---
title: Basic Concepts and Particle Classification
module: Foundations
moduleNumber: 1
lessonNumber: 2
order: 102
summary: >
  Every particle has an antiparticle of equal mass and opposite charge, a
  consequence of the Dirac equation confirmed by the positron. Feynman diagrams
  track interactions in spacetime; the material particles sort into leptons and
  the composite hadrons built from quarks, with baryons carrying three quarks
  and mesons a quark-antiquark pair.
topics: [Foundations]
draft: false
sources:
  - book: Tipler & Llewellyn
    ref: "Ch. 12 — Particle Physics; §12-1 Basic Concepts"
---

Ordinary matter reduces to three atoms of construction: leptons, quarks, and the
bosons that carry forces between them. Everything from a grain of sand to the
debris of a gold-on-gold collision at 99.99% of the speed of light is assembled
from a short list of particles with no measurable internal structure. This lesson
fixes the vocabulary needed to name and sort them: antiparticles, the Feynman
diagrams that depict their interactions, and the division of matter particles
into leptons and the composite hadrons.

## Antiparticles

The [Dirac equation](/particle-physics/relativistic-wave-equations/dirac-equation-spinors),
the relativistic wave equation for spin-$\tfrac{1}{2}$ particles, admits both
positive- and negative-energy solutions. The relativistic energy relation gives
two roots,

$$
E = \pm\sqrt{(pc)^2 + (mc^2)^2},
$$

and the mathematics of the Dirac equation forbids discarding the negative root
by fiat. Dirac's first interpretation filled every negative-energy state with
electrons (an infinite "sea"), so that only a **hole** in the sea (behaving as a
positive charge with positive energy) would be observable. Quantum
electrodynamics later removed the need for the sea: the negative-energy solutions
re-express as positive-energy solutions of a distinct particle, the
**antiparticle**.[^tl-anti]

> **Definition (Antiparticle).** For every particle QED requires a partner of
> identical mass and spin but opposite electric charge, baryon number, and
> strangeness. A particle with a nonzero value of any of these is distinct from
> its antiparticle; a particle for which all of them vanish (the photon) may be
> its own antiparticle.

Carl Anderson identified the first antiparticle, the **positron** $e^+$, in 1932
in cosmic-ray tracks: same mass and spin as the electron, charge $+e$, magnetic
moment parallel (not antiparallel) to its spin. The **antiproton** $\bar{p}$ was
produced at the Bevatron in 1955, and the **antineutron** $\bar{n}$ two years
after. Producing a proton-antiproton pair demands at least the rest energy of
both, $2m_p c^2 \approx 1877$ MeV, unavailable outside cosmic rays until GeV-scale
accelerators arrived.

Two processes convert between matter and radiation:

- **Pair production.** A photon of sufficient energy, in the field of a nucleus,
  converts to a particle-antiparticle pair: $\gamma \to e^+ e^-$. The threshold
  is $2m_e c^2 = 1.022$ MeV for an electron pair.
- **Pair annihilation.** A particle meets its antiparticle and both vanish into
  photons: $e^+ e^- \to \gamma\gamma$. Momentum conservation forbids a single
  final photon when the pair is at rest, so at least two are emitted.

$$
% caption: A photon materializes as an electron-positron pair (left); the pair
% recombines into two photons (right). Charge, energy, and momentum balance at
% every vertex.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  % --- pair production ---
  \draw[acc, thick, dashed] (0,1.6) -- (1.6,1.6) node[midway, above] {photon};
  \draw[->, acc, thick] (1.6,1.6) -- (3.0,2.5) node[right] {$e^+$};
  \draw[->, acc, thick] (1.6,1.6) -- (3.0,0.7) node[right] {$e$};
  \fill[acc] (1.6,1.6) circle (1.6pt);
  \node[align=center, font=\scriptsize] at (1.5,0.0) {pair production};
  % --- annihilation ---
  \begin{scope}[xshift=6.2cm]
    \draw[->, acc, thick] (0,2.5) -- (1.4,1.6) node[pos=0.1, left] {$e^+$};
    \draw[->, acc, thick] (0,0.7) -- (1.4,1.6) node[pos=0.1, left] {$e$};
    \fill[acc] (1.4,1.6) circle (1.6pt);
    \draw[acc, thick, dashed] (1.4,1.6) -- (3.0,2.3) node[right] {photon};
    \draw[acc, thick, dashed] (1.4,1.6) -- (3.0,0.9) node[right] {photon};
    \node[align=center, font=\scriptsize] at (1.5,0.0) {annihilation};
  \end{scope}
\end{tikzpicture}
$$

Although the positron is stable, it survives only briefly in a universe full of
electrons. A positron slowing to rest binds an electron into **positronium**
before annihilating, and the spin state fixes the photon count: the
antiparallel-spin singlet ($^1S$) annihilates to two photons, while the
parallel-spin triplet ($^3S$) annihilates to three, since a system of definite
parity and charge conjugation restricts the allowed final states.

The labelling of electrons as "particles" and positrons as "antiparticles" is a
convention reflecting the composition of our corner of the universe, not a
statement about which is more fundamental. Had matter here been built from
negative protons and positive electrons, those would carry the "particle" label.
Why the observable universe holds matter and almost no antimatter, despite the
symmetry of the relativistic wave equation, is the
[matter-antimatter asymmetry](/particle-physics/beyond-standard-model/matter-antimatter-open-questions)
problem, taken up later.

> **Example (Proton-antiproton annihilation).** A proton and antiproton at rest
> annihilate to two photons. With the pair at rest, momentum conservation forces
> the photons to carry equal and opposite momenta, hence equal energies. The
> total rest energy $2m_p c^2$ splits evenly:
>
> $$
> E_\gamma = m_p c^2 = 938 \text{ MeV}, \qquad
> \lambda = \frac{hc}{E_\gamma} = \frac{1240 \text{ eV·nm}}{9.38 \times 10^8 \text{ eV}}
> = 1.32 \text{ fm}.
> $$

## Feynman diagrams

Feynman diagrams are spacetime diagrams ($ct$ versus $x$) that depict
interactions among quarks, leptons, and force carriers. In the convention used
here time runs upward, though the axes are usually left undrawn. The rules
enforce conservation of energy and momentum at each **vertex**; the lines are
symbolic and do not trace real trajectories.

- **Fermion lines** carry an arrow. A line whose arrow points backward in time is
  read as the corresponding antiparticle moving forward in time, which lets the
  overbars be dropped from the diagram.
- **Force-carrier lines** (photon, gluon, $W$, $Z$) join vertices. A carrier that
  is its own antiparticle, such as the photon, carries no arrow.
- **Virtual particles** are lines that both begin and end inside the diagram.
  They cannot be observed and need not carry the physical mass of the
  corresponding real particle, since only energy and momentum are conserved at
  vertices, not mass. Only lines entering or leaving the diagram are real,
  observable particles.

The **primitive vertex** of QED is a single charged particle entering, emitting
or absorbing a photon, and leaving. Every electromagnetic process is built from
copies of it.

$$
% caption: The QED primitive vertex (left): a charged fermion emits or absorbs a
% photon. Coulomb repulsion of two electrons (right) is a single virtual-photon
% exchange between two such vertices.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  % --- primitive vertex ---
  \draw[->, acc, thick] (0,0) -- (1.0,1.1);
  \draw[->, acc, thick] (1.0,1.1) -- (2.0,2.2) node[right] {$e$};
  \node[left, acc] at (0,0) {$e$};
  \draw[acc, thick, dashed] (1.0,1.1) -- (2.3,0.9) node[right] {photon};
  \fill[acc] (1.0,1.1) circle (1.6pt);
  \node[font=\scriptsize] at (1.0,-0.5) {primitive vertex};
  % --- Coulomb repulsion ---
  \begin{scope}[xshift=5.6cm]
    \draw[->, acc, thick] (0,0) -- (0.9,0.9);
    \draw[->, acc, thick] (0.9,0.9) -- (1.8,1.8) node[above left] {$e$};
    \node[below, acc] at (0,0) {$e$};
    \draw[->, acc, thick] (3.0,0) -- (2.1,0.9);
    \draw[->, acc, thick] (2.1,0.9) -- (1.2,1.8) node[above right] {$e$};
    \node[below, acc] at (3.0,0) {$e$};
    \draw[acc, thick, dashed] (0.9,0.9) -- (2.1,0.9) node[midway, above] {photon};
    \fill[acc] (0.9,0.9) circle (1.6pt);
    \fill[acc] (2.1,0.9) circle (1.6pt);
    \node[font=\scriptsize] at (1.5,-0.5) {Coulomb repulsion};
  \end{scope}
\end{tikzpicture}
$$

Coulomb repulsion of two electrons is two electrons entering, exchanging a
virtual photon, and leaving. The same skeleton with attractive charges gives
Coulomb attraction. Because a virtual photon mediates the force in each case, the
electromagnetic interaction is said to be mediated by photons. There are many
diagrams for any given reaction; higher-order diagrams with more vertices
contribute progressively less, so the simplest usually dominates.

## Leptons

Research since the discovery of the electron has revealed 62 fundamental
particles and antiparticles, fundamental in the sense of having no internal
structure resolvable with present technology. They split into two families of
spin-$\tfrac{1}{2}$ fermions (leptons and quarks) plus the force carriers.

> **Definition (Lepton).** A structureless spin-$\tfrac{1}{2}$ fermion that does
> not carry color charge and so takes no part in the strong interaction. The
> leptons come in three generations, each a charged lepton paired with its
> neutrino.

| Generation | Charged lepton | $Q\,(e)$ | Mass $(\text{MeV}/c^2)$ | Neutrino | Neutrino mass |
| --- | --- | --- | --- | --- | --- |
| 1st | electron $e$ | $-1$ | $0.511$ | $\nu_e$ | $< 2.2$ eV$/c^2$ |
| 2nd | muon $\mu$ | $-1$ | $105.7$ | $\nu_\mu$ | $< 3.5$ eV$/c^2$ |
| 3rd | tau $\tau$ | $-1$ | $1784$ | $\nu_\tau$ | $< 8.4$ eV$/c^2$ |

The electron is the only stable charged lepton; the muon and tau decay. Each
charged lepton has a distinct antiparticle, and each neutrino a corresponding
antineutrino (whether a neutrino is its own antiparticle, a **Majorana**
particle, is unsettled). The three **flavors** are named electron, muon, and tau.
Leptons form no lepton-lepton bound states.

## Quarks and hadrons

There are six quarks, likewise in three generations, all spin-$\tfrac{1}{2}$
fermions with fractional electric charge and distinct antiparticles.

> **Definition (Quark).** A structureless spin-$\tfrac{1}{2}$ fermion carrying
> fractional electric charge ($+\tfrac{2}{3}e$ for up-type, $-\tfrac{1}{3}e$ for
> down-type), baryon number $B = \tfrac{1}{3}$, and one unit of color charge.
> Quarks bind into composite particles but are not observed in isolation.

| Generation | Up-type | $Q\,(e)$ | Down-type | $Q\,(e)$ |
| --- | --- | --- | --- | --- |
| 1st | up $u$ | $+\tfrac{2}{3}$ | down $d$ | $-\tfrac{1}{3}$ |
| 2nd | charm $c$ | $+\tfrac{2}{3}$ | strange $s$ | $-\tfrac{1}{3}$ |
| 3rd | top $t$ | $+\tfrac{2}{3}$ | bottom $b$ | $-\tfrac{1}{3}$ |

Each quark also carries **color charge**, taking one of three values labelled
red, blue, and green; antiquarks carry anticolor. So there are three up quarks
$u_r$, $u_b$, $u_g$, distinguished only by color. The names have nothing to do
with visual color; they label a property analogous to electric charge, and color
charge is conserved. Color is developed in the
[Standard Model](/particle-physics/electroweak-higgs/standard-model) lesson.

The bound states of quarks are the **hadrons** (Greek _hadros_, robust), and they
split into two subgroups by quark count.

> **Definition (Baryon and meson).** A **baryon** is a three-quark bound state
> with half-integer spin and baryon number $B = 1$; the proton ($uud$) and
> neutron ($udd$) are the lightest. A **meson** is a quark-antiquark bound state
> with integer spin and $B = 0$; the pions and kaons are examples.

$$
% caption: Matter particles sort into leptons and the composite hadrons; hadrons
% split by quark count into three-quark baryons and quark-antiquark mesons.
\begin{tikzpicture}[>=stealth, font=\footnotesize,
  box/.style={draw, minimum width=24mm, minimum height=10mm, align=center, font=\scriptsize},
  root/.style={draw, thick, minimum width=30mm, minimum height=10mm, align=center}]
  \definecolor{acc}{HTML}{4A6FA5}
  \node[root, draw=acc, text=acc] (m) at (0,0) {matter particles};
  \node[box] (lep) at (-3.4,-1.8) {leptons\\(no color)};
  \node[box] (had) at (3.4,-1.8) {hadrons\\(quark bound states)};
  \node[box] (bar) at (1.4,-3.6) {baryons\\three quarks};
  \node[box] (mes) at (5.4,-3.6) {mesons\\quark plus antiquark};
  \draw[->, acc, thick] (m) -- (lep);
  \draw[->, acc, thick] (m) -- (had);
  \draw[->, acc, thick] (had) -- (bar);
  \draw[->, acc, thick] (had) -- (mes);
  \node[font=\scriptsize, align=center] at (-3.4,-3.4) {electron, muon, tau\\and neutrinos};
\end{tikzpicture}
$$

Six quarks bind in many ways into more than 200 hadrons, which account for the
bulk of the visible mass of the universe. The proton and neutron are the only
hadrons stable (or nearly so) in isolation; all others decay, and every baryon
eventually decays to a proton. Single free quarks have not been observed and, for
reasons in the Standard Model lesson, are not expected to be.

The hadrons stable against strong-interaction decay (lifetimes well above
$10^{-23}$ s) span a wide range of mass and lifetime. Those decaying strongly
are far shorter-lived; electromagnetic decays run near $10^{-18}$ s, weak decays
near $10^{-10}$ s.

| Hadron | Class | Quarks | Mass $(\text{MeV}/c^2)$ | Spin | $Q\,(e)$ | Lifetime (s) |
| --- | --- | --- | --- | --- | --- | --- |
| $p$ | baryon | $uud$ | $938.3$ | $\tfrac{1}{2}$ | $+1$ | $> 10^{32}$ y |
| $n$ | baryon | $udd$ | $939.6$ | $\tfrac{1}{2}$ | $0$ | $930$ |
| $\Lambda^0$ | baryon | $uds$ | $1116$ | $\tfrac{1}{2}$ | $0$ | $2.5 \times 10^{-10}$ |
| $\Omega^-$ | baryon | $sss$ | $1672$ | $\tfrac{3}{2}$ | $-1$ | $1.3 \times 10^{-10}$ |
| $\pi^\pm$ | meson | $u\bar{d}$ | $139.6$ | $0$ | $\pm 1$ | $2.6 \times 10^{-8}$ |
| $\pi^0$ | meson | $u\bar{u}$ | $135$ | $0$ | $0$ | $0.8 \times 10^{-16}$ |
| $K^\pm$ | meson | $u\bar{s}$ | $493.7$ | $0$ | $\pm 1$ | $1.2 \times 10^{-8}$ |

Before the quark model this catalogue of more than 200 hadrons, growing with each
new accelerator, was an uninterpreted "particle zoo." The regularities in their
masses, charges, and quantum numbers are what the quark model of the
[Standard Model](/particle-physics/electroweak-higgs/standard-model) lesson
explains, much as the periodic table organized the chemical elements.

$$
% caption: Idealized bubble-chamber view: a charged kaon enters and decays; a
% neutral pion from the decay converts in a lead sheet to two photons, each
% producing an electron-positron pair whose curvature reveals its charge.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  \draw[black, thick] (-3,-2.6) rectangle (3,2.6);
  % incoming kaon
  \draw[acc, thick] (-1.2,-2.6) .. controls (-1.0,-1.2) and (-0.6,-0.4) .. (0,0.2);
  \node[acc, left, font=\scriptsize] at (-1.3,-2.3) {$K$};
  \fill[black] (0,0.2) circle (1.6pt);
  % charged pion off to the right
  \draw[acc, thick] (0,0.2) .. controls (1.2,0.5) and (2.0,0.9) .. (2.8,1.0);
  \node[acc, font=\scriptsize] at (2.5,1.3) {pion};
  % neutral pion (dashed, no track) then two photons
  \draw[black, dashed] (0,0.2) -- (0.4,1.6);
  \node[black, font=\scriptsize] at (0.05,1.0) {pi zero};
  \draw[black, dashed] (0.4,1.6) -- (-1.0,2.3);
  \draw[black, dashed] (0.4,1.6) -- (1.6,2.3);
  % lead sheet
  \draw[black, thick] (-2.6,2.0) -- (2.6,2.0);
  \node[black, font=\scriptsize, anchor=west] at (-2.55,2.2) {lead};
  % pair from left photon
  \draw[acc, thick] (-1.0,2.0) .. controls (-1.6,1.4) .. (-1.4,0.6);
  \draw[acc, thick] (-1.0,2.0) .. controls (-0.4,1.4) .. (-0.6,0.6);
  % pair from right photon
  \draw[acc, thick] (1.6,2.0) .. controls (1.0,1.4) .. (1.2,0.6);
  \draw[acc, thick] (1.6,2.0) .. controls (2.2,1.4) .. (2.0,0.6);
\end{tikzpicture}
$$

The distinction between particles and antiparticles is a bookkeeping device
grounded in the conserved quantum numbers introduced in the
[conservation laws](/particle-physics/symmetries/conservation-laws-symmetries)
lesson. What holds a nucleus together, and what turns one quark flavor into
another in a decay, is the subject of the
[fundamental interactions](/particle-physics/foundations/fundamental-interactions-force-carriers).

[^tl-anti]: Tipler & Llewellyn, §12-1 — Antiparticles: the Dirac hole picture and its replacement by the QED antiparticle, and the discoveries of the positron, antiproton, and antineutron.