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OCR for page 48
What We Have Learned in the
Past Two Decades
DEVELOPMENT OF THE QUARK MODEL OF HADRONS
The Beginnings of the Quark Model
It was first recognized in 1964 that all the known hadrons fell into the
particular symmetry scheme, or pattern, expected if all hadrons are
formed from three fundamental constituents. These were called
quarks, and they were given the names u, d, and s for up, down, and
strange. Each hadron would be composed of either three quarks [such
as the ten-member group shown in Figure 3. 1(A)] or of quark-antiquark
pairs [such as the octet group shown in Figure 3el(B)~.
Note that for each of these states the total charge of the particle is the
sum of the charges of the quarks of which it is composed. For example,
the A+ + (pronounced delta plus plus) shown in Figure 3.1(A) consists
of 3 u quarks, so its total charge is 3 x (+ 2/3) = ~ 2 (hence the + +
superscript). Similarly, the ~ + is composed of uad and has a charge of
2 x (+2/3) + (-1/3) = +1.
Each of these quarks is in a particular orbit or state of motion relative
to the other two quarks. If we were able to reach into the A+ + and
magically transform one of the u quarks into a d quark, without altering
the orbit of the quark, then we would have a A+ (delta plus) particle.
Similarly, if we were to change one of the two u quarks in the ~ + into
a d quark, then we would have a At (delta zero) and so on. The similar
48
OCR for page 49
WHAT WE HAVE f EARNED IN THE PAST ~0 DECADES 49
is- (ddd) ~°(ddu)
BAA ~~
\
\
co-eds)
(B)
-(dub
\
K-(su)
/
/
_~
K°( sd)
£* (dus)
.~s*-(dss) \
/
\ /
\ ~
n~ (Sss'
/
/
K°(ds) K+(us)
~~ —
/
~+(duu) ^++(uuu )
~ 7
/
, *US)
/
/
/'—*°(USS
\
\
77 7~° ~ 7~+(ud)
/
FIGURE 3.1 Hadrons are made out of quarks. (A) shows how the delta, sigma-star,
xi-star, and omega family of hadrons are made out of three quarks; (B) shows how the
meson family, which contains the plan and kaon, is made of a quark and an antiquark.
The positive pion, Tr+, and the positive kaon, K', have different properties because the
1r~ consists of an up quark (u) and a down antiquark (d), while the K+ consists of an up
quark (a) and a strange antiquark (s). The ~ and A are made up of combinations of uu,
dd, and ss quarks.
OCR for page 50
50 ELEMENTARY-PARTICLE PHYSICS
masses of all the As indicate that the u and d quarks have about the
same mass.
However, if we were to change one of the u quarks in the ~ + + into
an s quark, again without changing the orbit, we would then have a I* +
(sigma-star plus), which has a mass about 150 MeV greater than the
A+ +. This indicates that the s quark is about 150 MeV heavier than the
u or d quarks. If we were to change one of the two u quarks in the I;* +
into an s, we would get the _*° (xi-star zero), about 150 MeV heavier
than the I* +. And finally, if we were to change the remaining u into an
s, we would have the Q~ (omega minus). The Q- had not been seen
when the quark model was first proposed. Its discovery the following
year, with the predicted mass and the predicted charge, gave strong
support to the quark picture.
But even then many physicists emphasized that the symmetry did
not necessarily imply the actual physical existence of quarks. In
particular, the charge of the quarks had to be fractional (2/3 of the
standard unit for the u quark and -1/3 for the d and s quarks)' but no
fractionally charged particles had ever been observed. Thus although
the hadron classification scheme based on quarks was widely accepted,
the actual physical existence of quarks was questioned.
The Discovery of the Charmed Quark
During the years from 1964 through 1973, considerable progress was
made, both experimentally and theoretically, in support of the idea of
physical quarks. Some of this is described in Chapter 3 in the section
on How Quarks Interact. But perhaps the most important and compel-
ling new evidence for quarks began in 1974 with the discovery of a new
particle, the J/¢ ('~jay-psi"), which was discovered simultaneously at
Brookhaven National Laboratory (where it was called the J) and at
Stanford Linear Accelerator Center (where it was called the Off.
The J/¢ was unusually heavy (3.1 GeV in mass) and had a very long
lifetime, uncharacteristic of strongly interacting particles. Indeed,
heavy particles in general tend to be more unstable and therefore to
have shorter lifetimes. Thus the J/¢ definitely did not fit into the
symmetry scheme that had been so successful in classifying other
hadrons.
Physicists hypothesized that it contained a new kind of quark, called
c or charm, which had in fact been predicted earlier. The J/¢ was
believed to be a bound state of a charmed quark and a charmed
antiquark. In order for the J/¢ to have such a large mass, the mass of
the new quark would also have to be large (about 1.5 GeV). Thus the
OCR for page 51
WHAT WE HAVE LEARNED IN THE PAST ~0 DECADES 51
mass of the J/¢ would be about the mass of a c quark plus the mass of
a c antiquary. [An antiparticle is often symbolized by drawing a short
bar above the symbol for the corresponding particle. Thus c (pro-
nounced c bar) is the symbol for the charmed antiquark.]
If this hypothesis were correct, it would mean that a whole family of
new charmed particles would exist, consisting of a charmed quark
bound together with one or more other kinds of quarks. For example,
there would be a cu state (called the Do, with a mass of about 1.8 GeV),
a cd state (called the D+, with a similar mass), a cs (called the F+, with
a mass of about 2.0 GeV), and a uric state (a charmed baryon, with a
mass of about 2.2 GeV).
All these states, and others, have since been discovered! All have
had the masses, charges, decay modes, and other properties predicted
from the idea of constituent quarks. The excellent agreement between
prediction and experiment has established the validity of the quark
picture beyond any reasonable doubt.
Charmonium States
The discovery of the J/¢ was also important in establishing the
existence of quarks in a second way, since it was the first of several
states, referred to as '~charmonium" states, that are composed of a cc
pair. All these states have masses in the range 3.0 to 3.6 GeV. All are
believed to consist of a charmed quark bound together with a charmed
antiquary. The heavier ones are excited states in the sense that the two
quarks have more energetic orbits. The existence of these distinct but
similar particles, each formed by the same constituent quarks but in
different energy states, provided an important quantitative confi~n~a-
tion that quarks do indeed exist.
Such a range of different energy states in a two-body system is very
familiar to physicists. An analogous two-body system is the hydrogen
atom, composed of a single electron orbiting around a single proton.
The different energy levels of the excited states of hydrogen account
for the discrete lines in the spectrum of light emitted by hydrogen; the
spectral lines are produced by photons emitted in a transition from an
excited level to a less-excited level, and their energy is equal to the
difference in energy levels of the initial and final states. Spectral lines
were first observed in 1802, and the spectrum of excited states was first
quantitatively explained by the Bohr model of the hydrogen atom in
1913.
A similar set of different energy levels is seen in positronium, which
is a bound state of an electron and its antiparticle, the positron. Since
OCR for page 52
52 EfEMENTARY-PARTIC~E PHYSICS
POSIT RObJ ~ UM
7
2
._
_ ,
o
D'ssoclotion
E net gy
I<
23S, 23P2
2'P,
23P
23Po
2'So
X ~OtOOO
x 1000
n: 1 ~ l3S
~ 1lSo
AS Stotes ~PStctes
IS Stotes UP Stotes
CHARMObJ\UM
000
800
200
-
33s,
— 1
o
c
o
-
-
° 600
-°E 400 2iS ~' 21p' 25P2X
c,
-
0 0
c,
cr
-
23s.
' So Tic
15s,*
IS Stotes UP Stoles
25P,X,/2 PoXo c
ED
AS Stotes UP Stotes
FIGURE 3.2 The spectrum of energy states is similar in positronium and charmonium,
but the scale of the energy differences in charmonium is greater by a factor of roughly 100
million. The energy of a state is determined by the principal quantum number n and by
the orientation of the particle spins and the orbital angular momentum. The arrangement
of the energy levels is similar because both pairs of particles obey the same laws of
quantum mechanics. In positronium the venous combinations of angular momentum
cause only minuscule shifts in energy (shown by expanding the vertical scale), but in
charmonium the shifts are much larger. All energies are given with reference to the 135'
state. At 6.8 electron volts positronium dissociates. At 633 MeV above the energy of the
charmonium becomes quasi-bound because it can decay into D° and D° mesons.
charmonium states are also bound states of a particle (the c quark) and
its antiparticle, they should show a spectrum of energy levels similar to
those of positronium. However, since the charmed quark is about 3000
times more massive than the electron, and since the force holding the
quarks together in charmonium is the nuclear force (about 100 times
stronger than the electric force), one would expect the masses and the
mass difference between charmonium states to be much larger than
those of the positronium states.
This is exactly what is observed. Seven different charmonium bound
states have been found. These states are shown in Figure 3.2(b). The
similar states for positronium are shown in Figure 3.2(a). Note that the
energy spacing between the charmonium levels is about 100 million
times larger than the spacing between the positronium levels. But aside
from this expected difference, the close similarity of the structure of
the splittings speaks for itself and provides another strong proof of the
OCR for page 53
WHA T WE lIA VE LEARNED IN THE PAST TWO DECADES 53
physical existence of quarks and of the universality of quantum
mechanics.
DISCOVERY OF THE THIRD GENERATION OF LEPIONS
AND QUARKS
With the discovery of the charmed quark in 1974, the second
generation of quarks was completed. At that time, two generations of
leptons were also known: the electron and its neutrino, and the muon
and its neutrino. It is interesting to go back to 1974 to understand the
significance of the two generations and to give a brief history of how
the third generation was accidentally discovered in both the lepton and
the quark areas. In 1974 there was no explanation of why there was
more than one generation of either leptons or quarks, and indeed we
still have no explanation of this fact. As discussed in the next chapter,
this is one of the outstanding puzzles facing elementary-particle
physicists.
The Discovery of the Tau Lepton
The generations puzzle is most easily seen in terms of the charged-
lepton situation in 1974. At that time we knew that both the electron
and the muon existed, that the muon was about 200 times heavier than
the electron, and that botn the muon and the electron had the same
kind of behavior with respect to the electromagnetic force and the
weak force. We also knew that the muon was very different from the
electron in the sense that it could not decay into an electron in any
simple way. But there was absolutely no theoretical understanding of
why both particles existed or of how the mass of the muon was related
to the mass of the electron.
Experimenters at the SPEAR electron-positron collider at the
Stanford Linear Accelerator Center (SLAC) began to look at the
particles being produced in this machine to see if there might be
charged leptons other than the electron or muon being created in the
collisions. This was purely an experimental search, since there was no
theoretical motivation for it. This is an illustration of a theme that we
shall return to again and again in this report that experimenters often
explore the unknown without theoretical guidance. And such explora-
tions can be very fruitful, particularly at new accelerator facilities.
SPEAR was such a facility in 1974.
In 1975 these experimenters began to accumulate evidence for the
existence of the third charged lepton, now called the taut The tau has
OCR for page 54
54 ELEMENTARY-PARTICLE PHYSICS
Muon (It)
r A\ I
/
Yet
Electron (e)
/~. \
l
-
FIGURE 3.3 One of the electron-muon two-prong events that led to the discovery of
the tau lepton in 1975. At the time such events were unusual and could not be explained
by the production of any of the then known particles.
a mass of a little over 1780 MeV; hence it is about 3500 times heavier
than the electron. The discovery was made through the finding of
electron-muon two-charged-particle events as shown in Figure 3.3. The
tau lepton had too short a lifetime to be detected directly at that time,
but in an electron-positron collision a tau-antitau pair can be produced,
and this pair can then decay to an electron and a muon, plus unseen
neutrinos.
Subsequent studies of the tau lepton at SPEAR and other electron-
positron colliders showed that it behaved the same way as the electron
and muon with respect to the weak and electromagnetic force and that
it did not respond to the strong force.
Further studies of the decay of the tau lepton demonstrated that it
had its own unique neutrino associated with it. That is, the neutrino
associated with the tau lepton is not the same as the neutrino associated
with the electron, nor as the neutrino associated with a muon. Thus two
OCR for page 55
WHAT WE HAVE LEARNED IN THE PAST ~0 DECADES 55
new leptons were actually found, the tau lepton and its associated
neutrino.
It is still necessary for us to learn how the tan neutrino interacts, i.e.,
to see if it interacts in a manner similar to the way in which the electron
neutrino and the muon neutrino interact. Such an experiment cannot be
carried out in an electron-positron collider, where all other studies of
the tau and its neutrino have been done, but rather must make use of
a secondary neutrino beam produced at a proton accelerator.
The Discovery of the Bottom Quark
The discovery of the b or bottom quark was made at Fermilab in
1977. As in the case of the tau, this was a purely experimental
discovery. There was little theoretical guidance in looking for the b
quark and no indication of what energy might be required to find it. The
experiment at Fe~ilab that found the b quark was studying pairs of
electrons and pairs of muons produced in the collisions of the primary
proton beam of the 400-GeV proton accelerator with a fixed target. The
experimenters measured the masses of the pairs of electrons or muons
produced, and they plotted the frequency of occurrence of those
masses, as shown in the historic curve of Figure 3.4. A peak in that
mass frequency plot appears between 9 and 10 GeV.
This peak turned out to be due to the production of a new kind of
particle called the upsilon. Each of the upsilon particles consists of a
bottom quark bound together with its corresponding antiquary. Hence
the mass of the bottom quark is about half of 10 GeV, namely, 5 GeV.
This is how the bottom quark was discovered.
Information about the bottom quark can be obtained by studying the
upsilon family of particles or by studying mesons that consist of one
bottom quark and one of the lighter antiquarks (or vice versa). Such
particles are called B mesons. Extensive studies of upsilon particles
and B mesons have been and are being made, particularly at electron-
positron colliders. For example, Figure 3.5 shows the spectrum of the
upsilon family of particles, obtained at the Cornell Electron Storage
Ring (CESR) and DORIS [at the Deutsches Electronen Synchrotron
(DESY)] electron-positron colliders.
B mesons are probably also copiously produced in hadron-hadron
collisions, either in fixed-target experiments or at particle colliders. At
present, the large background of ordinary mesons also produced in
hadron-hadron collisions makes the detailed study of B mesons difficult
when produced in this way. But as particle detectors improve, it should
become possible to make detailed studies of B mesons at proton
OCR for page 56
56 ELEMENTARY-PARTICLE PHYSICS
, , ~
._
CL
~ 100
o
o
Q
i,_ 10
o
c
a)
or
a'
._
~ O
cr
_ ~
t
1 1, 1 1 1
~ .
rfL
6 8 10 12
Muon Pair Mass (GeV)
FIGURE 3.4 The upsilon was discovered in 1977 by studying the production of muon
pairs or electron pairs in proton collisions. Here the relative frequency of production of
muon pairs is shown to decrease as the muon pair mass increases. The bump in the curve
at 9-10 GeV is due to the upsilon.
accelerators as well as those currently done at electron-positron
colliders.
The Third Generation
As shown in Figure 3.6, we can now see how the third generation of
leptons and half of the third generation of quarks was added to our basic
OCR for page 57
WHAT WE HAVE LEARNED IN THE PAST ~0 DECADES 57
system of elementary particles. Most physicists believe that there is a
second member of the third generation of quarks, which is called the t or
top quark. The expectation for the existence of the top quark comes from
two sources: first is our belief that nature is simple, so that in each gen-
eration quarks like leptons should come in pairs; second, measure-
ments of the b quark lifetime give an indirect indication that there
should be a top quark associated with the bottom quark. As this report
was being completed in 1984, initial direct evidence was reported for
the existence of the top quark.
3S' states in ~ family
lo'
3.69 —
3.10 ~
3S' stotes in T family
Mass
(GeV)
, 10.55
To'
, ' 10.32
10.00
T; 9.43
FIGURE 3.5 The triplet 5 states (351) of the upsilon (Y) family are shown on the right.
Each of these states consists of a b quark bound to a ~ quark. For comparison the two
35~ states of the ~ family are shown on the left. Although the masses are very different,
the level separations are nearly equal.
OCR for page 58
58 ELEMENTARY-PARTICLE PHYSICS
Generation Particle Charge Mass
~ electron (e)
I ~ electron neutrino (~e)
0.51 MeV I
O less than 50 eV
—1
2 .4 muon (id)
| muon neutrino (v,,) O
106 MeV=0.106 GeV I
less then O.S MeV |
3 ~ tau ( T)
-1 1784 MeV = 1.784 GeV
tau neutrinos (V') O less then 160 MeV = 0. 160 GeV
*indirect evidence
Generation Porticle Charge Moss
Tup (u)
down(d)
~ 2/3 about 300 MeV - 0.3 GeV
- 1/3 about 300 MeV= 0.3 GeV
2 ~ charm (c)
strange (s)
+2/3 aboutl50OMeV= 1.5GeV
-1 /3 about 500 MeV= 0 5 GeV
36
bottom (b) - 1/3 about 5,000 MeV= S.O GeV |
1 —— ' — - - — . _
FIGURE 3.6 Our present knowledge of the lepton and quark families of particles.
Although nature does seem to be simple, that does not mean that we
understand it. Just as in 1974 we did not know why there were two
generations of leptons and quarks, so in 1985 we do not know why
there are three generations of leptons and quarks. What has been
gained, of course, is the experimental demonstration that there can be
more than two generations of leptons and quarks. Indeed, there may be
more than the present three generations. Some theoretical arguments
and some deductions from astrophysical considerations can be inter-
preted to mean that there are not more than four generations of leptons
and quarks. But physics is, in the end, an experimental science, and the
search for more than four generations of leptons and quarks will be
carried on by experimenters. There is probably nothing more challeng-
ing to a scientist than to be told that, theoretically, something cannot
exist.
OCR for page 70
70 ELEMENTARY-PARTICLE PHYSICS
STRONG INTERACTION AMONG QUARKS
We have seen already how the idea that the strongly interacting
particles are built up of quarks brought new order to hadron spectros-
copy and suggested new relations among mesons and baryons. But this
constituent description also brought with it a number of puzzles. These
seemed at first to indicate that the quark model was nothing more than
a convenient mnemonic recipe. In pursuing and resolving these puz-
zles' physicists have found a dynamical basis for the quark model that
promises to give a complete description of the strong interactions.
An obvious question concerns the rules by which the hadrons are
built up out of quarks. Mesons are composed of one quark and one
antiquary, while baryons are made of three quarks. What prevents
two-quark or four-quark combinations? Within this innocent question
lurks a serious problem of principle. The Pauli exclusion principle of
quantum mechanics is the basis for our understanding of the periodic
table of the elements. It restricts the configurations of electrons within
atoms and of protons and neutrons within nuclei. We should expect it
to be a reliable guide to the spectrum of hadrons as well. But according
to the Pauli principle, the observed baryons such as ~ + + (uuu) and Q~
(sss), which would be composed of three identical quarks in the same
state, cannot exist.
To comply with the Pauli principle, it is necessary to make the three
otherwise identical quarks distinguishable by supposing that every type
of quark exists in three varieties, fancifully labeled by the colors red,
green, and blue. Then each baryon can be constructed as a colorless (or
white) state of a red quark, a green quark, and a blue quark. Similarly,
a meson will be a colorless quark-antiquark combination. The rule for
constructing hadrons may then be rephrased as the statement that only
colorless states can be isolated.
A second issue is raised by the fact that free quarks have not been
observed. This suggests that the interaction between quarks must be
extraordinarily strong, and perhaps permanently confining. That free
quarks are not seen is of course consistent with the idea that colored
states cannot exist in isolation. On the other hand, the quark model
description of violent collisions rests on the assumption that quarks
within hadrons may be regarded as essentially free.
This paradoxical state of affairs may be visualized as follows. We
may think of a hadron as a bubble within which the constituent quarks
are imprisoned. The quarks move freely within the bubble but cannot
escape from it. This picturesque representation yields an operational
understanding of many aspects of hadron structure and interactions,
OCR for page 71
WHAT WE HAVE [EARNED IN THE PAST TWO DECADES 71
ma)
3~O
(O )
iota
(b)
FIGURE 3.13 Electrically polarized molecules weaken the effect of an electric charge.
In (a) the molecules point in random directions. In (b) a negative charge is present, and
the positive ends of the molecules point toward this charge and partially cancel it.
Outside of this area the electric charge will appear weaker.
but it falls far short of a dynamical explanation for the puzzling
behavior of quarks. We still do not understand completely why quarks
apparently interact only weakly when they are close together and yet
cannot be pulled apart. To see why this is surprising, and to learn how
it might come about, it is helpful to consider the interactions of
electrically charged objects.
We customarily speak of the electric charge carried by an object as
a fixed and definite quantity, as indeed it is. However, if a charge is
placed in surroundings in which other charges are free to move about,
the effect of the charge may be modified. An example is a medium
composed of many molecules, each of which has a positively charged
end and a negatively charged end. In the absence of an intruding
charged particle, the molecules are oriented randomly [Figure 3.13(a)],
and the medium is electrically neutral not only in the large, but locally
as well, down to the submolecular scale. Placing an electron in the
medium polarizes the molecules [Figure 3.13(b)~: the negatively
charged ends of the molecules are repelled by the electron, while the
positively charged ends are attracted to it. The effect of this orientation
of the molecules is that at finite distances from the electron its influence
is screened, or reduced, by the opposite charges it has attracted. Only
when we inspect the electron at very close range—smaller than
molecular size is the full magnitude of the electron's charge apparent.
We may say that the effective charge is larger at short distances than at
long distances.
We normally think of the vacuum, or empty space, as the essence of
nothingness. However, in quantum theory the vacuum is a complicated
and seething medium in which virtual pairs of charged particles, most
OCR for page 72
72 ELEMENTARY-PARTICLE PHYSICS
blue Time
quork~_
( a ) (~)_ gluon
green",>
quark
,~
( b )
green
'~ quark
blue
quork
oll gluons
q = quark
it) 9=gluon
FIGURE 3.14 How quarks and gluons interact. In (a) quarks change their color through
the emission and absorption of a gluon. In (b) gluons interact with each other.
importantly electrons and positrons, have a fleeting existence. These
ephemeral vacuum fluctuations are polarizable in the same way as the
molecules of our example. Consequently in QED it is also expected
that the effective electric charge should increase at short distances, and
indeed the consequences of this variation are observed in atomic
spectra. The behavior of the effective charge in QED is opposite to that
required in the realm of the strong interactions, where the interaction
between quarks must diminish in strength at short distances.
An explanation for the contrary behavior of the strong force emerged
unexpectedly from the ideas that had proved so fruitful for the
electroweak interactions: the strategy of gauge theories. Since color is
an attribute of quarks but not of leptons, it can be considered as a
strong-interaction charge. When the color symmetry among red, blue,
and green quarks is taken as the basis for a gauge theory, the resulting
interactions among quarks are mediated by force particles called
gluons. There are eight gluons corresponding to the distinct color-
anticolor combinations. (The white combination corresponding to an
equal mixture of red-antired, blue-antiblue, and green-antigreen is not
included.) In quantum chromodynamics, or QCD as the theory is
called, quarks may interact as shown in Figure 3.14(a), where a blue
OCR for page 73
WHAT WE HAVE LEARNED IN THE PAST TWO DECADES 73
quark and a green quark exchange color. Because the gluons carry
color, they can interact among themselves as well, as shown in Figure
3.14(b). The photons of QED, being electrically neutral, have no such
self-interactions.
The fact that the gluons are (color) charged is responsible for the
crucial difference between the behavior of the effective charge in QED
and QCD. In the strong-interaction theory there are two competing
effects: a screening brought about by the color charges in the fluctu-
ating vacuum and a camouflage effect that is not present in QED. The
screening, or vacuum polarization, may be understood just as in
electrodynamics. This time we think of the vacuum as a collection of
randomly oriented three-cornered objects, as shown in Figure 3.15(a).
By placing a green quark in the vacuum, we orient the triangles [Figure
3.15(b)] and screen the color charge.
The behavior of the strong interaction charge is the result of a
competition between these two opposing effects. In QCD, the outcome
is that the effective color charge does have the properties necessary to
reconcile the simple quark model and quark confinement. The steady
weakening of the charge at short distances is known as asymptotic
freedom because quarks become effectively free at very small separa-
tions.
In the regime of short distances probed in violent high-energy
collisions, the strong interactions are sufficiently feeble that reaction
rates may be calculated using the diagrammatic methods developed for
QED. In some measure these calculations reproduce the simple quark
model results as first approximations. This is the case, for example, in
electron-positron annihilations into hadrons. The quark-antiquark pro-
duction rate, represented by the diagram in Figure 3.16(a), correctly
anticipates both the structure of the dominant twojet events and the
D V R/\B <0
°5o eG Dm
eVa
9
(a) ~ b)
FIGURE 3.15 An illustration of how the force exerted by a quark owing to its color
charge can be weakened by vacuum effects.
OCR for page 74
74 ELEMENTARY-PARTICLE PHYSICS
Time
Q
(b) Q:(,*
,~
`~> ~ becomes
_` I hod rons
(a) W{~)*~(
(/ Am) ~ h o d ro n s
~~ ~ becomes
,,~J J hod rons
~ ~ ~ becomes
i!} ~ hadrons
becomes
~! hodrons
e~- electron
r = photon q = antiquark
q = quark g = g loon
FIGURE 3.16 An example of how interactions of gluons with quarks lead to more
complicated processes. In (a) an electron-positron pair annihilate to produce a virtual
photon, which in turn produces a quark-antiquark pair. In (b) one of those quarks also
emits a gluon.
approximate rate of hadron production. The strong-interaction correc-
tions to this process include the diagram shown in Figure 3.16(b)' in
which a gluon is radiated by one of the outgoing quarks. Like the
quarks, the gluon materializes as a jet of hadrons. The resulting
threejet events are commonplace in the electron-positron annihilations
studied at the PEP and PETRA storage rings.
The highest energies yet attained in collisions of the fundamental
constituents are those reached in proton-antiproton interactions at the
CERN SppS machine. Already collisions among quarks and gluons
have been recorded at energies approaching 300 GeV. The hard
scatterings of these particles lead to striking jets of hadrons at large
angles to the direction defined by the incident proton and antiproton
beams. Events of this kind are observed at approximately the fre-
quency suggested by QCD.
While diagrammatic methods are of great value in the study of strong
interactions, several considerations prevent the resulting calculations
from being as precise as those long familiar in the electroweak domain.
The first is that at the energies currently accessible (or, in other words,
at the distances currently probed), the strong interaction is still con-
siderably stronger than electromagnetism.
A more serious sticking point is that the diagrammatic methods
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WHAT WE HAVE LEARNED IN THE PAST TWO DECADES 75
describe reactions that involve isolated quarks and gluons, whereas in
the laboratory quarks and gluons are found only within hadrons. We
have not yet succeeded in solving the theory in the regime of potent
strong interactions characteristic of hadron structure. In some cases
this problem may be circumvented by using QCD only to predict how
observables change from one energy to the next and not the value they
take at one particular energy. This is the case, for example, in deeply
inelastic electron-proton scattering, for which the reaction rate de-
pends in an essential way on the internal structure of the proton. This
prediction and observation of gradual but systematic change is one of
the notable successes of the theory.
To deal with the existence and properties of the hadrons themselves
it is necessary to devise a new computational approach that does not
break down when the interaction becomes strong. The most promising
approach has been the crystal-lattice formulation of the theory, in
which space-time is accorded a discrete, rather than continuous,
structure. By considering the values of the color field only on individ-
ual lattice sites, one is able to make use of many of the techniques
developed in statistical physics for the study of spin systems such as
magnetic substances.
One of the most valuable methods has been the use of computer
simulations in which different gluon configurations are explored by
random sampling (Monte Carlo) techniques. This program makes
extremely heavy demands on computer time and has spurred the de-
velopment and implementation of new computer architectures. Already
calculations of this sort have yielded suggestive evidence that quarks
and gluons are indeed permanently confined in QCD. Work is continu-
ing actively, with the eventual goal of computing the spectrum and
properties of hadrons ab initio.
Attempts to understand confinement and the nature of the QCD
vacuum have led to the prediction of new phenomena. It seems likely
that when hadronic matter is compressed to very great densities and
heated to extremely high temperatures hadrons will lose their individ-
ual identities. When the hadronic bubbles of our earlier image overlap
and merge, quarks and gluons may be free to migrate over great
distances. A similar phenomenon occurs when atoms are squashed
together in stars. The resulting new state of matter, called quark-gluon
plasma, may exist in the cores of collapsing supernovas and neutron
stars. The possibility of creating QCD plasma in the laboratory in
collisions of energetic heavy ions is under active study.
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76 ELEMENTARY-PARTICLE PHYSICS
UNIFIED THEORIES
We have seen in this chapter that developments in elementary-
particle physics during the past decade have brought us to a new level
of understanding of fundamental physical laws. The establishment-
tentative though it beef the electroweak theory and QCD has brought
us a coherent point of view and a single language appropriate for the
description of all subnuclear phenomena. The new maturity of elemen-
tary-particle physics has made more fruitful the interaction with other
areas of physics and promises new insights into the origin of our world.
With QCD and the electroweak theory in hand, what remains to be
understood? If both theories are correct, can they also be complete?
There are, in fact, many observations that are explained only in part,
if at all, by the separate theories of the strong and electroweak
interactions. Many of these seem to invite a further unification of the
strong, weak, and electromagnetic interactions. This has important
consequences not only for our worldview but also for experimental
initiatives. Let us examine a few of the patterns unexplained by the
separate strong and electroweak theories.
First, there is the striking resemblance among quarks and leptons.
Both classes of particles appear fundamental, in that they are struc-
tureless at our present limits of resolution. Apart from the fact that
quarks carry color but leptons do not, they appear nearly identical. Is
this a coincidence, or are quarks and leptons related?
The hint of a connection between quarks and leptons comes from the
electroweak theory itself. Unless each lepton family like (e,v~) is
matched by a color-triplet quark family such as (u,d), the theory will be
beset with mathematical inconsistencies. These matched sets are
known as quark-lepton generations.
The second puzzling aspect of the theory has to do with the existence
of distinct forces of diverse strengths. Here we recall that the electro-
magnetic interaction, which is of only modest strength between ele-
mentary particles, becomes stronger and stronger at short distances. In
contrast, the strong interaction becomes increasingly feeble at short
distances. Could all the interactions become comparable at some tiny
distance, which is to say at some gigantic energy? This would raise the
possibility of a common origin for the strong, weak, and electromag-
netic interactions. A unification is also suggested by the fact that both
QCD and the electroweak theory are gauge theories, with similar
mathematical structure.
The strategy for constructing a unified theory is to treat the quarks
and leptons symmetrically by joining the quark and lepton families into
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WHAT WE HAVE LEARNED IN THE PAST TWO DECADES 77
extended families of fundamental constituents. In the simplest example
of a unified theory, each quark and lepton generation is identified with
a different extended family. In this way the long-standing mystery of
the electric neutrality of stable matter is explained, because the proton
and electron must have equal and opposite charges if quarks are
combined with leptons in extended families. One branch of the first
extended family is the set (dreg Doreen dare ever.
In a gauge theory, each particle in a set can be transformed into any
other. Some of these transformations are familiar, such as
dreg ~
dgreen ~ ~ gluons
dblue ~
e:
~1
Low+
but others are novel. The transformations between quarks and leptons,
such as
~ dred ~
r ~ dgreen ~ ~
Y dhtlle X
'~~ ~ pe
can enable protons and bound neutrons to decay. One of the mecha-
nisms for proton decay is shown in Figure 3.17. Here X and Y are
hypothetical particles that connect the quarks with the leptons.
In a specific gauge theory, we can compute precisely how the
effective interaction strengths change with energy or distance. The
evolution of the interaction strengths in the theory is depicted in Figure
3.18. The strong, weak, and electromagnetic interactions strengths are
calculated to become comparable at an energy of approximately 10'5
GeV. The predictions of the theory for the relative strengths of the
interactions at current energies agree with precision measurements of
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78 ELEMENTARY-PARTICLE PHYSICS
IS
~3
-
d t
U , U tO
u
in
a;<
or
_ i~
FIGURE 3.17 An example of how a proton might decay in some proposed theories that
connect quarks and leptons. In the top diagram, two up quarks unite, leading to the
production of a positron and a down antiquark. The down antiquark unites with a down
quark to form a neutral pion. Thus in this proposed theory a proton could decay to a
positron plus a neutral pion. X and Y are hypothetical particles that connect the quarks
and leptons.
the weak interactions and with the masses of the W+ and Z° bosons
recently observed. Some unified theories also successfully relate the
masses of some quarks and leptons in the same generation, but the
meaning of these partial successes is less clear.
The prediction of proton instability is a key consequence of unified
theories, and dedicated experiments have been mounted to search for
proton decay. The large unification energy implies that the mean pro-
ton lifetime must be extraordinarily long about 103° years or more.
Since it is not practical to observe a single proton for such a long period
(102° times the age of the universe), it is necessary to monitor
extremely large numbers of protons. The largest experiment mounted
to date is an instrumented tank of 8000 cubic meters of purified water
in a salt mine near Cleveland (Figure 3.191. Currently the searches have
yielded negative results that seem to conflict with the predictions of the
simplest unified theories.
While the specific prediction of proton decay is a dramatic conse-
quence of unification, the difficulty of studying quark-lepton transitions
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WHAT WE HAVE LEARNED IN THE PAST TWO DECADES 79
in the laboratory is apparent. We live in a world in which energies-
even in the most powerful accelerators that we can contemplate are
very low compared with the unification scale. However, the discovery
of the cosmic microwave background radiation (together with many
supporting pieces of evidence) makes it likely that the universe began
in a hot big bang of extremely high-energy density. Many aspects of the
observed universe find natural explanations in terms of this cosmolog-
ical model.
Other features of the universe are not so easily understood. Among
these, the net baryon number of the universe is of particular interest.
The prediction of baryon-number-violating processes, such as proton
decay, in unified theories opens the way to understanding why matter
dominates over antimatter in the universe.
The phenomenon, technically known as CP violation in K-meson
decay, was discovered almost two decades ago. We have no basic
explanation for this phenomenon; it may or may not have anything to
do with the unified theories discussed in this section. But we should not
end this brief survey of what we know in elementary-particle physics
without mentioning CP violation. Briefly the phenomenon is as follows.
When a K° meson, that is, a neutral K meson, is produced, it goes into
0.15
at
0.10
.0s
is
H
o
(OLD)
Weoh
Unificotion
Point
Electromognelic (x8/3)
10° 105 101° lol5
ENERGY ( GeV )
FIGURE 3.18 Example of how in some proposed theories the strong interaction can
eventually be combined with the electromagnetic and weak interactions. The idea is that
the strength of the interactions depends on the energy at which the interaction occurs.
The proposal is that at very high energies say 10'5 GeV, all three interactions would
have the same strength. This is far beyond any energy that we know how to achieve with
present accelerator technology or even with advanced accelerator concepts (see Chapter
5, section on Research on Advanced Concepts for Accelerators and Colliders).
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80 ELEMENTARY-PARTICLE PHYSICS
~ .. -
.= .~, . . = . .
- ~
FIGURE 3.19 The lrvine-Michigan-Brookhaven experiment searching for proton de-
cay uses 2000 photomultiplier tubes arrayed in an 8000-cubic-meter tank of very pure
water. The tank is located deep underground in a large chamber of a working salt mine.
A physicist working under water to adjust the tubes wears a special diver's suit to avoid
contaminating the water through contact with his skin.
two different states, called ~~ and K`s, with different lifetimes. The K~°
has the longer lifetime, 500 times that of the KOs. The KOs decays through
the weak interaction into two pions. According to a general invariance
principle called CP symmetry, the K0r should never decay into two
pions, but it does, about 0.002 of the time. This is the only reaction or
decay in all of elementary-particle physics where CP symmetry has
been observed to be violated. We do not know what is special about the
decay of the Ki,. Perhaps it is an indication of another basic force that
is very weak and is so far manifest only in this decay process; perhaps
it has another explanation. One of the basic principles of relativistic
quantum mechanics is that all physical phenomena must be invariant
under a combination of CP symmetry and time-reversal symmetry.
Therefore this CP violation also represents a violation of time-reversal
symmetry.
Representative terms from entire chapter:
quark model
