8.8.3.2. Mesons

Table of Contents

Basic idea

Mesons are hadrons made of one quark and one antiquark. This is the simplest way to distinguish them from baryons, which are made of three quarks. Because mesons contain a quark paired with an antiquark, they are not ordinary matter particles in the same sense as protons and neutrons. They are usually unstable and decay into lighter particles.

A meson can be written schematically as

$$
\text{meson} = q\bar q
$$

where $q$ is a quark and $\bar q$ is the corresponding antiquark type, or a different antiquark type.

A meson is a hadron composed of exactly one quark and one antiquark in the basic quark model.
$$
\text{Meson} = q\bar q
$$

Why mesons are hadrons

Hadrons are particles that feel the strong interaction and are built from quarks. Mesons belong to this family because quarks are held together by the strong force. The quark and antiquark are bound inside the meson and cannot normally be isolated as free particles. This is connected to confinement, which is treated elsewhere.

Mesons are therefore composite particles, not elementary ones.

Mesons compared with baryons

Mesons and baryons are both hadrons, but their internal structure is different. This difference leads to different quantum properties.

Property	Mesons	Baryons
Basic quark content	$q\bar q$	$qqq$
Example	$\pi^+$, $K^0$	proton, neutron
Baryon number	$0$	$1$
Typical spin type	integer	half integer

Because a quark has baryon number $+\tfrac13$ and an antiquark has baryon number $-\tfrac13$, the total baryon number of a meson is

$$
B = \frac13 + \left(-\frac13\right) = 0
$$

Mesons have baryon number zero because the quark and antiquark contributions cancel.
$$
B_{\text{meson}} = 0
$$

Electric charge of mesons

The electric charge of a meson is found by adding the charge of the quark and the charge of the antiquark. Antiquarks have the opposite electric charge of their corresponding quarks.

For the light quarks,

$$
Q_u = +\frac23 e, \qquad Q_d = -\frac13 e, \qquad Q_s = -\frac13 e
$$

and for antiquarks,

$$
Q_{\bar u} = -\frac23 e, \qquad Q_{\bar d} = +\frac13 e, \qquad Q_{\bar s} = +\frac13 e
$$

So, for example,

$$
\pi^+ = u\bar d
$$

has charge

$$
Q = \frac23 e + \frac13 e = +e
$$

and

$$
\pi^- = d\bar u
$$

has charge

$$
Q = -\frac13 e - \frac23 e = -e
$$

while

$$
\pi^0
$$

is neutral.

Common meson families

The most important beginner examples are the pions and kaons. They are made from the lighter quarks and are common in nuclear and particle processes.

Meson	Quark content	Charge
$\pi^+$	$u\bar d$	$+e$
$\pi^-$	$d\bar u$	$-e$
$\pi^0$	mixture of $u\bar u$ and $d\bar d$	$0$
$K^+$	$u\bar s$	$+e$
$K^-$	$s\bar u$	$-e$
$K^0$	$d\bar s$	$0$
$\bar K^0$	$s\bar d$	$0$

The neutral pion is a little more subtle than the charged pions. It is not just one simple quark-antiquark pair, but a quantum combination of light quark states. At an introductory level, it is enough to know that it is a neutral meson built from light quarks.

Spin and statistics

Mesons usually have integer spin. Because particles with integer spin are bosons, mesons belong to the boson family.

This is different from baryons, which usually have half integer spin and are fermions.

Mesons are hadrons with integer spin, so they are bosons.

Mesons as force carriers inside nuclei

Historically, mesons were important because they helped explain the strong interaction between nucleons. In nuclear physics, pions can be exchanged between protons and neutrons, producing an effective force between them. This does not mean that mesons are the fundamental carriers of the strong force in the same way photons carry electromagnetism. At the deeper level, gluons act between quarks. But at the nuclear scale, meson exchange is a useful description.

Stability and decay

Most mesons are unstable. Since they are made of a quark and an antiquark, they can transform into lighter particles through strong, electromagnetic, or weak processes, depending on the meson and what final states are allowed.

For example, charged pions decay mainly into muons and neutrinos:

$$
\pi^+ \to \mu^+ + \nu_\mu
$$

$$
\pi^- \to \mu^- + \bar\nu_\mu
$$

Neutral pions often decay into photons:

$$
\pi^0 \to \gamma + \gamma
$$

This instability is one reason mesons are usually seen in high energy processes rather than as ordinary stable matter around us.

Visual picture of a meson

A simple picture is a quark and an antiquark bound together by the strong interaction.

Rendering scientific sketch…

Simple meson picture

Examples from heavier quarks

Mesons can also contain heavier quarks such as charm or bottom. Then we get heavier mesons, such as $D$ mesons and $B$ mesons. These are important in modern particle physics because their decays help scientists study weak interactions and symmetries.

A few examples are

$$
D^+ = c\bar d
$$

$$
D^0 = c\bar u
$$

$$
B^+ = u\bar b
$$

$$
B^0 = d\bar b
$$

These heavier mesons are also unstable.

Summary

Mesons are hadrons made of one quark and one antiquark. They have baryon number zero, usually have integer spin, and are therefore bosons. Their electric charge comes from the sum of the quark and antiquark charges. Familiar examples include pions and kaons. Most mesons are unstable and decay into lighter particles. They are essential in particle physics and also help describe forces inside atomic nuclei.

Key facts about mesons:
$$
\text{Meson} = q\bar q
$$
$$
B = 0
$$
Mesons are hadrons, usually bosons, and are generally unstable.

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