Quark quantum numbers

Quarks have properties called quantum numbers. The electric charge, baryon number and strangeness of the up, down and strange quarks are:

[Use the table shape for tabular content — GFM tables are disabled in md_block]QuarkElectric chargeBaryon numberStrangenessUp ($$u$$)$$+\frac{2}{3}e$$$$+\frac{1}{3}$$$$0$$Down ($$d$$)$$-\frac{1}{3}e$$$$+\frac{1}{3}$$$$0$$Strange ($$s$$)$$-\frac{1}{3}e$$$$+\frac{1}{3}$$$$-1$$

Here, $$$e$$$ is the magnitude of the elementary charge. Baryon number and strangeness have no units.

Antiquark quantum numbers

An antiquark has the opposite charge, baryon number and strangeness to its corresponding quark. For example, an anti-strange quark, $\bar{s}$ , has charge $+\frac{1}{3}e$ , baryon number $-\frac{1}{3}$ and strangeness $$$+1$$$ .

Quantum numbers of composite particles

A particle made from quarks or antiquarks has the sum of its constituents’ values for each quantum number. Add charges to find its charge, baryon numbers to find its baryon number, and strangeness values to find its strangeness.

For example, a particle containing $u\bar{s}$ has:

Charge: $+\frac{2}{3}e + \frac{1}{3}e = +e$
Baryon number: $+\frac{1}{3} - \frac{1}{3} = 0$
Strangeness: $$$0 + 1 = +1$$$

Quark composition of nucleons and antinucleons

Protons and neutrons are nucleons. Each is a baryon: a particle made of three quarks. The two quark types in nucleons are the up quark, $$$u$$$ , and the down quark, $$$d$$$ .

An up quark has charge $+\frac{2}{3}e$ and a down quark has charge $-\frac{1}{3}e$ , where $$$e$$$ is the elementary charge. Adding the quark charges gives the charge of the nucleon:

Proton: $$$uud$$$ . Its two up quarks and one down quark give a total charge of $$$+e$$$ .
Neutron: $$$udd$$$ . Its one up quark and two down quarks give a total charge of zero.

Each quark has baryon number $+\frac{1}{3}$ , so both the proton and neutron have baryon number $$$+1$$$ . Both have strangeness zero.

Antinucleon composition

An antibaryon consists of three antiquarks. Replacing every quark in a nucleon with its corresponding antiquark gives its antiparticle. An antiquark has the opposite charge and baryon number to its corresponding quark.

Antiproton: $\bar{u}\bar{u}\bar{d}$ . Its charge is $$$-e$$$ .
Antineutron: $\bar{u}\bar{d}\bar{d}$ . Its charge is zero.

Each antiquark has baryon number $-\frac{1}{3}$ , so both antinucleons have baryon number $$$-1$$$ . Their strangeness is zero. Although the neutron and antineutron are both uncharged, they have different compositions: one contains quarks and the other contains antiquarks.

Quark composition of pions and kaons

A meson consists of a quark and an antiquark. A quark has baryon number $+\frac{1}{3}$ and an antiquark has baryon number $-\frac{1}{3}$ , so every meson has baryon number zero.

The electric charge of a meson is the sum of the charges of its quark and antiquark. In units of the elementary charge $$$e$$$ , an up quark $$$u$$$ has charge $+\frac{2}{3}$ , while down $$$d$$$ and strange $$$s$$$ quarks each have charge $-\frac{1}{3}$ . Each antiquark has the opposite charge to its corresponding quark.

Pion compositions

The positive pion is $\pi^+ = u\bar{d}$ .
The negative pion is $\pi^- = d\bar{u}$ .
The neutral pion $\pi^0$ is a quantum superposition of the $u\bar{u}$ and $d\bar{d}$ states, rather than a single fixed quark–antiquark composition.

For example, the charge of $\pi^+$ is $+\frac{2}{3}+\frac{1}{3}=+1$ in units of $$$e$$$ . Each component of the neutral pion has zero total charge.

Kaon compositions and strangeness

$K^+ = u\bar{s}$ has charge $$$+1$$$ and strangeness $$$+1$$$ .
$K^- = s\bar{u}$ has charge $$$-1$$$ and strangeness $$$-1$$$ .
$K^0 = d\bar{s}$ has charge $$$0$$$ and strangeness $$$+1$$$ .
$\bar{K}^0 = s\bar{d}$ has charge $$$0$$$ and strangeness $$$-1$$$ .

The strangeness follows from the strange constituent: an anti-strange quark $\bar{s}$ gives a kaon strangeness $$$+1$$$ , while a strange quark $$$s$$$ gives it strangeness $$$-1$$$ . For example, $$$K^0$$$ is electrically neutral because its $$$d$$$ and $\bar{s}$ charges add to $-\frac{1}{3}+\frac{1}{3}=0$ , but it has strangeness $$$+1$$$ because it contains $\bar{s}$ .

Neutron beta decay

In beta-minus decay, a neutron changes into a proton and emits an electron and an electron antineutrino. The decay is written as:

n \rightarrow p + e^- + \bar{\nu}_e

Here, $$$n$$$ represents the neutron, $$$p$$$ the proton, $$$e^-$$$ the electron and $\bar{\nu}_e$ the electron antineutrino.

Quark change in neutron beta decay

A neutron contains one up quark and two down quarks, written $$$udd$$$ . During the decay, the weak interaction changes one down quark into an up quark. The resulting combination is $$$uud$$$ , which is a proton. The electron and electron antineutrino are emitted during the decay.

Conservation in neutron beta decay

Electric charge is conserved. The neutron has charge zero. After the decay, the proton has charge $$$+1$$$ and the electron has charge $$$-1$$$ , while the electron antineutrino has charge zero. The total charge is therefore still zero.

Baryon number is also conserved. The neutron and proton each have baryon number $$$1$$$ ; the electron and electron antineutrino each have baryon number $$$0$$$ . The total baryon number remains $$$1$$$ .