8.12.2.1. Baryon Number

Table of Contents

What Baryon Number Means

Baryon number is a quantum number used in particle physics to keep track of baryons. A baryon is a particle made of three quarks, such as the proton and the neutron. Baryon number tells us whether a process creates, destroys, or preserves the amount of baryonic matter.

The rule is simple. Every baryon is assigned baryon number

$$B = +1$$

and every antibaryon is assigned baryon number

$$B = -1.$$

Particles that are not baryons, such as electrons, neutrinos, and photons, have

$$B = 0.$$

This number is very useful when studying particle reactions and decays, because many known processes preserve the total baryon number.

Important rule:
The total baryon number of an isolated system is usually conserved in ordinary particle and nuclear processes.
$$\sum B_{\text{before}} = \sum B_{\text{after}}$$

Baryon Number of Quarks

Since baryons are made of three quarks, it is convenient to assign a baryon number to each quark. Each quark carries

$$B = \frac{1}{3}$$

and each antiquark carries

$$B = -\frac{1}{3}.$$

This makes the counting work naturally. A proton or neutron contains three quarks, so its total baryon number is

$$3 \times \frac{1}{3} = 1.$$

An antibaryon contains three antiquarks, so its total baryon number is

$$3 \times \left(-\frac{1}{3}\right) = -1.$$

A meson contains one quark and one antiquark, so

$$\frac{1}{3} + \left(-\frac{1}{3}\right) = 0.$$

This is why mesons do not carry baryon number.

Particle type	Quark content idea	Baryon number
Baryon	3 quarks	$+1$
Antibaryon	3 antiquarks	$-1$
Meson	quark + antiquark	$0$
Lepton	no quarks	$0$
Photon	no quarks	$0$

Familiar Examples

The proton and neutron are the most common baryons, so both have baryon number $+1$. Their antiparticles have baryon number $-1$.

Particle	Symbol	Baryon number
Proton	$p$	$+1$
Neutron	$n$	$+1$
Antiproton	$\bar p$	$-1$
Antineutron	$\bar n$	$-1$
Electron	$e^-$	$0$
Positron	$e^+$	$0$
Neutrino	$\nu$	$0$
Pion	$\pi$	$0$
Photon	$\gamma$	$0$

How Conservation Works

To test whether a reaction respects baryon number, add the baryon numbers of all particles before and after the process.

For example, in beta decay a neutron changes into a proton, an electron, and an antineutrino:

$$n \to p + e^- + \bar\nu_e$$

The baryon numbers are

$$+1 \to +1 + 0 + 0$$

so baryon number is conserved.

As another example, proton and antiproton annihilation can produce photons:

$$p + \bar p \to \gamma + \gamma$$

Before the reaction,

$$B = +1 + (-1) = 0$$

and after the reaction,

$$B = 0 + 0 = 0.$$

So baryon number is conserved again.

Now consider a hypothetical process

$$p \to e^+ + \gamma$$

The baryon number before is $+1$, but after it is $0$. This would violate baryon number conservation, so such a decay is not allowed in the ordinary Standard Model description.

To check baryon number conservation, always add the baryon numbers of all incoming particles and compare with the sum for all outgoing particles.

Why It Matters

Baryon number helps explain why protons are extremely stable in observed ordinary matter. Since the proton is the lightest baryon, there is no lighter particle with baryon number $+1$ into which it can easily decay while conserving baryon number.

This conservation law is also important in nuclear physics. A nucleus contains protons and neutrons, and each contributes baryon number $+1$. So the total baryon number of a nucleus equals its total number of nucleons.

For a nucleus with mass number $A$,

$$B = A.$$

This makes baryon number closely related to counting nucleons in nuclear reactions.

Baryon Number in Reactions

Here are some quick checks.

For nuclear fusion of deuterium and tritium,

$$^2\mathrm{H} + {}^3\mathrm{H} \to {}^4\mathrm{He} + n$$

the baryon number is

$$2 + 3 \to 4 + 1,$$

$$5 \to 5.$$

It is conserved.

For pair production of a proton and antiproton,

$$\gamma + \gamma \to p + \bar p$$

the baryon number is

$$0 + 0 \to +1 + (-1),$$

$$0 \to 0.$$

Again it is conserved.

Visual Picture

A simple way to think about baryon number is as a bookkeeping label attached to matter built from three quarks.

Rendering scientific sketch…

Baryon number bookkeeping

Baryon Number and the Universe

In everyday matter, baryons are abundant because protons and neutrons make up atoms. Antibaryons are rare in the visible universe. This means the universe contains a large positive net baryon number in ordinary matter. Understanding why matter is more common than antimatter is an important question in modern physics, and baryon number plays a central role in that discussion.

Key Summary

Baryon number is a conserved quantum number associated with baryons. Baryons have $B=+1$, antibaryons have $B=-1$, and nonbaryonic particles have $B=0$. At the quark level, quarks carry $B=\frac13$ and antiquarks carry $B=-\frac13$. In most known reactions,

$$\sum B_{\text{before}} = \sum B_{\text{after}}.$$

Essential facts:
$$B_{\text{quark}}=\frac13,\qquad B_{\text{antiquark}}=-\frac13$$
$$B_{\text{baryon}}=+1,\qquad B_{\text{antibaryon}}=-1,\qquad B_{\text{nonbaryon}}=0$$
$$\sum B_{\text{before}}=\sum B_{\text{after}}$$

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