# 33.5 Quarks: is that all there is?  (Page 2/20)

 Page 2 / 20

We see that this is equivalent to a down quark changing flavor to become an up quark:

$d\to u+{\beta }^{-}+{\stackrel{-}{v}}_{e}$

Quarks and antiquarks The lower of the $±$ symbols are the values for antiquarks.
Name Symbol Antiparticle Spin Charge $B$ $B$ is baryon number, S is strangeness, $c$ is charm, $b$ is bottomness, $t$ is topness. $S$ $c$ $b$ $t$ Mass $\left(\text{GeV}/{c}^{2}\right)$ Values are approximate, are not directly observable, and vary with model.
Up $u$ $\stackrel{-}{u}$ 1/2 $±\frac{2}{3}{q}_{e}$ $±\frac{1}{3}$ 0 0 0 0 0.005
Down $d$ $\stackrel{-}{d}$ 1/2 $\mp \frac{1}{3}{q}_{e}$ $±\frac{1}{3}$ 0 0 0 0 0.008
Strange $s$ $\stackrel{-}{s}$ 1/2 $\mp \frac{1}{3}{q}_{e}$ $±\frac{1}{3}$ $\mp 1$ 0 0 0 0.50
Charmed $c$ $\stackrel{-}{c}$ 1/2 $±\frac{2}{3}{q}_{e}$ $±\frac{1}{3}$ 0 $±1$ 0 0 1.6
Bottom $b$ $\stackrel{-}{b}$ 1/2 $\mp \frac{1}{3}{q}_{e}$ $±\frac{1}{3}$ 0 0 $\mp 1$ 0 5
Top $t$ $\stackrel{-}{t}$ 1/2 $±\frac{2}{3}{q}_{e}$ $±\frac{1}{3}$ 0 0 0 $±1$ 173
Quark composition of selected hadrons These two mesons are different mixtures, but each is its own antiparticle, as indicated by its quark composition.
Particle Quark Composition
Mesons
${\pi }^{+}$ $u\stackrel{-}{d}$
${\pi }^{-}$ $\stackrel{-}{u}d$
${\pi }^{0}$ $u\stackrel{-}{u}$ , $d\stackrel{-}{d}$ mixture These two mesons are different mixtures, but each is its own antiparticle, as indicated by its quark composition.
${\eta }^{0}$ $u\stackrel{-}{u}$ , $d\stackrel{-}{d}$ mixture These two mesons are different mixtures, but each is its own antiparticle, as indicated by its quark composition.
${K}^{0}$ $d\stackrel{-}{s}$
${\stackrel{-}{K}}^{0}$ $\stackrel{-}{d}s$
${K}^{+}$ $u\stackrel{-}{s}$
${K}^{-}$ $\stackrel{-}{u}s$
$J/\psi$ $c\stackrel{-}{c}$
$\Upsilon$ $b\stackrel{-}{b}$
Baryons Antibaryons have the antiquarks of their counterparts. The antiproton $\stackrel{-}{p}$ is $\stackrel{-}{u}\stackrel{-}{u}\stackrel{-}{d}$ , for example. , Baryons composed of the same quarks are different states of the same particle. For example, the ${\text{Δ}}^{+}$ is an excited state of the proton.
$p$ $\text{uud}$
$n$ $\text{udd}$
${\text{Δ}}^{0}$ $\text{udd}$
${\text{Δ}}^{+}$ $\text{uud}$
${\text{Δ}}^{-}$ $\text{ddd}$
${\text{Δ}}^{\text{++}}$ $\text{uuu}$
${\text{Λ}}^{0}$ $\text{uds}$
${\text{Σ}}^{0}$ $\text{uds}$
${\text{Σ}}^{+}$ $\text{uus}$
${\text{Σ}}^{-}$ $\text{dds}$
${\text{Ξ}}^{0}$ $\text{uss}$
${\text{Ξ}}^{-}$ $\text{dss}$
${\Omega }^{-}$ $\text{sss}$

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 $d\to u$ , we can also get $u\to d$ . Furthermore, the strange quark can be changed by the weak force, too, making $s\to u$ and $s\to d$ 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 [link] , we see that the ${\pi }^{+}$ meson (one of the three pions) is composed of an up quark plus an antidown quark, or $u\stackrel{-}{d}$ . Its total charge is thus $+\left(\frac{2}{3}\right){q}_{e}+\left(\frac{1}{3}\right){q}_{e}={q}_{e}$ , as expected. Its baryon number is 0, since it has a quark and an antiquark with baryon numbers $+\left(\frac{1}{3}\right)-\left(\frac{1}{3}\right)=0$ . The ${\pi }^{+}$ half-life is relatively long since, although it is composed of matter and antimatter, the quarks are different flavors and the weak force should cause the decay by changing the flavor of one into that of the other. The spins of the $u$ and $\stackrel{-}{d}$ quarks are antiparallel, enabling the pion to have spin zero, as observed experimentally. Finally, the ${\pi }^{-}$ meson shown in [link] is the antiparticle of the ${\pi }^{+}$ meson, and it is composed of the corresponding quark antiparticles. That is, the ${\pi }^{+}$ meson is $u\stackrel{-}{d}$ , while the ${\pi }^{-}$ meson is $\stackrel{-}{u}d$ . These two pions annihilate each other quickly, because their constituent quarks are each other’s antiparticles.

Two general rules for combining quarks to form hadrons are:

1. Baryons are composed of three quarks, and antibaryons are composed of three antiquarks.
2. Mesons are combinations of a quark and an antiquark.

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
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Boniface