11.3 Quarks

In the 1960s, particle physicists began to realize that hadrons are not elementary particles but are made of particles called quarks. (The name ‘quark’ was coined by the physicist Murray Gell-Mann, from a phrase in the James Joyce novel Finnegans Wake.) Initially, it was believed there were only three types of quarks, called up (u), down (d), and strange (s). However, this number soon grew to six—interestingly, the same as the number of leptons—to include charmed (c), bottom (b), and top (t).

All quarks are spin-half fermions $open parenthesis s equals 1 / 2 close parenthesis,$ have a fractional charge $open parenthesis 1 / 3 or 2 / 3 e close parenthesis$ , and have baryon number $B equals 1 / 3.$ Each quark has an antiquark with the same mass but opposite charge and baryon number. The names and properties of the six quarks are listed in Table 11.3.

**Table 11.3** Quarks
Quark	Charge (units of e)	Spin (s)	Baryon number	Strangeness number
Down (d)	$−1 / 3$	1/2	1/3	0
Up (u)	$plus 2 / 3$	1/2	1/3	0
Strange (s)	$−1 / 3$	1/2	1/3	$−1$
Charm (c)	$plus 2 / 3$	1/2	1/3	0
Bottom (b)	$−1 / 3$	1/2	1/3	0
Top (t)	$plus 2 / 3$	1/2	1/3	0

Quark Combinations

As mentioned earlier, quarks bind together in groups of two or three to form hadrons. Baryons are formed from three quarks. Sample baryons, including quark content and properties, are given in Table 11.4. Interestingly, the delta plus ( $Δ^{+}$ ) baryon is formed from the same three quarks as the proton, but the total spin of the particle is 3/2 rather than 1/2. Similarly, the mass of $Δ^{+}$ with spin 3/2 is 1.3 times the mass of the proton, and the delta zero ( $Δ to the power 0$ ) baryon with a spin 3/2 is 1.3 times the neutron mass. Evidently, the energy associated with the spin (or angular momentum) of the particle contributes to its mass energy. It is also interesting that no baryons are believed to exist with top quarks, because top quarks decay too quickly to bind to the other quarks in their production.

**Table 11.4** Baryon Quarks
Name	Symbol	Quarks	Charge (unit of e)	Spin (s)	Mass ( $GeV/ c squared$ )
Proton	p	u u d	1	1/2	0.938
Neutron	n	u d d	0	1/2	0.940
Delta plus plus	∆⁺⁺	u u u	2	3/2	1.232
Delta plus	∆⁺	u u d	1	3/2	1.232
Delta zero	∆⁰	u d d	0	3/2	1.232
Delta minus	∆⁻	d d d	$– 1$	3/2	1.232
Lambda zero	$Λ to the power 0$	u d s	0	1/2	1.116
Positive sigma	$Σ^{+}$	u u s	1	1/2	1.189
Neutral sigma	$Σ to the power 0$	u d s	0	1/2	1.192
Negative xi	$Ξ to the power −$	s d s	$−1$	1/2	1.321
Neutral xi	$Ξ to the power 0$	s u s	0	1/2	1.315
Omega minus	$Ω to the power −$	s s s	$−1$	3/2	1.672
Charmed lambda	$Λ_{C}^{+}$	u d c	1	1/2	2.281
Bottom lambda	$Λ b 0$	u d b	0	1/2	5.619

Mesons are formed by two quarks—a quark-antiquark pair. Sample mesons, including quark content and properties, are given in Table 11.5. Consider the formation of the pion ( $π^{+} = u \overset{−}{d}$ ). Based on its quark content, the charge of the pion is

$\frac{2}{3} e + \frac{1}{3} e = e .$

Both quarks are spin-half ( $s = ½$ ), so the resultant spin is either 0 or 1. The spin of the $π^{+}$ meson is 0. The same quark-antiquark combination gives the rho ( $ρ$ ) meson with spin 1. This meson has a mass approximately 5.5 times that of the $π^{+}$ meson.

Example 1 Quark Structure

Show that the quark composition given in Table 11.5 for $Ξ to the power 0$ is consistent with the known charge, spin, and strangeness of this baryon.

Strategy $Ξ to the power 0$ is composed of two strange quarks and an up quark (s u s). We can add together the properties of quarks to predict the resulting properties of the $Ξ to the power 0$ baryon.

Solution The charge of the s quark is $− e / 3$ and the charge of the u quark is 2e/3. Thus, the combination (s u s) has no net charge, in agreement with the known charge of $Ξ to the power 0$ . Since three spin $− 1 / 2$ quarks can combine to produce a particle with spin of either 1/2 or 3/2, the quark composition is consistent with the known spin ( $s equals 1 / 2$ ) of $Ξ to the power 0$ . Finally, the net strangeness of the (s u s) combination is $(− 1) + 0 + (− 1) = − 2,$ which also agrees with experiment.

Significance The charge, spin, and strangeness of the $Ξ to the power 0$ particle can be determined from the properties of its constituent quarks. The great diversity of baryons and mesons can be traced to the properties of just six quarks: up, down, charge, strange, top, and bottom.

**Table 11.5** Meson Quarks
Name	Symbol	Quarks	Charge (e)	Spin	Mass $open parenthesis GeV/ c squared close parenthesis$
Positive pion	$π^{+}$	$u d −$	1	0	0.140
Positive rho	$ρ^{+}$	$u d −$	1	1	0.768
Negative pion	$π to the power −$	$u − d$	$−1$	0	0.140
Negative rho	$ρ to the power −$	$u − d$	$−1$	1	0.768
Neutral Pion	$π to the power 0$	$u − u$ or $d − d$	0	0	0.135
Neutral eta	$η to the power 0$	$u − u$ , $d − d$ or $s − s$	0	0	0.547
Positive kaon	$K^{+}$	$u s −$	1	0	0.494
Neutral kaon	$K to the power 0$	$d s −$	0	0	0.498
Negative kaon	$K to the power −$	$u − s$	$−1$	0	0.494
J/Psi	$J/ψ$	$c − c$	0	1	3.10
Charmed eta	$η sub to the power 0$	$c c −$	0	0	2.98
Neutral D	$D to the power 0$	$u − c$	0	0	1.86
Neutral D	$D to the power *0$	$u − c$	0	1	2.01
Positive D	$D^{+}$	$d − c$	1	0	1.87
Neutral B	$B to the power 0$	$d − b$	0	0	5.26
Upsilon	$ϒ$	$b b −$	0	1	9.46

Color

Quarks are fermions that obey Pauli’s exclusion principle, so it might be surprising to learn that three quarks can bind together within a nucleus. For example, how can two up quarks exist in the same small region of space within a proton? The solution is to invent a third new property to distinguish them. This property is called color, and it plays the same role in the strong nuclear interaction as charge does in electromagnetic interactions. For this reason, quark color is sometimes called “strong charge.”

Quarks come in three colors: red, green, and blue. (These are just labels—quarks are not actually colored.) Each type of quark $(u, d, c, s, b, t)$ can possess any other colors. For example, three strange quarks exist: a red strange quark, a green strange quark, and a blue strange quark. Antiquarks have anticolor. Quarks that bind together to form hadrons (baryons and mesons) must be color neutral, colorless, or “white.” Thus, a baryon must contain a red, blue, and green quark. Likewise, a meson contains either a red-antired, blue-antiblue, or green-antigreen quark pair. Thus, two quarks can be found in the same spin state in a hadron, without violating Pauli’s exclusion principle, because their colors are different.

Quark Confinement

The first strong evidence for the existence of quarks came from a series of experiments performed at the Stanford Linear Accelerator Center (SLAC) and at CERN around 1970. This experiment was designed to probe the structure of the proton, much like Rutherford studied structure inside the atom with his $α$ -particle scattering experiments. Electrons were collided with protons with energy in excess of 20 GeV. At this energy, $E \approx p c$ , so the de Broglie wavelength of an electron is

$λ = \frac{h}{p} = \frac{h c}{E} \approx 6 \times 10^{−17} m .$

(11.1)

The wavelength of the electron is much smaller than the diameter of the proton (about $10 to the power −15 m close parenthesis.$ Thus, like an automobile traveling through a rocky mountain range, electrons can be used to probe the structure of the nucleus.

The SLAC experiments found that some electrons were deflected at very large angles, indicating small scattering centers within the proton. The scattering distribution was consistent with electrons being scattered from sites with spin 1/2, the spin of quarks. The experiments at CERN used neutrinos instead of electrons. This experiment also found evidence for the tiny scattering centers. In both experiments, the results suggested that the charges of the scattering particles were either $plus 2 / 3 e$ or $− 1 / 3 e$ , in agreement with the quark model.

The quark model has been extremely successful in organizing the complex world of subatomic particles. Interestingly, however, no experiment has ever produced an isolated quark. All quarks have fractional charge and should therefore be easily distinguishable from the known elementary particles, whose charges are all an integer multiple of e. Why are isolated quarks not observed? In current models of particle interactions, the answer is expressed in terms of quark confinement. Quark confinement refers to the confinement of quarks in groups of two or three in a small region of space. The quarks are completely free to move about in this space, and send and receive gluons (the carriers of the strong force). However, if these quarks stray too far from one another, the strong force pulls them back it. This action is likened to a bola, a weapon used for hunting (Figure 11.5). The stones are tied to a central point by a string, so none of the rocks can move too far from the others. The bola corresponds to a baryon, the stones correspond to quarks, and the string corresponds to the gluons that hold the system together.

Three strings are tied together at one end. A weight is attached to the other end of each. The strings are labeled quark confinement. The weights are labeled quarks. — **Figure 11.5** A baryon is analogous to a bola, a weapon used for hunting. The rocks in this image correspond to the baryon quarks. The quarks are free to move about but must remain close to the other quarks.

Summary

Six known quarks exist: up (u), down (d), charm (c), strange (s), top (t), and bottom (b). These particles are fermions with half-integral spin and fractional charge.
Baryons consist of three quarks, and mesons consist of a quark-antiquark pair. Due to the strong force, quarks cannot exist in isolation.
Evidence for quarks is found in scattering experiments.

Conceptual Questions

What are the six known quarks? Summarize their properties.

What is the general quark composition of a baryon? Of a meson?

3 quarks, 2 quarks (a quark-antiquark pair)

What evidence exists for the existence of quarks?

Why do baryons with the same quark composition sometimes differ in their rest mass energies?

Baryons with the same quark composition differ in rest energy because this energy depends on the internal energy of the quarks $open parenthesis m equals E / c squared close parenthesis$ . So, a baryon that contains a quark with a large angular momentum is expected to be more massive than the same baryon with less angular momentum.

Problems

Based on quark composition of a proton, show that its charge is $plus 1$ .

A proton consists of two up quarks and one down quark. The total charge of a proton is therefore $+ \frac{2}{3} + \frac{2}{3} + − \frac{1}{3} = + 1 .$

Based on the quark composition of a neutron, show that is charge is 0.

Argue that the quark composition given in Table 11.5 for the positive kaon is consistent with the known charge, spin, and strangeness of this baryon.

The $K^{+}$ meson is composed of an up quark and a strange antiquark ( $u s −$ ). Since the changes of this quark and antiquark are 2e/3 and e/3, respectively, the net charge of the $K^{+}$ meson is e, in agreement with its known value. Two spin $−1 / 2$ particles can combine to produce a particle with spin of either 0 or 1, consistent with the $K^{+}$ meson’s spin of 0. The net strangeness of the up quark and strange antiquark is $0 + 1 = 1$ , in agreement with the measured strangeness of the $K^{+}$ meson.

Mesons are formed from the following combinations of quarks (subscripts indicate color and $A R = antired$ ): $open parenthesis d sub R, d − sub AR close parenthesis$ , ( $s sub G, u − sub AG$ ), and ( $s sub R, s − sub AR$ ).

(a) Determine the charge and strangeness of each combination. (b) Identify one or more mesons formed by each quark-antiquark combination.

Why can’t either set of quarks shown below form a hadron?

Figure a has three red circles, each labeled u subscript R. Figure b has a blue circle labeled d subscript B and a purple circle labeled u subscript G.

a. color; b. quark-antiquark

Experimental results indicate an isolate particle with charge $plus 2 / 3$ —an isolated quark. What quark could this be? Why would this discovery be important?

Express the $β$ decays $n \to p + e^{−} + \overset{−}{ν}$ and $p \to n + e^{+} + ν$ in terms of $β$ decays of quarks. Check to see that the conservation laws for charge, lepton number, and baryon number are satisfied by the quark $β$ decays.

$d \to u + e^{−} + {\overset{−}{v}}_{e}; u \to d + e^{+} + v_{e}$