Quarks Explained: The Building Blocks Inside Protons and Neutrons

The Discovery of Quarks

By the early 1960s, physicists had discovered dozens of seemingly fundamental particles in cosmic ray experiments and accelerator collisions, a confusing zoo of hadrons including protons, neutrons, pions, kaons, sigma particles, and many others. In 1964, Murray Gell-Mann and, independently, George Zweig proposed that all these hadrons were not fundamental at all but were built from smaller, more basic constituents. Gell-Mann called them "quarks," borrowing the word from a line in James Joyce's Finnegans Wake ("Three quarks for Muster Mark"). Zweig called them "aces," but Gell-Mann's name stuck.

The original quark model proposed three flavors: up, down, and strange. The up and down quarks explained protons and neutrons, while the strange quark accounted for a class of unusual particles that seemed to be produced easily in high-energy collisions but decayed surprisingly slowly. This pattern suggested they carried a conserved quantum number, which Gell-Mann had earlier called "strangeness." The quark model elegantly organized all known hadrons into families based on their quark content and correctly predicted the existence of new particles, most dramatically the omega-minus baryon, discovered in 1964 at Brookhaven National Laboratory, exactly as predicted.

Experimental confirmation that quarks were real physical objects, not just mathematical constructs, came from deep inelastic scattering experiments at the Stanford Linear Accelerator Center (SLAC) between 1967 and 1973. Physicists fired high-energy electrons at protons and observed that the electrons occasionally bounced off at large angles, just as Rutherford's alpha particles had bounced off atomic nuclei in 1911. This indicated that protons contained small, hard, point-like objects. The scattering patterns matched predictions for spin-1/2, fractionally charged quarks, confirming the quark model. Jerome Friedman, Henry Kendall, and Richard Taylor received the 1990 Nobel Prize for these experiments, and Gell-Mann had already won in 1969 for his theoretical work on quarks and hadron classification.

The Six Quark Flavors

The up quark has an electric charge of +2/3 and a mass of approximately 2.2 MeV/c2, making it the lightest quark. The down quark has a charge of -1/3 and a mass of about 4.7 MeV/c2. These two quarks build all stable matter: a proton is two up quarks and one down quark (uud), giving it a charge of +1, while a neutron is one up quark and two down quarks (udd), giving it a charge of 0. The slight mass difference between the up and down quarks has profound consequences. Because the down quark is heavier, a free neutron (udd) is slightly heavier than a proton (uud) and can decay into a proton through beta decay, with a half-life of about 10.2 minutes. This asymmetry determines which elements are stable and ultimately which atoms exist in the universe.

The strange quark, with charge -1/3 and a mass of about 96 MeV/c2, is the third lightest quark and was the first to be inferred from the properties of unusual particles discovered in cosmic ray experiments in the 1940s and 1950s. Particles containing strange quarks, such as the kaon (a meson made of an up or down quark paired with a strange antiquark) and the lambda baryon (containing up, down, and strange quarks), are produced in high-energy collisions through the strong force but decay through the weaker weak force, giving them relatively long lifetimes of roughly 10^-8 to 10^-10 seconds, an eternity by particle physics standards.

The charm quark, with charge +2/3 and a mass of about 1,270 MeV/c2, was predicted in 1970 by Sheldon Glashow, John Iliopoulos, and Luciano Maiani to explain the absence of certain rare decay processes. Its existence was dramatically confirmed in November 1974 when two teams, one at Brookhaven led by Samuel Ting and one at SLAC led by Burton Richter, independently discovered the J/psi meson, a bound state of a charm quark and a charm antiquark with a mass of 3,097 MeV/c2. The discovery, announced within days of each other, was so revolutionary that it is called the "November Revolution" in particle physics. Ting and Richter shared the 1976 Nobel Prize.

The bottom quark (sometimes called the beauty quark), with charge -1/3 and a mass of about 4,180 MeV/c2, was discovered in 1977 at Fermilab when Leon Lederman's team found the upsilon meson, a bound state of a bottom quark and bottom antiquark with a mass of about 9,460 MeV/c2. The bottom quark is important in studies of CP violation, the tiny difference between the behavior of matter and antimatter. The BaBar experiment at SLAC and the Belle experiment at KEK in Japan measured CP violation in B meson decays (mesons containing bottom quarks) with high precision, confirming the Cabibbo-Kobayashi-Maskawa (CKM) theory of quark mixing and earning Makoto Kobayashi and Toshihide Maskawa the 2008 Nobel Prize.

The top quark is the heaviest known fundamental particle, with a mass of approximately 173,000 MeV/c2, roughly the mass of an entire gold atom concentrated in a single point-like particle. It was discovered in 1995 at Fermilab's Tevatron collider by the CDF and D0 experiments, completing the six-quark pattern predicted by the Standard Model. The top quark is unique among quarks because it decays before it has time to form a hadron. Its lifetime of roughly 5 x 10^-25 seconds is about 20 times shorter than the timescale for the strong force to bind it with other quarks. This means the top quark decays as a free quark, transferring its spin and momentum directly to its decay products, allowing physicists to study quark properties more directly than with any other quark flavor.

Color Charge and the Strong Force

Every quark carries one of three "color charges": red, green, or blue. These names are purely metaphorical and have nothing to do with visible light, but the analogy works well: just as mixing red, green, and blue light produces white, combining quarks of all three colors produces a "colorless" (color-neutral) hadron. Antiquarks carry anti-colors (anti-red, anti-green, anti-blue), and a quark of one color paired with an antiquark of the corresponding anti-color also produces a color-neutral state. All observable hadrons are color-neutral, which is why quarks always appear in groups of three (baryons, one of each color) or quark-antiquark pairs (mesons, one color and its anti-color).

The strong force between quarks is carried by eight types of gluons, each carrying a combination of color and anti-color charge. Because gluons themselves carry color charge, they interact with each other as well as with quarks. This self-interaction makes the strong force radically different from electromagnetism, where photons are electrically neutral and do not interact with each other directly. Gluon self-interaction is responsible for two extraordinary properties of the strong force that have no parallel in electromagnetism.

The first property is confinement. As you try to pull two quarks apart, the gluon field between them does not spread out and weaken like an electromagnetic field. Instead, it contracts into a narrow tube, called a flux tube or color string, that stores energy roughly proportional to its length, about 1 GeV per femtometer. Pull the quarks far enough apart and the energy stored in the tube exceeds the mass-energy needed to create a new quark-antiquark pair. At that point, the string "breaks," creating new quarks that pair with the originals, producing two hadrons instead of two free quarks. This is why no isolated quark has ever been detected, and it is why smashing hadrons together at high energy produces jets of new hadrons rather than free quarks.

The second property is asymptotic freedom. At very short distances (or equivalently, very high energies), the strong force becomes progressively weaker, and quarks behave almost as free particles. This is the opposite of what intuition based on gravity or electromagnetism would suggest. Asymptotic freedom was discovered theoretically in 1973 by David Gross, Frank Wilczek, and David Politzer, earning them the 2004 Nobel Prize. It explains why the deep inelastic scattering experiments at SLAC were able to see quarks as nearly free objects inside protons: the high-energy electrons probed the proton at such short distances that the quarks were only weakly bound. It also makes high-energy QCD calculations possible using perturbation theory, the same mathematical approach that makes QED calculations so successful.

Where Proton Mass Really Comes From

A proton weighs about 938 MeV/c2. Its three valence quarks (two up quarks at about 2.2 MeV each and one down quark at about 4.7 MeV) contribute a total of only about 9.1 MeV, less than 1% of the proton's mass. The remaining 99% comes from three sources: the kinetic energy of the quarks moving around inside the proton at nearly the speed of light (contributing roughly 32% of the mass), the energy of the gluon field binding the quarks (roughly 36%), and the energy associated with the quantum fluctuations of quark-antiquark pairs and gluons constantly appearing and disappearing inside the proton (roughly 23%). A small additional contribution comes from the electromagnetic energy of the quarks' electric charges and the quark mass terms themselves.

This means that the mass of everything around you, your body, the chair you sit in, the Earth beneath you, comes overwhelmingly from the energy of the strong force, not from the Higgs mechanism. The Higgs field gives quarks and electrons their individual masses, but those masses are tiny compared to the mass generated by QCD dynamics inside hadrons. The equation E=mc2 works both ways: mass can be converted into energy (as in nuclear reactions), but energy also manifests as mass (as in the proton). The proton is, in essence, a knot of energy held together by the strong force, and that energy is what gives matter its heft.

Calculating the proton mass from first principles using QCD is one of the great achievements of computational physics. Lattice QCD, a technique that simulates the strong force on a discrete grid of spacetime points using supercomputers, has reproduced the proton mass to within about 2% of its experimental value. These calculations confirm quantitatively that QCD dynamics, not quark masses, generate most of the proton's mass. This result was first achieved with reasonable precision around 2008 and has been refined steadily since then, providing one of the strongest validations of QCD as the correct theory of the strong force.

Exotic Hadrons: Beyond Baryons and Mesons

For decades, all known hadrons fit neatly into two categories: baryons (three quarks) and mesons (quark-antiquark pairs). QCD, however, allows more exotic combinations as long as they are color-neutral. In 2003, the Belle experiment in Japan discovered the X(3872), a particle whose properties did not match any conventional quark-antiquark meson, suggesting it might be a tetraquark (two quarks and two antiquarks) or a loosely bound "molecular" state of two mesons. Since then, a flood of exotic hadrons has been discovered, particularly at the LHCb experiment at CERN.

In 2015, LHCb announced the discovery of two pentaquark states, particles containing four quarks and one antiquark, found in the decay of a bottom baryon. These pentaquarks had been sought since the 1960s. In 2021, LHCb discovered a doubly-charmed tetraquark, called Tcc+, containing two charm quarks, an up antiquark, and a down antiquark. This particle is particularly interesting because it is the first exotic hadron clearly containing two heavy quarks, providing a new test of how the strong force operates.

The internal structure of exotic hadrons is actively debated. Some may be compact tetraquarks or pentaquarks, with all the quarks bound tightly together by gluons in a small volume. Others may be "molecular" states, loosely bound pairs of ordinary hadrons orbiting each other at relatively large distances, analogous to how protons and neutrons bind to form atomic nuclei. Distinguishing between these possibilities requires detailed measurements of each state's mass, width, quantum numbers, and production patterns, a task that will keep experimenters busy for years.

Quark Mixing and the CKM Matrix

When the weak force acts on a quark, it can change the quark's flavor. For example, beta decay occurs when a down quark inside a neutron transforms into an up quark by emitting a W- boson, which then decays into an electron and an antineutrino. However, the weak force does not act on the quarks' mass states directly. Instead, it acts on quantum mechanical superpositions of quark flavors, a phenomenon described by the Cabibbo-Kobayashi-Maskawa (CKM) matrix.

The CKM matrix is a 3x3 matrix of complex numbers that describes the probability amplitudes for each up-type quark (up, charm, top) to transform into each down-type quark (down, strange, bottom) through the weak force. The matrix element Vud, approximately 0.974, gives the amplitude for an up quark to become a down quark, the dominant transition in beta decay. Vus, approximately 0.225, gives the amplitude for an up quark to become a strange quark, a rarer but measurable process. Vub, approximately 0.004, describes the very rare transition from up to bottom. The off-diagonal elements explain why strange and bottom quarks can be produced in some weak decays even though they are much heavier than up and down quarks.

The CKM matrix contains a single complex phase that is responsible for CP violation in quark interactions, the tiny asymmetry between the behavior of quarks and antiquarks under the combined operation of charge conjugation and parity reflection. This CP violation is real and has been measured precisely in kaon and B meson decays, confirming the CKM framework and earning Kobayashi and Maskawa the 2008 Nobel Prize (shared with Yoichiro Nambu for related work on symmetry breaking). However, the CP violation from the CKM matrix is far too small to explain why the universe contains so much more matter than antimatter, implying that additional sources of CP violation must exist.