Quarks and gluons: a story of confinement

Quantum chromodynamics: the theory that binds quarks

The elementary constituents of matter

Quarks, leptons and bosons are the elementary particles that make up all known matter. These quantum entities are described by the Standard Model, experimentally validated by the discovery of quarks (1995), the tau neutrino (2000) and the Higgs boson (2012).

Protons, neutrons and hadrons: assemblies of quarks

Protons and neutrons, the constituents of atomic nuclei, are composite particles (non-elementary). They belong to the family of hadrons, alongside a hundred or so other ephemeral particles such as mesons (pion, kaon, eta, rho, etc.). All mesons are unstable, with lifetimes ranging from 10^-8 to 10^-23 second. Only the proton is stable, with an estimated lifetime of 10³⁶ years. Neutrons, stable inside a nucleus, decay in about 880.3 seconds (≈ 15 minutes) when free.

Quantum chromodynamics (QCD) and the missing mass

The theory describing the strong interaction, responsible for the cohesion of nuclei and the mass of quarks and gluons, is quantum chromodynamics (QCD), proposed in 1973 by David Gross, Frank Wilczek and Hugh David Politzer (Nobel Prize 2004).

The mass of a proton (2 up quarks + 1 down quark) or a neutron (1 up quark + 2 down quarks) does not correspond to the sum of the masses of its constituents:

• Proton mass: 1.673 × 10^-24 g (1.673 yg),
• Neutron mass: 1.675 × 10^-24 g,
• Mass of an up quark: ~0.002 to 0.005 yg,
• Mass of a down quark: ~0.004 to 0.008 yg.

N.B.:
Quarks represent only about 1% of the mass of nucleons. All the rest of the mass comes from the kinetic energy of the quarks and the binding energy of the gluons (according to the formula $E=mc^2$).

Energy and confinement: the origin of mass

The missing mass is explained by:

1. the kinetic energy of the moving quarks,
2. the binding energy of the strong interaction (via E=mc²), which largely dominates the mass of nucleons.

Quark confinement prevents their isolation: they are bound by gluons, particles that are electrically neutral but carry a color charge.

Quark confinement: why are they prisoners?

The paradox of confinement

Unlike the other fundamental forces (electromagnetic, weak, gravitational), the strong interaction increases with distance between quarks. This phenomenon, called asymptotic freedom, implies that:

• the closer the quarks are, the less they interact,
• the more one tries to separate them, the more intense the force becomes, like an elastic spring.

The sea of quarks and gluons

Inside hadrons, quark-antiquark pairs appear and disappear constantly, forming a dynamic sea. If a quark is ejected during a collision, the released energy immediately creates new particles (pions, kaons, etc.), never leaving an isolated quark.

Example: During an energetic collision, a quark torn from a proton generates a new hadron (such as a pion), but the initial quarks remain confined in the original nucleon.

Mechanism of confinement

QCD describes this mechanism by:

1. the creation of quark-antiquark pairs from the energy of the gluon (via E=mc²),
2. the annihilation of these pairs, returning energy to the gluons.

Thus, a proton or neutron is not a static set of 3 quarks, but a quantum soup where quarks, antiquarks and gluons interact continuously. The net balance remains constant, however: 2 up quarks + 1 down for a proton, and 2 down + 1 up for a neutron.

Why is confinement crucial?

This complex structure enables:

• the stability of atomic nuclei,
• the diversity of chemical elements, via optimal bonding configurations.

N.B.:
Confinement applies to particles that carry a color charge, which can never be isolated. They are only observed as white combinations with zero charge, such as hadrons, a principle that is at the origin of all visible matter.

Stability and instability of particles

Why do some live forever and others vanish in the blink of an eye?

In the world of particles, some are of unshakeable stability, like immutable rocks, while others vanish in an instant, as fleeting as lightning. For example, a proton can persist for billions upon billions of years, whereas a rho meson survives only for an infinitely brief time — so short that a light ray would travel less than the thickness of a hair during its entire lifetime. Where does this radical difference come from? It is explained by the fundamental laws of quantum physics and by the specific interactions that determine the behavior of each particle.

In brief: The longevity of a particle is mainly dictated by:

• Its mass and energy (the heavier it is, the more possible decay channels there are)
• The conservation laws it must obey
• The fundamental interactions that govern its behavior
• The presence of lighter particles into which it can convert

Stable particles: the pillars of matter

Only three particles of the Standard Model are considered absolutely stable (or at least, with a lifetime so long that it exceeds the age of the universe).

N.B.:
Theoretically, the electron could decay into a neutrino and a photon, but this has never been observed. Experimental limits (2025) place its lifetime well beyond 10²⁰ years.
Neutrinos are stable in the Standard Model, but theories beyond it (such as Grand Unification) predict an extremely slow decay.

Why are only 3 particles stable?

If the vast majority of elementary particles eventually decay, a few escape this rule for fundamental reasons of physics:

• Principle of charge conservation: The electron cannot simply vanish, since its electric charge of -1 must be conserved. Since no lighter particle with a non-zero charge exists to receive it, it remains unalterable.
• Stability linked to baryon number: As the lightest baryon, the proton cannot decay without violating current conservation laws. Only bold theories predict the existence of such proton decay, actively hunted by cutting-edge facilities such as Super-Kamiokande in Japan and DUNE in the United States.
• Energy lock and absence of channel: Lacking energetically viable options to transform into, the photon and neutrinos have no possible decay path.

Unstable particles: quantum fireworks

The majority of particles are ephemeral, with lifetimes ranging from the nanosecond to the second. Their instability comes from two factors:

1. Violation of symmetries: Certain interactions (such as the weak force) allow a particle to transform into a lighter one, while respecting conservation laws (energy, charge, etc.).
2. High mass: The heavier a particle is, the more "room" it has to decay into lighter particles (via E=mc²).

Why some particles are unstable: the case of the neutron

While it remains stable at the heart of atomic nuclei thanks to the cohesion of the strong interaction, a free neutron eventually decays in about a quarter of an hour under the action of the weak force: n → p⁺ + e⁻ + ν̅_e (neutron → proton + electron + electron antineutrino). This fundamental mechanism is directly at the origin of beta radioactivity, a phenomenon with major applications both in medicine (notably in PET imaging) and in archaeology (with the famous carbon-14 dating).

Exotic hadrons: a veritable zoo of ephemeral particles

Beyond the traditional protons and neutrons, large particle accelerators such as the CERN's LHC have revealed much more complex structures, called exotic hadrons:

• Tetraquarks: Composed of 2 quarks and 2 antiquarks (such as X(4140), identified in 2020), with a lightning-fast lifetime of the order of ~10^-23 s.
• Pentaquarks: Made of 4 quarks and 1 antiquark (such as P_c(4312), confirmed in 2019), with an ephemeral existence of about ~10^-20 s.
• Glueballs: Theoretical configurations made exclusively of gluons, actively hunted by physicists although their formal observation remains to be confirmed.

What explains their extreme instability?

These entities resemble highly excited states of matter. Overloaded with energy, they decay almost instantaneously into lighter, more stable hadrons (such as pions or kaons), thus obeying the universal tendency toward a state of minimum energy.

Proton decay: the Holy Grail of physics

Is the proton absolutely eternal? While the Standard Model asserts so, bold theories such as Grand Unification or supersymmetry suggest that it could eventually decay into a neutral pion and a positron according to the reaction: p⁺ → π⁰ + e⁺. Its hypothetical lifetime exceeds comprehension: it is estimated at more than 10³⁶ years, or about 10²⁶ times the current age of the universe!

How do physicists hunt for this phenomenon?

Giant observatories buried underground, such as Super-Kamiokande and its successor Hyper-Kamiokande (designed to offer tenfold sensitivity), keep watch over millions of tons of pure water to catch this improbable decay. To date, no observation has validated this hypothesis, but these colossal research efforts continue to push back the frontiers of knowledge.

What is the major issue?

Detecting proton decay would be a scientific shockwave comparable to the discovery of the Higgs boson, validating the idea that the fundamental forces — strong nuclear, weak and electromagnetism — were one at the very beginning of the universe.

Instability and technology: unsuspected applications

Far from being limited to theoretical physics, particle instability irrigates many technological and scientific fields of everyday life:

• Nuclear medicine and imaging: Short-lived radioactive isotopes, such as technetium-99m (whose lifetime is about 6 hours), are invaluable for performing precise scintigraphy.
• Archaeology and dating: The measured decay of carbon-14 (with a half-life of 5,730 years) makes it possible to date organic artifacts nearly 50,000 years old.
• Energy production: The intrinsic instability of uranium-235 (with a half-life of 700 million years) is the energy source of civilian nuclear reactors.
• Astrophysics and cosmology: The balance of neutron instability dictated primordial nucleosynthesis, enabling the emergence of the very first atomic nuclei in the aftermath of the Big Bang.

N.B.:
If the neutron decays rapidly when free, its stability is miraculously ensured within nuclei thanks to the strong interaction. It is precisely this phenomenon that allows the existence of neutron stars: in the aftermath of a supernova collapse, these particles, compressed under colossal pressures, form a stable quantum fluid capable of crossing the eons!

Frontiers of knowledge: what if stability were only an illusion?

At the dawn of this decade, several areas of shadow continue to stimulate fundamental research:

• The enigmatic nature of dark matter: If it turns out to be corpuscular (carried by hypothetical candidates such as WIMPs), the longevity of these particles would justify its domination of the universe without dissipating.
• Evaporation of quantum black holes: Predicted by Stephen Hawking through a specific radiation, this disintegration of black holes remains to this day a purely theoretical object of study, for lack of experimental validation.
• The asymmetry of antimatter: How to explain that our universe is exclusively shaped of matter rather than a parity equilibrium with antimatter? A tiny nuance of stability between particles and antiparticles could well hold the answer.

To watch closely

The giant collider project, the Future Circular Collider (FCC), whose commissioning at CERN is envisaged for the 2040s, aims to reach energies of the order of 100 TeV (eclipsing the 13 TeV of the LHC). Enough to hunt highly unstable entities and probe physics beyond the Standard Model.

In conclusion, the balance between stability and disintegration is not the fruit of chance, but the expression of fundamental laws harmonizing energy, symmetries and interactions. Penetrating these intimate workings amounts to deciphering the greatest secrets of the universe, from the infinitely small to the infinitely large.