Hadrons, Baryons, Mesons, and Antimatter

Hadrons are particles made of quarks and held together by the strong interaction; they are divided into baryons (three quarks, such as the proton uud and neutron udd) and mesons (a quark and an antiquark, such as the pion π⁺ = u d̄), and every particle has an antiparticle with the same mass and opposite charge and other quantum numbers. In brief: baryons have baryon number +1 (antibaryons −1), and mesons have baryon number 0. When a particle meets its antiparticle they annihilate, converting their mass into energy (for example e⁺ + e⁻ → 2γ, each photon 0.511 MeV). Antimatter was predicted by Dirac in 1928, and the positron was found in 1932. Why the universe contains almost only matter is an unsolved problem.

Protons, neutrons and the many short-lived particles seen in accelerators are hadrons. This guide explains how quarks combine to form baryons and mesons, why protons and neutrons are composite particles, what antimatter is and how it is produced and used in PET scanners, compares baryons and mesons in a table, works through numerical examples with quark content and corrects common mistakes.

What are hadrons?

Hadrons (from the Greek for “strong”) are all particles that feel the strong interaction. Hundreds of them have been found, but all are combinations of the six quarks and antiquarks held together by gluons, with the requirement that the total color charge is neutral (“white”). The combinations that occur: three quarks of different colors (red + green + blue) form a baryon, and a quark with an antiquark of the opposite color (color + anticolor) forms a meson. The quantum numbers of a hadron are those of its quarks added: electric charge, baryon number (each quark has B = +1/3), strangeness (the strange quark has S = −1), charm, bottomness and topness. Almost all the hadrons are unstable and decay (by strong, electromagnetic or weak interactions) within times ranging from 10⁻²³ s to 10⁻⁸ s. Only the proton (possibly stable, with a lifetime longer than 10³⁴ years) and the neutron (stable inside nuclei, but in free state it decays with a mean life of about 880 s) are long-lived.

What are baryons?

Baryons consist of three quarks (qqq). The proton (uud) has charge +1 and mass 938.3 MeV/c²; the neutron (udd) has charge 0 and mass 939.6 MeV/c². Heavier baryons contain strange or heavier quarks: Λ⁰ (uds, 1,116 MeV/c²), Σ⁺ (uus), Ξ⁻ (dss) and Ω⁻ (sss, 1,672 MeV/c²), whose existence and mass were predicted by Gell-Mann in 1962 and confirmed in 1964. The total baryon number is conserved in all known reactions: this is why the proton is so stable (it is the lightest baryon, so it has nothing to decay into). The proton and the neutron are composite particles with a radius of about 0.84 fm. Their mass is mostly due to the energy of the gluon field and the kinetic energy of the quarks.

What are mesons?

Mesons consist of a quark and an antiquark (q q̄). They have baryon number 0 and integer spin, so they are bosons. The lightest mesons are the pions: π⁺ (u d̄, charge +1, 139.6 MeV/c²), π⁻ (d ū) and π⁰ (a mixture of u ū and d d̄, 135.0 MeV/c²), and the kaons: K⁺ (u s̄), K⁻ (s ū), K⁰ (d s̄), with masses of about 494 and 498 MeV/c². Mesons are unstable: the charged pion lives 26 ns and decays by the weak interaction (π⁺ → μ⁺ + ν_μ), and the neutral pion lives 8.5 × 10⁻¹⁷ s (π⁰ → 2γ). Heavier mesons contain charm or bottom quarks (J/ψ = c c̄, discovered in 1974; Υ = b b̄). Pions are the particles exchanged between nucleons in the (effective) description of nuclear forces by Yukawa (1935), and are produced copiously in cosmic-ray collisions and accelerators.

What is antimatter?

For every particle there is an antiparticle with the same mass and spin, and opposite electric charge and other charge-like quantum numbers (baryon number, lepton number, strangeness): the positron (e⁺, charge +1), the antiproton (p̄ = ū ū d̄, charge −1), the antineutron, antineutrinos, and antiquarks. Some neutral particles (photon, π⁰) are their own antiparticles. When a particle and its antiparticle meet, they annihilate, and their total mass-energy is converted into other particles, typically photons; the reverse process, pair production, creates a particle-antiparticle pair from energy (a photon of energy of at least 2mc² near a nucleus). Paul Dirac predicted the positron in 1928 from relativistic quantum mechanics, and Carl Anderson discovered it in cosmic rays in a cloud chamber in 1932. The antiproton was produced at Berkeley in 1955, and atoms of antihydrogen at CERN in 1995 and trapped in 2010. Positrons from the beta-plus decay of radioisotopes are used in PET scans. Antimatter is not “anti-gravity”: experiments (ALPHA-g at CERN, 2023) showed that antihydrogen atoms fall downward like ordinary matter. The universe appears to contain almost no antimatter (the baryon asymmetry), a puzzle that requires processes that violate the symmetry between matter and antimatter (CP violation), observed in kaon and B-meson decays but not enough to explain the observed asymmetry.

Baryons and mesons compared

Worked example: quark content and annihilation

1. Charge from quarks. π⁺ = u d̄: +2/3 + (+1/3) = +1 ✓. K⁺ = u s̄: +2/3 + 1/3 = +1. Antiproton ū ū d̄: −2/3 − 2/3 + 1/3 = −1 ✓. Σ⁺ = uus: 2/3 + 2/3 − 1/3 = +1.
2. Baryon number. Proton: 3 × (1/3) = 1; π⁺: 1/3 − 1/3 = 0; antiproton: −1. In the reaction p + p → p + p + π⁰, the baryon number is 2 → 2 ✓.
3. Strangeness. Ω⁻ = sss: S = −3, charge 3 × (−1/3) = −1 ✓. The Λ (uds) has S = −1 and charge 2/3 − 1/3 − 1/3 = 0.
4. Annihilation of an electron and a positron at rest: e⁻ + e⁺ → γ + γ. The total energy 2 × 0.511 = 1.022 MeV is shared by two photons of 0.511 MeV, emitted in opposite directions (momentum conservation). Their wavelength is 1,240 ÷ 511,000 = 2.4 × 10⁻³ nm. A single photon cannot be produced, because it would violate momentum conservation.
5. Proton-antiproton annihilation. The rest energy of the pair is 2 × 938.3 MeV = 1,876.5 MeV, enough to produce several pions (each 139.6 MeV for charged pions) with kinetic energy, typically about 5 pions on average.
6. Energy from 1 gram of antimatter. When 1 g of antimatter annihilates with 1 g of matter, the energy released is E = 2 × 10⁻³ × (3.00 × 10⁸)² = 1.8 × 10¹⁴ J (about 43 kilotons of TNT). The total amount of antimatter ever produced in laboratories is a few nanograms.

How were they discovered?

Hideki Yukawa predicted mesons in 1935; the pion was discovered in cosmic rays by Cecil Powell, César Lattes and Giuseppe Occhialini in 1947. Kaons and “strange” particles were discovered in cosmic rays in 1947 to 1950. Murray Gell-Mann and Yuval Ne’eman classified the hadrons by the “Eightfold Way” in 1961, which led to the quark model (1964). The J/ψ was discovered simultaneously at Brookhaven (Ting) and SLAC (Richter) in the “November Revolution” of 1974, and the bottom quark in the Υ in 1977. In 2015, the LHCb experiment reported pentaquarks, hadrons of four quarks and an antiquark.

Which mistakes are common?

Mistake 1: Thinking that antimatter is science fiction or has negative mass

Antiparticles have positive mass and are produced routinely in accelerators and by radioactive decay.

Mistake 2: Confusing baryons with leptons

Baryons are made of three quarks and feel the strong force. Leptons (electrons, neutrinos) are elementary.

Mistake 3: Saying that the neutral pion has no antiparticle

It is its own antiparticle. A neutral particle may or may not be its own antiparticle (the neutron is not).

Mistake 4: Treating the proton as a point particle

It has a size (about 0.84 fm) and a structure of quarks and gluons.