KAHIBARO
Table of Contents
Three-Quark Particles
Baryons are hadrons made of three quarks. They are one of the two main families of hadrons, the other being mesons, which are made of a quark and an antiquark. A baryon is therefore a composite particle, not an elementary one.
The most familiar baryons are the proton and the neutron. These are the particles that make up atomic nuclei, except for the simplest hydrogen nucleus, which contains only a proton. Because matter around us is built from nuclei, baryons are a central part of ordinary matter.
A baryon is a hadron composed of three quarks.
Examples:
$ p = uud $
$ n = udd $
Basic Examples
The proton contains two up quarks and one down quark, written as $uud$. The neutron contains one up quark and two down quarks, written as $udd$.
The electric charge of a baryon is found by adding the charges of its quarks. An up quark has charge $+\frac{2}{3}e$, and a down quark has charge $-\frac{1}{3}e$.
For the proton,
$$
Q_p = \frac{2}{3}e + \frac{2}{3}e - \frac{1}{3}e = +e
$$
For the neutron,
$$
Q_n = \frac{2}{3}e - \frac{1}{3}e - \frac{1}{3}e = 0
$$
This explains why the proton is positively charged and the neutron is electrically neutral.
Baryon Number
Baryons carry baryon number $B = 1$. Each quark contributes $\frac{1}{3}$ to baryon number, so three quarks together give
$$
B = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1
$$
Antibaryons are made of three antiquarks and have baryon number $B = -1$.
For baryons:
$$
B = 1
$$
For antibaryons:
$$
B = -1
$$
Baryon number is an important identifying property in particle physics.
Baryons as Fermions
Because baryons are built from three quarks, and quarks are fermions with spin $\frac{1}{2}$, baryons themselves are also fermions. This means baryons have half integer spin, such as $\frac{1}{2}$ or $\frac{3}{2}$.
The proton and neutron are spin $\frac{1}{2}$ baryons. Some heavier baryons, such as the $\Delta$ particles, have spin $\frac{3}{2}$.
Common Baryons
There are many baryons besides the proton and neutron. Some contain strange, charm, bottom, or even top quarks, although top containing baryons do not form as ordinary bound hadrons because the top quark decays too quickly.
Here are some common examples.
| Baryon | Quark content | Charge |
|---|---|---|
| Proton $p$ | $uud$ | $+1e$ |
| Neutron $n$ | $udd$ | $0$ |
| Lambda $\Lambda^0$ | $uds$ | $0$ |
| Sigma plus $\Sigma^+$ | $uus$ | $+1e$ |
| Sigma zero $\Sigma^0$ | $uds$ | $0$ |
| Sigma minus $\Sigma^-$ | $dds$ | $-1e$ |
| Xi zero $\Xi^0$ | $uss$ | $0$ |
| Xi minus $\Xi^-$ | $dss$ | $-1e$ |
| Omega minus $\Omega^-$ | $sss$ | $-1e$ |
These heavier baryons are unstable and decay into lighter particles.
Antibaryons
Every baryon has a corresponding antibaryon. An antibaryon is made of three antiquarks. For example, the antiproton has quark content $\bar{u}\bar{u}\bar{d}$.
The charge of an antibaryon is opposite to that of the corresponding baryon. So the antiproton has charge $-e$, while the antineutron has charge $0$.
Why Baryons Matter
Baryons are especially important because the stable matter we see is mostly made from them. Protons are stable in ordinary observations, and neutrons are stable when bound inside many nuclei. Even though many other baryons exist, they are usually short lived and appear in high energy processes.
In this sense, baryons connect the world of particle physics to the everyday world of atoms, nuclei, and matter.
Visual Picture
A simple picture of a baryon is three quarks bound together inside one particle.
Summary
Baryons are hadrons made of three quarks. They include the proton and neutron, which form the matter in atomic nuclei. Baryons have baryon number $1$ and are fermions. Many heavier baryons also exist, but most are unstable. Antibaryons are made of three antiquarks and have baryon number $-1$.
Key facts about baryons:
$$
\text{Baryon} = qqq
$$
$$
B = 1
$$
Proton:
$$
uud
$$
Neutron:
$$
udd
$$