23.2 Quarks

Quarks are the fundamental constituents of protons, neutrons, and other hadrons. They carry fractional electric charges and interact through the strong nuclear force, making them central to how matter holds together at the smallest scales. This section covers quark properties, how quarks combine into larger particles, and how they fit into the Standard Model.

Quarks and Particle Physics

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Properties and role of quarks

Quarks are elementary particles, meaning they have no known substructure. They're classified as fermions because they have an intrinsic spin of $\frac{1}{2}$. Unlike more familiar particles, quarks carry fractional electric charges: either $+\frac{2}{3}e$ or $-\frac{1}{3}e$, where $e$ is the elementary charge.

Quarks come in six flavors: up, down, charm, strange, top, and bottom. Each flavor has a corresponding antiquark with opposite charge and quantum numbers.

Beyond electric charge, quarks also carry color charge (red, green, or blue). Color charge is the source of the strong nuclear force, analogous to how electric charge is the source of the electromagnetic force. Gluons mediate this force between quarks.

Quarks combine to form composite particles called hadrons:

• Baryons are made of three quarks. A proton is $uud$ (two up quarks and one down quark, giving a total charge of $+\frac{2}{3} + \frac{2}{3} - \frac{1}{3} = +1$). A neutron is $udd$ (total charge of $0$).
• Mesons are made of one quark and one antiquark. Pions ($\pi$) and kaons ($K$) are common examples.

Every hadron must be color-neutral (sometimes called "colorless" or "white"). Baryons achieve this by combining one red, one green, and one blue quark. Mesons achieve it by pairing a color with its corresponding anticolor.

Two important features of the strong force between quarks:

• Color confinement: quarks cannot be isolated individually. If you try to pull two quarks apart, the energy in the gluon field grows until it creates a new quark-antiquark pair instead. This is why free quarks are never observed.
• Asymptotic freedom: at very short distances (or equivalently, very high energies), the strong force between quarks actually weakens. This allows quarks inside a hadron to behave almost as free particles when probed at high energies.

Hadrons vs. leptons

These are the two broad families of matter particles, and the key distinction is straightforward: hadrons are made of quarks, while leptons are elementary with no internal structure.

• Hadrons (protons, neutrons, pions, kaons) participate in the strong nuclear force because they contain quarks carrying color charge.
• Leptons (electrons, muons, taus, and their associated neutrinos) do not carry color charge and are unaffected by the strong force. They are considered point-like particles with no known substructure.

Both families participate in the weak nuclear force. Charged members of both families (like protons and electrons) also interact electromagnetically. The defining difference is that only hadrons feel the strong force.

Matter and antimatter composition

Every quark flavor has an antimatter counterpart with opposite electric charge, opposite color charge, and opposite quantum numbers.

• A proton ($uud$) has an antiparticle called the antiproton ($\bar{u}\bar{u}\bar{d}$), with a total charge of $-1$.
• A neutron ($udd$) has an antiparticle called the antineutron ($\bar{u}\bar{d}\bar{d}$), which is also electrically neutral but differs in its quark content.

When a particle meets its corresponding antiparticle, they annihilate: their combined mass converts entirely into energy, typically producing high-energy photons. The energy released follows Einstein's relation:

$E = mc^2$

where $m$ is the total rest mass of the particle-antiparticle pair. This process also works in reverse: sufficient energy can produce a particle-antiparticle pair (pair production).

Quarks in the Standard Model

The Standard Model organizes all known fundamental particles and describes three of the four fundamental forces (it does not include gravity).

Quarks are arranged in three generations of increasing mass:

Ordinary matter is built from first-generation quarks only. Second- and third-generation quarks are unstable and decay rapidly into lighter quarks through the weak force. They're produced in high-energy collisions and cosmic ray interactions.

The Standard Model also includes:

• Leptons, similarly arranged in three generations (electron, muon, tau, plus their neutrinos)
• Gauge bosons that mediate forces: gluons (strong), photons (electromagnetic), and $W^{\pm}$/$Z^0$ bosons (weak)
• The Higgs boson, responsible for mass generation

The theory describing quark interactions specifically is called quantum chromodynamics (QCD). QCD explains how gluons bind quarks together inside hadrons and accounts for both color confinement and asymptotic freedom.

Higgs boson and quark mass

A natural question arises: why do quarks (and other fundamental particles) have mass at all, and why do different flavors have such wildly different masses?

The answer involves the Higgs field, a quantum field that permeates all of space. Particles acquire mass through their interaction with this field. The stronger a particle couples to the Higgs field, the more massive it is. This explains why the top quark (~173 GeV/$c^2$) is far heavier than the up quark (~2 MeV/$c^2$): the top quark couples much more strongly to the Higgs field.

The Higgs boson is the quantum excitation of the Higgs field. It was predicted by the Standard Model decades before its experimental confirmation at CERN's Large Hadron Collider in 2012. Its discovery was a major validation of the Standard Model's explanation for how particles acquire mass.

That said, the Higgs mechanism doesn't explain why the coupling strengths differ between flavors. This remains an open question and a motivation for research into physics beyond the Standard Model.

Quark theory and high-energy physics

Murray Gell-Mann (and independently George Zweig) proposed the quark model in 1964 to explain the patterns observed among the many hadrons discovered in the mid-20th century. At the time, quarks were a theoretical organizing tool. Experimental confirmation came through deep inelastic scattering experiments at SLAC in the late 1960s, which revealed that protons had point-like internal constituents.

These internal constituents were initially called partons by Richard Feynman. They were later identified as quarks and gluons, unifying Feynman's parton model with Gell-Mann's quark model.

Under extreme conditions of temperature and energy density, such as those present microseconds after the Big Bang or recreated in heavy-ion collisions at facilities like CERN and Brookhaven, quarks and gluons can become deconfined. This state of matter is called quark-gluon plasma (QGP), where quarks move freely rather than being bound inside hadrons. Studying QGP helps physicists understand the early universe and the behavior of the strong force at extreme scales.