# 11.3 Quarks  (Page 2/3)

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Check Your Understanding What is the baryon number of a pion?

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Meson quarks
Name Symbol Quarks Charge ( e ) Spin Mass $\left(\text{GeV/}{c}^{2}\right)$
Positive pion ${\pi }^{+}$ $u\stackrel{\text{−}}{d}$ 1 0 0.140
Positive rho ${\rho }^{+}$ $u\stackrel{\text{−}}{d}$ 1 1 0.768
Negative pion ${\pi }^{\text{−}}$ $\stackrel{\text{−}}{u}d$ $-1$ 0 0.140
Negative rho ${\rho }^{\text{−}}$ $\stackrel{\text{−}}{u}d$ $-1$ 1 0.768
Neutral Pion ${\pi }^{0}$ $\stackrel{\text{−}}{u}u$ or $\stackrel{\text{−}}{d}d$ 0 0 0.135
Neutral eta ${\eta }^{0}$ $\stackrel{\text{−}}{u}u$ , $\stackrel{\text{−}}{d}d$ or $\stackrel{\text{−}}{s}s$ 0 0 0.547
Positive kaon ${\text{K}}^{+}$ $u\stackrel{\text{−}}{s}$ 1 0 0.494
Neutral kaon ${\text{K}}^{0}$ $d\stackrel{\text{−}}{s}$ 0 0 0.498
Negative kaon ${\text{K}}^{\text{−}}$ $\stackrel{\text{−}}{u}s$ $-1$ 0 0.494
J/Psi $\text{J/ψ}$ $\stackrel{\text{−}}{c}c$ 0 1 3.10
Charmed eta ${\eta }_{{}^{0}}$ $c\stackrel{\text{−}}{c}$ 0 0 2.98
Neutral D ${\text{D}}^{0}$ $\stackrel{\text{−}}{u}c$ 0 0 1.86
Neutral D ${\text{D}}^{\text{*0}}$ $\stackrel{\text{−}}{u}c$ 0 1 2.01
Positive D ${\text{D}}^{+}$ $\stackrel{\text{−}}{d}c$ 1 0 1.87
Neutral B ${\text{B}}^{0}$ $\stackrel{\text{−}}{d}b$ 0 0 5.26
Upsilon $\Upsilon$ $b\stackrel{\text{−}}{b}$ 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 $\left(u,d,c,s,b,t\right)$ 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 $\text{α}$ -particle scattering experiments. Electrons were collided with protons with energy in excess of 20 GeV. At this energy, $E\approx pc$ , so the de Broglie wavelength of an electron is

$\lambda =\frac{h}{p}=\frac{hc}{E}\approx 6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-17}\phantom{\rule{0.2em}{0ex}}\text{m}.$

The wavelength of the electron is much smaller than the diameter of the proton (about ${10}^{-15}\phantom{\rule{0.2em}{0ex}}\text{m}\right)\text{.}$ 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 $+2\text{/}3e$ or $\text{−}1\text{/}3e$ , 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 ( [link] ). 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.

## 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 $\left(m=E\text{/}{c}^{2}\right)$ . 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 $+1$ .

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

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

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

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

Mesons are formed from the following combinations of quarks (subscripts indicate color and $AR=\text{antired}$ ): $\left({d}_{\text{R}},{\stackrel{\text{−}}{d}}_{\text{AR}}\right)$ , ( ${s}_{\text{G}},{\stackrel{\text{−}}{u}}_{\text{AG}}$ ), and ( ${s}_{\text{R}},{\stackrel{\text{−}}{s}}_{\text{AR}}$ ).

(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?

a. color; b. quark-antiquark

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

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

$d\to u+{e}^{\text{−}}+{\stackrel{\text{−}}{v}}_{e};u\to d+{e}^{+}+{v}_{e}$

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