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Classifying Particles

Friday, April 8, 2022

Particle Families

Elementary particles can be organized into three categories: leptons, mesons, and baryons based on their masses (leptons have the lightest mass, baryons the heaviest, and mesons in the middle). While the mass classification is obsolete, these names of groups are still used based on the properties of the particles. The family of a particle determines what forces it interacts with and other properties such as its spin.

Family	Structure	Interactions	Spin	Examples
Leptons	Fundamental	Weak, electromagnetic	Half-integral	$\text{e}, \nu$
Mesons	Composite	Weak, electromagnetic, strong	Integral	$\pi, \text{K}$
Baryons	Composite	Weak, electromagnetic, strong	Half-integral	$\text{p}, \text{n}$

Antiparticles

Every particle has an antiparticle, whose properties like mass and lifetime are exactly the same but whose electric charge(and the sign of other certain properties) are the opposite. For instance, the antiparticle of the electron, $\text{e}^-$, is the positron, $\text{e}^+$. Similarly, the antiproton, $\overline{\text{p}}$, has charge $-e$ and can form a stable atom of anti-hydrogen with a positron, whose properties would be indistinguishable from regular hydrogen.

Annihilation

Although antiparticles of stable particles are themselves stable, when the antiparticle and particle meet, they annihilate and produce two or more photons. The two photons, due to the conservation of energy, have the rest energies of the particles annihilated.

$$\text{e}^-+\text{e}^+\rightarrow\gamma_1+\gamma_2~~~~~\left(E_{\gamma_1}=E_{\gamma_2}=0.511~\text{MeV}\right)\newline\text{p}+\overline{\text{p}}\rightarrow\gamma_1+\gamma_2~~~~~\left(E_{\gamma_1}=E_{\gamma_2}=938~\text{MeV}\right)$$

Everything we are made of is called matter and the other kinds of particles are called antimatter. However, it is not possible to tell using conventional techniques if something far away is matter or antimatter since light and anti-light are identical. We define particles to be everything ordinary matter is made (electrons, protons, and neutrons). For particles like neutrinos that do not compose matter, we use other properties likes its role in radioactive decays to determine the particle versus the antiparticle.

Leptons

The leptons only interact with the weak and electromagnetic interactions. There appears to be no composite structure of leptons; they seem to be truly fundamental. All known leptons have spin $\frac{1}{2}$. There are three pairs of leptons, each with one charged particle $\left(\text{e}^-,\mu^-,\tau^-\right)$ and a corresponding uncharged neutrino $\left(\nu_\text{e},\nu_\mu,\nu_\tau\right)$. Each lepton also has a corresponding antiparticle, shown in the table below. While the masses of neutrinos are known to not be zero, their exact masses are not yet known. The limits in the table are from attempts at direct measurements but are probably vast overestimates (they are likely to be less than $1~\text{eV}$).

Particle	Antiparticle	Charge $\left(e\right)$	Spin $\left(\hbar\right)$	Rest Energy $\left(\text{MeV}\right)$	Mean Life $\left(s\right)$	Decay Products
$\text{e}^-$	$\text{e}^+$	$-1$	$\frac{1}{2}$	$0.511$	$\infty$
$\nu_\text{e}$	$\overline{\nu_\text{e}}$	$0$	$\frac{1}{2}$	$\lt~2~\text{eV}$	$\infty$
$\mu^-$	$\mu^+$	$-1$	$\frac{1}{2}$	$105.7$	$2.2~\times~10^{-6}$	$\text{e}^-+\overline{\nu_\text{e}}+\nu_\mu$
$\nu_\mu$	$\overline{\nu_\mu}$	$0$	$\frac{1}{2}$	$\lt~0.19$	$\infty$
$\tau^-$	$\tau^+$	$-1$	$\frac{1}{2}$	$1776.9$	$2.9~\times~10^{-13}$	$\mu^-+\overline{\nu_\mu}+\nu_\tau$
$\nu_\tau$	$\overline{\nu_\tau}$	$0$	$\frac{1}{2}$	$\lt~18$	$\infty$

Mesons

The mesons interact with the strong force and have integral spins. Mesons can be produced in reactions with the strong interaction and typically decay to other mesons or leptons. An example of a meson reaction is

$$\text{p}+\text{n}\rightarrow\text{p}+\text{p}+\pi^-~~~~\text{or}~~~~~\text{p}+\text{n}\rightarrow\text{p}+\text{n}+\pi^0$$

then the pion can decay as such:

$$\pi^-\rightarrow\mu^-+\overline{\nu_\mu}\newline\pi^0\rightarrow\gamma+\gamma$$

Mesons are not observed in ordinary matter, so the distinction between particle and antiparticle is somewhat arbitrary. And while charged mesons have the antiparticle with the opposite charge, uncharged mesons are sometimes their own antiparticle but sometimes have distinct antiparticles.

The table below shows some (but not all) mesons.

Particle	Antiparticle	Charge $\left(e\right)$	Spin $\left(\hbar\right)$	Strangeness	Rest Energy $\left(\text{MeV}\right)$	Mean Life $\left(s\right)$	Decay Products
$\pi^+$	$\pi^-$	$+1$	$0$	$0$	$140$	$2.6~\times~10^{-8}$	$\mu^++\nu_\mu$
$\pi^0$	$\pi^0$	$0$	$0$	$0$	$135$	$8.5~\times~10^{-17}$	$\gamma+\gamma$
$\text{K}^+$	$\text{K}^-$	$+1$	$0$	$+1$	$494$	$1.2~\times~10^{-8}$	$\mu^++\nu_\mu$
$\text{K}^0$	$\overline{\text{K}}^0$	$0$	$0$	$+1$	$498$	$0.9~\times~10^{-10}$	$\pi^++\pi^-$
$\eta$	$\eta$	$0$	$0$	$0$	$548$	$5.1~\times~10^{-19}$	$\gamma+\gamma$
$\rho^+$	$\rho^-$	$+1$	$1$	$0$	$775$	$4.4~\times~10^{-24}$	$\pi^++\pi^0$
$\eta'$	$\eta'$	$0$	$0$	$0$	$958$	$3.4~\times~10^{-21}$	$\eta+\pi^++\pi^-$
$\text{D}^+$	$\text{D}^-$	$+1$	$0$	$0$	$1870$	$1.0~\times~10^{-12}$	$\text{K}^-+\pi^++\pi^+$
$\text{J}/\Psi$	$\text{J}/\Psi$	$0$	$1$	$0$	$3097$	$7.1~\times~10^{-21}$	$\text{e}^++\text{e}^-$
$\text{B}^+$	$\text{B}^-$	$+1$	$0$	$0$	$5279$	$1.6~\times~10^{-12}$	$\text{D}^-+\pi^++\pi^-$
$\Upsilon$	$\Upsilon$	$0$	$1$	$0$	$9460$	$1.2~\times~10^{-20}$	$\text{e}^++\text{e}^-$

Baryons

The baryons interact with the strong force and have half-integral spins. Baryons have distinct antiparticles (like the leptons) and are produced in reactions with nucleons via the strong force (like mesons). For example,

$$\text{p}+\text{p}\rightarrow\text{p}+\Lambda^0+\text{K}^+$$

which then decays to

$$\Lambda^0\rightarrow\text{p}+\pi^-$$

via the weak interaction.

The table below shows some (but not all) baryons.

Particle	Antiparticle	Charge $\left(e\right)$	Spin $\left(\hbar\right)$	Strangeness	Rest Energy $\left(\text{MeV}\right)$	Mean Life $\left(s\right)$	Decay Products
$\text{p}$	$\overline{\text{p}}$	$+1$	$\frac{1}{2}$	$0$	$938$	$\infty$
$\text{n}$	$\overline{\text{n}}$	$0$	$\frac{1}{2}$	$0$	$940$	$880$	$\text{p}+\text{e}^-+\overline{\nu_\text{e}}$
$\Lambda^0$	$\overline{\Lambda}^0$	$0$	$\frac{1}{2}$	$-1$	$1116$	$2.6~\times~10^{-10}$	$\text{p}+\pi^-$
$\Sigma^+$	$\overline{\Sigma}^+$	$+1$	$\frac{1}{2}$	$-1$	$1189$	$8.0~\times~10^{-11}$	$\text{p}+\pi^0$
$\Sigma^0$	$\overline{\Sigma}^0$	$0$	$\frac{1}{2}$	$-1$	$1193$	$7.4~\times~10^{-20}$	$\Lambda^0+\gamma$
$\Sigma^-$	$\overline{\Sigma}^-$	$-1$	$\frac{1}{2}$	$-1$	$1197$	$1.5~\times~10^{-10}$	$\text{n}+\pi^-$
$\Xi^0$	$\overline{\Xi}^0$	$0$	$\frac{1}{2}$	$-2$	$1315$	$2.9~\times~10^{-10}$	$\Lambda^0+\pi^0$
$\Xi^-$	$\overline{\Xi}^-$	$-1$	$\frac{1}{2}$	$-2$	$1322$	$1.6~\times~10^{-10}$	$\Lambda^0+\pi^-$
$\Delta^*$	$\overline{\Delta}^*$	$+2,+1,0,-1$	$\frac{3}{2}$	$0$	$1232$	$5.6~\times~10^{-24}$	$\text{p}+\pi$
$\Sigma^*$	$\overline{\Sigma}^*$	$+1,0,-1$	$\frac{3}{2}$	$-1$	$1385$	$1.8~\times~10^{-23}$	$\Lambda^0+\pi$
$\Xi^*$	$\overline{\Xi}^*$	$-1,0$	$\frac{3}{2}$	$-2$	$1533$	$7.2~\times~10^{-23}$	$\Xi+\pi$
$\Omega^-$	$\overline{\Omega}^-$	$-1$	$\frac{3}{2}$	$-3$	$1672$	$8.2~\times~10^{-11}$	$\Lambda^0+\text{K}^-$