How Does It Work?
How Does it Work?
To understand how these quark substructures work, let us specifically examine the proton, neutron, and the two pions pictured in this figure before moving on to more general considerations. First, the proton p is composed of the three quarks uud, so that its total charge is \(+\left(\cfrac{2}{3}\right){q}_{e}+\left(\cfrac{2}{3}\right){q}_{e}-\left(\cfrac{1}{3}\right){q}_{e}={q}_{e}\), as expected. With the spins aligned as in the figure, the proton’s intrinsic spin is \(+\left(\cfrac{1}{2}\right)+\left(\cfrac{1}{2}\right)-\left(\cfrac{1}{2}\right)=\left(\cfrac{1}{2}\right)\), also as expected.
Note that the spins of the up quarks are aligned, so that they would be in the same state except that they have different colors (another quantum number to be elaborated upon a little later). Quarks obey the Pauli exclusion principle. Similar comments apply to the neutron n, which is composed of the three quarks udd. Note also that the neutron is made of charges that add to zero but move internally, producing its well-known magnetic moment. When the neutron \({\beta }^{-}\) decays, it does so by changing the flavor of one of its quarks. Writing neutron \({\beta }^{-}\) decay in terms of quarks,
\(n\to p+{\beta }^{-}+{\stackrel{-}{v}}_{e}\text{ becomes } udd \to uud+{\beta }^{-}+{\stackrel{-}{v}}_{e}\text{.}\)
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
| Name | Symbol | Antiparticle | Spin | Charge | \(B\) | \(S\) | \(c\) | \(b\) | \(t\) | Mass \((\text{GeV}/{c}^{2})\) |
|---|---|---|---|---|---|---|---|---|---|---|
| Up | \(u\) | \(\stackrel{-}{u}\) | 1/2 | \(±\cfrac{2}{3}{q}_{e}\) | \(±\cfrac{1}{3}\) | 0 | 0 | 0 | 0 | 0.005 |
| Down | \(d\) | \(\stackrel{-}{d}\) | 1/2 | \(\mp \cfrac{1}{3}{q}_{e}\) | \(±\cfrac{1}{3}\) | 0 | 0 | 0 | 0 | 0.008 |
| Strange | \(s\) | \(\stackrel{-}{s}\) | 1/2 | \(\mp \cfrac{1}{3}{q}_{e}\) | \(±\cfrac{1}{3}\) | \(\mp 1\) | 0 | 0 | 0 | 0.50 |
| Charmed | \(c\) | \(\stackrel{-}{c}\) | 1/2 | \(±\cfrac{2}{3}{q}_{e}\) | \(±\cfrac{1}{3}\) | 0 | \(±1\) | 0 | 0 | 1.6 |
| Bottom | \(b\) | \(\stackrel{-}{b}\) | 1/2 | \(\mp \cfrac{1}{3}{q}_{e}\) | \(±\cfrac{1}{3}\) | 0 | 0 | \(\mp 1\) | 0 | 5 |
| Top | \(t\) | \(\stackrel{-}{t}\) | 1/2 | \(±\cfrac{2}{3}{q}_{e}\) | \(±\cfrac{1}{3}\) | 0 | 0 | 0 | \(±1\) | 173 |
Quark Composition of Selected Hadrons
| Particle | Quark Composition | |
|---|---|---|
| Mesons | ||
| \({\pi }^{+}\) | \(u\stackrel{-}{d}\) | |
| \({\pi }^{-}\) | \(\stackrel{-}{u}d\) | |
| \({\pi }^{0}\) | \(u\stackrel{-}{u}\), \(d\stackrel{-}{d}\) mixture | |
| \({\eta }^{0}\) | \(u\stackrel{-}{u}\), \(d\stackrel{-}{d}\) mixture | |
| \({K}^{0}\) | \(d\stackrel{-}{s}\) | |
| \({\stackrel{-}{K}}^{0}\) | \(\stackrel{-}{d}s\) | |
| \({K}^{+}\) | \(u\stackrel{-}{s}\) | |
| \({K}^{-}\) | \(\stackrel{-}{u}s\) | |
| \(J/\psi \) | \(c\stackrel{-}{c}\) | |
| \(\Upsilon \) | \(b\stackrel{-}{b}\) | |
| Baryons, | ||
| \(p\) | \(\text{uud}\) | |
| \(n\) | \(\text{udd}\) | |
| \({\text{Δ}}^{0}\) | \(\text{udd}\) | |
| \({\text{Δ}}^{+}\) | \(\text{uud}\) | |
| \({\text{Δ}}^{-}\) | \(\text{ddd}\) | |
| \({\text{Δ}}^{\text{++}}\) | \(\text{uuu}\) | |
| \({\text{Λ}}^{0}\) | \(\text{uds}\) | |
| \({\text{Σ}}^{0}\) | \(\text{uds}\) | |
| \({\text{Σ}}^{+}\) | \(\text{uus}\) | |
| \({\text{Σ}}^{-}\) | \(\text{dds}\) | |
| \({\text{Ξ}}^{0}\) | \(\text{uss}\) | |
| \({\text{Ξ}}^{-}\) | \(\text{dss}\) | |
| \({\Omega }^{-}\) | \(\text{sss}\) | |
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 this figure, 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 \(+\left(\cfrac{2}{3}\right){q}_{e}+\left(\cfrac{1}{3}\right){q}_{e}={q}_{e}\), as expected. Its baryon number is 0, since it has a quark and an antiquark with baryon numbers \(+\left(\cfrac{1}{3}\right)-\left(\cfrac{1}{3}\right)=0\). 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 this figure 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:
- Baryons are composed of three quarks, and antibaryons are composed of three antiquarks.
- Mesons are combinations of a quark and an antiquark.
One of the clever things about this scheme is that only integral charges result, even though the quarks have fractional charge.
This lesson is part of:
Particle Physics