 10 ⁻¹⁰
	Xi	$Ξ^{0} Ξ^{0} size 12{Ξ rSup { size 8{0} } } {}$	${\bar{Ξ}}^{0} {\bar{Ξ}}^{0} size 12{ { bar {Ξ}} rSup { size 8{0} } } {}$	1314.9	± 1	0	0	0	$\mp 2 \mp 2 size 12{ -+ 2} {}$	2.90 × 10 ⁻¹⁰
	Xi	$Ξ^{-} Ξ^{-} size 12{Ξ rSup { size 8{ - {}} } } {}$	$Ξ^{+} Ξ^{+} size 12{Ξ rSup { size 8{+{}} } } {}$	1321.7	± 1	0	0	0	$\mp 2 \mp 2 size 12{ -+ 2} {}$	1.64 × 10 ⁻¹⁰
	Omega	$Ω^{-} Ω^{-} size 12{ %OMEGA rSup { size 8{ - {}} } } {}$	$Ω^{+} Ω^{+} size 12{ %OMEGA rSup { size 8{+{}} } } {}$	1672.5	± 1	0	0	0	$\mp 3 \mp 3 size 12{ -+ 3} {}$	0.82 × 10 ⁻¹⁰
(many other baryons known)

Table 33.2 Selected Particle Characteristics7

The lower of the

\mp \mp size 12{ -+ {}} {}

\pm \pm size 12{ +- {}} {}

symbols are the values for antiparticles.

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 $10^{- 18} m 10^{- 18} size 12{"10" rSup { size 8{ - "18"} } m} {}$ . The leptons fall into three families, implying three conservation laws for three quantum numbers. One of these was known from $β β size 12{β} {}$ decay, where the existence of the electron’s neutrino implied that a new quantum number, called the electron family number $L_{e} L_{e} size 12{L rSub { size 8{e} } } {}$ is conserved. Thus, in $β β size 12{β} {}$ decay, an antielectron’s neutrino ${\bar{v}}_{e} {\bar{v}}_{e} size 12{ { bar {v}} rSub { size 8{e} } } {}$ must be created with $L_{e} = - 1 L_{e} = - 1 size 12{L rSub { size 8{e} } = - 1} {}$ when an electron with $L_{e} =+ 1 L_{e} =+ 1 size 12{L rSub { size 8{e} } "=+"1} {}$ is created, so that the total remains 0 as it was before decay.

Once the muon was discovered in cosmic rays, its decay mode was found to be

μ^{-} \to e^{-} + {\bar{v}}_{e} + v_{μ}, μ^{-} \to e^{-} + {\bar{v}}_{e} + v_{μ}, size 12{μ rSup { size 8{ - {}} }  rightarrow e rSup { size 8{ - {}} } + { bar  {v}} rSub { size 8{e} } +v rSub { size 8{μ} } ","} {}

33.7

which implied another “family” and associated conservation principle. The particle $v_{μ} v_{μ} size 12{L rSub { size 8{μ} } } {}$ is a muon’s neutrino, and it is created to conserve muon family number $L_{μ} L_{μ} size 12{L rSub { size 8{μ} } } {}$ . So muons are leptons with a family of their own, and conservation of total $L_{μ} L_{μ} size 12{L rSub { size 8{μ} } } {}$ also seems to be obeyed in many experiments.

More recently, a third lepton family was discovered when $τ τ size 12{τ} {}$ particles were created and observed to decay in a manner similar to muons. One principal decay mode is

τ^{-} \to μ^{-} + {\bar{v}}_{μ} + v_{τ} . τ^{-} \to μ^{-} + {\bar{v}}_{μ} + v_{τ} . size 12{τ rSup { size 8{ - {}} }  rightarrow μ rSup { size 8{ - {}} } + { bar  {v}} rSub { size 8{u} } +v rSub { size 8{τ} } "."} {}

33.8

Conservation of total $L_{τ} L_{τ} size 12{L rSub { size 8{μ} } } {}$ seems to be another law obeyed in many experiments. In fact, particle experiments have found that lepton family number is not universally conserved, due to neutrino “oscillations,” or transformations of neutrinos from one family type to another.

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 $B B size 12{B} {}$ seems to always be conserved in nature and is listed for the various particles in the table given above. Mesons and leptons have $B = 0 B = 0 size 12{B=0} {}$ so that they can decay to other particles with $B = 0 B = 0 size 12{B=0} {}$ . But baryons have $B =+ 1 B =+ 1 size 12{B"=+"1} {}$ if they are matter, and $B = - 1 B = - 1 size 12{B= - 1} {}$ if they are antimatter. The conservation of total baryon number is a more general rule than first noted in nuclear physics, where it was observed that the total number of nucleons was always conserved in nuclear reactions and decays. That rule in nuclear physics is just one consequence of the conservation of the total 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 $8 Be \to α + α 8 Be \to α + α size 12{"" lSup { size 8{8} } "Be" rightarrow α+α} {}$ with a lifetime of about $10^{- 16} s 10^{- 16} size 12{"10" rSup { size 8{ - "16"} } `s} {}$ . The neutron is a good example of decay via the weak force. The process $n \to p + e^{-} + {\bar{v}}_{e} n \to p + e^{-} + {\bar{v}}_{e} size 12{n rightarrow p+e rSup { size 8{ - {}} } + { bar {v}} rSub { size 8{e} } } {}$ has a longer lifetime of 882 s. The weak force causes this decay, as it does all $β β size 12{β} {}$ decay. An important clue that the weak force is responsible for $β β size 12{β} {}$ decay is the creation of leptons, such as $e^{-} e^{-} size 12{e rSup { size 8{ - {}} } } {}$ and ${\bar{v}}_{e} {\bar{v}}_{e} size 12{ { bar {v}} rSub { size 8{e} } } {}$ . None would be created if the strong force was responsible, just as no leptons are created in the decay of $8 Be 8 Be size 12{"" lSup { size 8{8} } "Be"} {}$ . The systematics of particle lifetimes is a little simpler than nuclear lifetimes when hundreds of particles are examined (not just the ones in the table given above). Particles that decay via the weak force have lifetimes mostly in the range of $10^{- 16} 10^{- 16} size 12{"10" rSup { size 8{ - "16"} } } {}$ to $10^{- 12} 10^{- 12} size 12{"10" rSup { size 8{ - "12"} } } {}$ s, whereas those that decay via the strong force have lifetimes mostly in the range of $10^{- 16} 10^{- 16} size 12{"10" rSup { size 8{ - "16"} } } {}$ to $10^{- 23} 10^{- 23} size 12{"10" rSup { size 8{ - "23"} } } {}$ s. Turning this around, if we measure the lifetime of a particle, we can tell if it decays via the weak or strong force.

Yet another quantum number emerges from decay lifetimes and patterns. Note that the particles $Λ, Σ, Ξ Λ, size 12{Λ,`Σ,`Ξ} {}$ , and $Ω Ω size 12{ %OMEGA } {}$ decay with lifetimes on the order of $10^{- 10} 10^{- 10} size 12{"10" rSup { size 8{ - "10"} } } {}$ s (the exception is $Σ^{0} Σ^{0} size 12{Σ rSup { size 8{0} } } {}$ , whose short lifetime is explained by its particular quark substructure.), implying that their decay is caused by the weak force alone, although they are hadrons and feel the strong force. The decay modes of these particles also show patterns—in particular, certain decays that should be possible within all the known conservation laws do not occur. Whenever something is possible in physics, it will happen. If something does not happen, it is forbidden by a rule. All this seemed strange to those studying these particles when they were first discovered, so they named a new quantum number strangeness, given the symbol $S S size 12{S} {}$ in the table given above. The values of strangeness assigned to various particles are based on the decay systematics. It is found that strangeness is conserved by the strong force, which governs the production of most of these particles in accelerator experiments. However, strangeness is not conserved by the weak force. This conclusion is reached from the fact that particles that have long lifetimes decay via the weak force and do not conserve strangeness. All of this also has implications for the carrier particles, since they transmit forces and are thus involved in these decays.

Example 33.3

Calculating Quantum Numbers in Two Decays

(a) The most common decay mode of the $Ξ^{-} Ξ^{-} size 12{Ξ rSup { size 8{ - {}} } } {}$ particle is $Ξ^{-} \to Λ^{0} + π^{-} Ξ^{-} \to Λ^{0} + π^{-} size 12{Ξ rSup { size 8{ - {}} } rightarrow Λ rSup { size 8{0} } +π rSup { size 8{ - {}} } } {}$ . Using the quantum numbers in the table given above, show that strangeness changes by 1, baryon number and charge are conserved, and lepton family numbers are unaffected.

(b) Is the decay $K^{+} \to μ^{+} + ν_{μ} K^{+} \to μ^{+} + ν_{μ} size 12{K rSup { size 8{+{}} } rightarrow μ rSup { size 8{+{}} } +ν rSub { size 8{μ} } } {}$ allowed, given the quantum numbers in the table given above?

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 $Ξ^{-} Ξ^{-}$ has strangeness $S = - 2 S = - 2 size 12{S= - 2} {}$ . After the decay, the total strangeness is –1 for the $Λ^{0} Λ^{0} size 12{Λ rSup { size 8{0} } } {}$ , plus 0 for the $π^{-} π^{-}$ . Thus, total strangeness has gone from –2 to –1 or a change of +1. Baryon number for the $Ξ^{-} Ξ^{-}$ is $B = + 1 B = + 1$ before the decay, and after the decay the $Λ^{0} Λ^{0}$ has $B = + 1 B = + 1$ and the $π^{-} π^{-}$ has $B = 0 B = 0 size 12{B=0} {}$ so that the total baryon number remains +1. Charge is –1 before the decay, and the total charge after is also $0 - 1 = - 1 0 - 1 = - 1 size 12{0 - 1= - 1} {}$ . Lepton numbers for all the particles are zero, and so lepton numbers are conserved.

Discussion for (a)

The $Ξ^{-} Ξ^{-} size 12{Ξ rSup { size 8{ - {}} } } {}$ decay is caused by the weak interaction, since strangeness changes, and it is consistent with the relatively long $1 . 64 \times 10^{- 10} -s 1 . 64 \times 10^{- 10} -s size 12{1 "." "64" times "10" rSup { size 8{ - "10"} } "-s"} {}$ lifetime of the $Ξ^{-} Ξ^{-} size 12{Ξ rSup { size 8{ - {}} } } {}$ .

Solution for (b)

The decay $K^{+} \to μ^{+} + ν_{μ} K^{+} \to μ^{+} + ν_{μ} size 12{K rSup { size 8{+{}} } rightarrow μ rSup { size 8{+{}} } +ν rSub { size 8{μ} } } {}$ is allowed if charge, baryon number, mass-energy, and lepton numbers are conserved. Strangeness can change due to the weak interaction. Charge is conserved as $s \to d s \to d size 12{s rightarrow d} {}$ . Baryon number is conserved, since all particles have $B = 0 B = 0 size 12{B=0} {}$ . Mass-energy is conserved in the sense that the $K^{+} K^{+} size 12{K rSup { size 8{+{}} } } {}$ has a greater mass than the products, so that the decay can be spontaneous. Lepton family numbers are conserved at 0 for the electron and tau family for all particles. The muon family number is $L_{μ} = 0 L_{μ} = 0 size 12{L rSub { size 8{μ} } =0} {}$ before and $L_{μ} = - 1 + 1 = 0 L_{μ} = - 1 + 1 = 0 size 12{L rSub { size 8{μ} } = - 1+1=0} {}$ after. Strangeness changes from +1 before to 0 + 0 after, for an allowed change of 1. The decay is allowed by all these measures.

Discussion for (b)

This decay is not only allowed by our reckoning, it is, in fact, the primary decay mode of the $K^{+} K^{+} size 12{K rSup { size 8{+{}} } } {}$ meson and is caused by the weak force, consistent with the long $1 . 24 \times 10^{- 8} -s 1 . 24 \times 10^{- 8} -s size 12{1 "." "24" times "10" rSup { size 8{ - 8} } "-s"} {}$ lifetime.

There are hundreds of particles, all hadrons, not listed in Table 33.2, 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. Quarks: Is That All There Is? explores the basics of the underlying quark building blocks.

The image shows a picture of physicist Murray Gell Mann, who looks like a pleasant white-haired gentleman.

Figure 33.14 Murray Gell-Mann (b. 1929) proposed quarks as a substructure of hadrons in 1963 and was already known for his work on the concept of strangeness. Although quarks have never been directly observed, several predictions of the quark model were quickly confirmed, and their properties explain all known hadron characteristics. Gell-Mann was awarded the Nobel Prize in 1969. (credit: Luboš Motl)