# 11.3 Quarks

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By the end of this section, you will be able to:
• Compare and contrast the six known quarks
• Use quark composition of hadrons to determine the total charge of these particles
• Explain the primary evidence for the existence of 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 $\left(s=1\text{/}2\right),$ have a fractional charge $\left(1\text{/}3\phantom{\rule{0.2em}{0ex}}\text{or}\phantom{\rule{0.2em}{0ex}}2\text{/}3e\right)$ , and have baryon number $B=1\text{/}3.$ 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 [link] .

Quarks
Quark Charge (units of e ) Spin ( s ) Baryon number Strangeness number
Down ( d ) $-1\text{/}3$ 1/2 1/3 0
Up ( u ) $+2\text{/}3$ 1/2 1/3 0
Strange ( s ) $-1\text{/}3$ 1/2 1/3 $-1$
Charm ( c ) $+2\text{/}3$ 1/2 1/3 0
Bottom ( b ) $-1\text{/}3$ 1/2 1/3 0
Top ( t ) $+2\text{/}3$ 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 [link] . Interestingly, the delta plus ( ${\text{Δ}}^{+}$ ) 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 ${\text{Δ}}^{+}$ with spin 3/2 is 1.3 times the mass of the proton, and the delta zero ( ${\text{Δ}}^{0}$ ) 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.

Baryon quarks
Name Symbol Quarks Charge (unit of e ) Spin ( s ) Mass ( $\text{GeV/}{c}^{2}$ )
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 $\text{–}1$ 3/2 1.232
Lambda zero ${\text{Λ}}^{0}$ u d s 0 1/2 1.116
Positive sigma ${\text{Σ}}^{+}$ u u s 1 1/2 1.189
Neutral sigma ${\text{Σ}}^{0}$ u d s 0 1/2 1.192
Negative xi ${\text{Ξ}}^{\text{−}}$ s d s $-1$ 1/2 1.321
Neutral xi ${\text{Ξ}}^{0}$ s u s 0 1/2 1.315
Omega minus ${\text{Ω}}^{\text{−}}$ s s s $-1$ 3/2 1.672
Charmed lambda ${\text{Λ}}_{C+}^{}$ u d c 1 1/2 2.281
Charmed bottom ${\text{Λ}}_{b0}^{}$ 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 [link] . Consider the formation of the pion ( ${\pi }^{+}=u\stackrel{\text{−}}{d}$ ). 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 ${\pi }^{+}$ meson is 0. The same quark-antiquark combination gives the rho ( $\rho$ ) meson with spin 1. This meson has a mass approximately 5.5 times that of the ${\pi }^{+}$ meson.

## Quark structure

Show that the quark composition given in [link] for ${\text{Ξ}}^{0}$ is consistent with the known charge, spin, and strangeness of this baryon.

## Strategy

${\text{Ξ}}^{0}$ 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 ${\text{Ξ}}^{0}$ baryon.

## Solution

The charge of the s quark is $\text{−}e\text{/}3$ and the charge of the u quark is 2 e /3. Thus, the combination ( s u s ) has no net charge, in agreement with the known charge of ${\text{Ξ}}^{0}$ . Since three spin $\text{−}1\text{/}2$ 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 ( $s=1\text{/}2$ ) of ${\text{Ξ}}^{0}$ . Finally, the net strangeness of the ( s u s ) combination is $\left(\text{−}1\right)+0+\left(\text{−}1\right)=\text{−}2,$ which also agrees with experiment.

## Significance

The charge, spin, and strangeness of the ${\text{Ξ}}^{0}$ 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.

#### Questions & Answers

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