Σ-−
1189.4
± 1
0
0
0
∓1 0.80 × 10 −10
Baryons
Σ0
Σ-0
1192.6
± 1
0
0
0
∓1 7.4 × 10 −20
Sigma
Σ−
Σ-+
1197.4
± 1
0
0
0
∓1 1.48 × 10 −10
Ξ0
Ξ-0
1314.9
± 1
0
0
0
∓2 2.90 × 10 −10
Xi
Ξ−
Ξ+
1321.7
± 1
0
0
0
∓2 1.64 × 10 −10
Omega
Ω−
Ω+
1672.5
± 1
0
0
0
∓3 0.82 × 10 −10
(many other baryons known)
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 . The leptons fall into three families, implying three conservation laws for three quantum numbers. One of these was known from β
decay, where the existence of the electron’s neutrino implied that a new quantum number, called the electron family number Le is conserved.
Thus, in β decay, an antielectron’s neutrino v- e must be created with Le = −1 when an electron with Le =+1 is created, so that the total
remains 0 as it was before decay.
4. The lower of the ∓ or ± symbols are the values for antiparticles.
5. Lifetimes are traditionally given as t 1 / 2 / 0.693 (which is 1 / λ , the inverse of the decay constant).
6. Neutrino masses may be zero. Experimental upper limits are given in parentheses.
7. Experimental lower limit is >5×1032 for proposed mode of decay.
CHAPTER 33 | PARTICLE PHYSICS 1191
Once the muon was discovered in cosmic rays, its decay mode was found to be
(33.7)
µ− → e− + v- e + vµ,
which implied another “family” and associated conservation principle. The particle vµ is a muon’s neutrino, and it is created to conserve muon
family number Lµ . So muons are leptons with a family of their own, and conservation of total Lµ also seems to be obeyed in many experiments.
More recently, a third lepton family was discovered when τ particles were created and observed to decay in a manner similar to muons. One
principal decay mode is
(33.8)
τ− → µ− + v- µ + vτ.
Conservation of total Lτ 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 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 so that they can decay to other
particles with B = 0 . But baryons have B=+1 if they are matter, and 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 → α + α with a lifetime of
about 10−16 s . The neutron is a good example of decay via the weak force. The process n → p + e− + v- e has a longer lifetime of 882 s. The
weak force causes this decay, as it does all β decay. An important clue that the weak force is responsible for β decay is the creation of leptons,
such as e− and v- e . None would be created if the strong force was responsible, just as no leptons are created in the decay of 8Be . 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 to 10−12 s, whereas those that decay via the strong
force have lifetimes mostly in the range of 10−16 to 10−23 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 , and Ω decay with lifetimes on the order
of 10−10 s (the exception is Σ0 , 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 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− particle is Ξ− → Λ0 + π− . 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 + → µ+ + νµ 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.
1192 CHAPTER 33 | PARTICLE PHYSICS
Solution for (a)
Before the decay, the Ξ− has strangeness S = −2 . After the decay, the total strangeness is –1 for the Λ0 , plus 0 for the π − . Thus, total
strangeness has gone from –2 to –1 or a change of +1. Baryon number for the Ξ − is B = +1 before the decay, and after the decay the Λ0
has B = +1 and the π− has 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 . Lepton numbers for all the particles are zero, and so lepton numbers are conserved.
Discussion for (a)
The Ξ− decay is caused by the weak interaction, since strangeness changes, and it is consistent with the relatively long 1.64×10−10-s
lifetime of the Ξ− .
Solution for (b)
The decay K + → µ+ + νµ 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 → d . Baryon number is conserved, since all particles have B = 0 . Mass-energy is
conserved in the sense that the K + 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 Lµ = 0 before and Lµ = −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 + meson and is caused by the weak force,
consistent with the long 1.24×10−8-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.
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)
33.5 Quarks: Is That All There Is?
Quarks have been mentioned at various points in this text as fundamental building blocks and members of the exclusive club of truly elementary
particles. Note that an elementary or fundamental particle has no substructure (it is not made of other particles) and has no finite size other than its
wavelength. This does not mean that fundamental particles are stable—some decay, while others do not. Keep in mind that all leptons seem to be
CHAPTER 33 | PARTICLE PHYSICS 1193
fundamental, whereas no hadrons are fundamental. There is strong evidence that quarks are the fundamental building blocks of hadrons as seen in
Figure 33.15. Quarks are the second group of fundamental particles (leptons are the first). The third and perhaps final group of fundamental particles is the carrier particles for the four basic forces. Leptons, quarks, and carrier particles may be all there is. In this module we will discuss the quark
substructure of hadrons and its relationship to forces as well as indicate some remaining questions and problems.
Figure 33.15 All baryons, such as the proton and neutron shown here, are composed of three quarks. All mesons, such as the pions shown here, are composed of a quark-
antiquark pair. Arrows represent the spins of the quarks, which, as we shall see, are also colored. The colors are such that they need to add to white for any possible
combination of quarks.
Conception of Quarks
Quarks were first proposed independently by American physicists Murray Gell-Mann and George Zweig in 1963. Their quaint name was taken by
Gell-Mann from a James Joyce novel—Gell-Mann was also largely responsible for the concept and name of strangeness. (Whimsical names are
common in particle physics, reflecting the personalities of modern physicists.) Originally, three quark types—or flavors—were proposed to account
for the then-known mesons and baryons. These quark flavors are named up ( u), down ( d), and strange ( s). All quarks have half-integral spin and are thus fermions. All mesons have integral spin while all baryons have half-integral spin. Therefore, mesons should be made up of an even number
of quarks while baryons need to be made up of an odd number of quarks. Figure 33.15 shows the quark substructure of the proton, neutron, and two
⎞
⎛ ⎞
pions. The most radical proposal by Gell-Mann and Zweig is the fractional charges of quarks, which are ±⎛2
1
⎝3⎠ qe and ⎝3⎠ qe , whereas all directly
observed particles have charges that are integral multiples of qe . Note that the fractional value of the quark does not violate the fact that the e is the
smallest unit of charge that is observed, because a free quark cannot exist. Table 33.3 lists characteristics of the six quark flavors that are now thought to exist. Discoveries made since 1963 have required extra quark flavors, which are divided into three families quite analogous to leptons.
How Does it Work?
To understand how these quark substructures work, let us specifically examine the proton, neutron, and the two pions pictured in Figure 33.15 before moving on to more general considerations. First, the proton p is composed of the three quarks uud, so that its total charge is
+⎛2⎞
2⎞
1⎞
1⎞
1⎞
1⎞
1⎞
⎝3⎠ qe + ⎛⎝3⎠ qe − ⎛⎝3⎠ qe = qe , as expected. With the spins aligned as in the figure, the proton’s intrinsic spin is +⎛⎝2⎠ + ⎛⎝2⎠ − ⎛⎝2⎠ = ⎛⎝2⎠, also
as expected. Note that the spins of the up quarks are aligned, so that they would be in the same state except that they have different colors (another
quantum number to be elaborated upon a little later). Quarks obey the Pauli exclusion principle. Similar comments apply to the neutron n, which is
composed of the three quarks udd. Note also that the neutron is made of charges that add to zero but move internally, producing its well-known
magnetic moment. When the neutron β− decays, it does so by changing the flavor of one of its quarks. Writing neutron β− decay in terms of
quarks,
(33.9)
n → p + β− + v- e becomes udd → uud + β− + v- e.
We see that this is equivalent to a down quark changing flavor to become an up quark:
(33.10)
d → u + β− + v- e
1194 CHAPTER 33 | PARTICLE PHYSICS
Table 33.3 Quarks and Antiquarks[8]
Name
Symbol
Antiparticle
Spin
Charge
B [9]
S
c
b
t
Mass (GeV / c2)
[10]
Up
u
u-
1/2
±23 qe
±13
0
0
0
0
0.005
Down
d
d-
1/2
∓13 qe
±13
0
0
0
0
0.008
Strange
s
s-
1/2
∓13 qe
±13
∓1 0
0
0
0.50
Charmed c
c-
1/2
±23 qe
±13
0
±1 0
0
1.6
Bottom
b
b-
1/2
∓13 qe
±13
0
0
∓1 0
5
Top
t
t-
1/2
±23 qe
±13
0
0
0
±1 173
8. The lower of the ± symbols are the values for antiquarks.
9. B is baryon number, S is strangeness, c is charm, b is bottomness, t is topness.
10. Values are approximate, are not directly observable, and vary with model.
CHAPTER 33 | PARTICLE PHYSICS 1195
Table 33.4 Quark Composition of
Selected Hadrons[11]
Particle
Quark Composition
Mesons
π+
ud-
π−
u- d
π 0
u u- , d d- mixture[12]
η 0
u u- , d d- mixture[13]
K 0
d s-
K- 0
d- s
K+
u s-
K−
u- s
J / ψ
c c-
ϒ
b b-
Baryons[14],[15]
p
uud
n
udd
Δ0
udd
Δ+
uud
Δ−
ddd
Δ++
uuu
Λ0
uds
Σ0
uds
Σ+
uus
Σ−
dds
Ξ0
uss
Ξ−
dss
Ω−
sss
This is an example of the general fact that the weak nuclear force can change the flavor of a quark. By general, we mean that any quark can be
converted to any other (change flavor) by the weak nuclear force. Not only can we get d → u , we can also get u → d . Furthermore, the strange
quark can be changed by the weak force, too, making s → u and s → d possible. This explains the violation of the conservation of strangeness by
the weak force noted in the preceding section. Another general fact is that the strong nuclear force cannot change the flavor of a quark.
Again, from Figure 33.15, we see that the π+ meson (one of the three pions) is composed of an up quark plus an antidown quark, or u d- . Its total
⎞
⎞
charge is thus +⎛2
1
⎝3⎠ qe + ⎛⎝3⎠ qe = qe , as expected. Its baryon number is 0, since it has a quark and an antiquark with baryon numbers
+⎛1⎞
1⎞
⎝3⎠ − ⎛⎝3⎠ = 0 . The π+ half-life is relatively long since, although it is composed of matter and antimatter, the quarks are different flavors and the
11. These two mesons are different mixtures, but each is its own antiparticle, as indicated by its quark composition.
12. These two mesons are different mixtures, but each is its own antiparticle, as indicated by its quark composition.
13. These two mesons are different mixtures, but each is its own antiparticle, as indicated by its quark composition.
-
14. Antibaryons have the antiquarks of their counterparts. The antiproton p- is u- u- d , for example.
15. Baryons composed of the same quarks are different states of the same particle. For example, the Δ + is an excited state of the proton.
1196 CHAPTER 33 | PARTICLE PHYSICS
weak force should cause the decay by changing the flavor of one into that of the other. The spins of the u and d- quarks are antiparallel, enabling
the pion to have spin zero, as observed experimentally. Fin