Quark
A quark is a type of elementary particle and a fundamental constituent of matter, combining in groups to form composite particles known as hadrons, such as protons and neutrons, which are the building blocks of atomic nuclei.[1][2] Quarks were independently proposed in 1964 by physicists Murray Gell-Mann and George Zweig as part of a theoretical model to explain the structure of hadrons under the strong nuclear force, with Gell-Mann introducing the term "quark" inspired by a line from James Joyce's Finnegans Wake.[1][3] Experimental evidence for their existence came in 1968 from deep inelastic scattering experiments at the Stanford Linear Accelerator Center (SLAC), led by Jerome Friedman, Henry Kendall, and Richard Taylor, who observed point-like scattering consistent with substructure inside protons; this work earned them the 1990 Nobel Prize in Physics.[4][5] Quarks are fermions with spin ½ and carry fractional electric charges of either +2/3 or -1/3 times the elementary charge, distinguishing them from other particles like leptons.[3][2] They also possess a property called color charge—red, green, or blue—which mediates the strong force via gluons, ensuring quarks are perpetually confined within hadrons and cannot be observed in isolation, a phenomenon known as quark confinement.[2] There are six distinct types, or "flavors," of quarks: up (u), down (d), strange (s), charm (c), bottom (b), and top (t), each with an associated antiquark; the up and down quarks are the lightest and most common, forming ordinary matter, while the heavier flavors are short-lived and produced in high-energy conditions.[2] Baryons like protons (uud) and neutrons (udd) consist of three quarks, whereas mesons comprise one quark and one antiquark.[3][2] In the Standard Model of particle physics, quarks alongside leptons form all known matter, interacting through the electromagnetic, weak, and strong forces, with ongoing research at facilities like CERN probing their masses, mixing, and potential beyond-Standard-Model behaviors.[1][2]Classification
Flavors and Generations
In the Standard Model of particle physics, quarks are fundamental fermions classified into six distinct flavors: up (u), down (d), strange (s), charm (c), bottom (b), and top (t). These flavors represent different types of quarks, each characterized by specific quantum numbers that determine their interactions and roles in forming composite particles.[6] The six quark flavors are organized into three generations, reflecting a hierarchical structure in mass and properties. The first generation includes the lightest up and down quarks, which primarily constitute protons and neutrons in ordinary matter. The second generation comprises the strange and charm quarks, while the third generation consists of the heavier bottom and top quarks. This generational organization arises from the symmetries and mixing patterns observed in weak interactions, with each generation pairing an up-type quark (positive charge) and a down-type quark (negative charge).[6][7] Each quark flavor has a corresponding antiparticle, known as an antiquark, which possesses opposite quantum numbers, including electric charge, baryon number, and flavor-specific quantum numbers like strangeness or charm. Antiquarks combine with quarks to form mesons, while three quarks form baryons, contributing to the rich spectrum of hadrons. The necessity of six flavors stems from the need to explain the observed diversity of hadrons, as experimental discoveries of particles like the J/ψ (charm) and Υ (bottom) required additional flavors beyond the initial three to match the variety of meson and baryon states.[6] Quarks of all flavors carry one of three color charges (red, green, or blue), enabling the strong force to bind them into color-neutral hadrons. The following table summarizes the quark flavors, their electric charges, and approximate masses (in the \overline{\rm MS} scheme at a scale of about 2 GeV for light quarks (u, d, s), at the quark mass scale for c and b, and the pole mass for t) as of the 2025 Particle Data Group review:| Flavor | Symbol | Electric Charge | Approximate Mass (GeV/c^2) |
|---|---|---|---|
| up | u | +\frac{2}{3} | ~0.0022 |
| down | d | -\frac{1}{3} | ~0.0047 |
| strange | s | -\frac{1}{3} | ~0.094 |
| charm | c | +\frac{2}{3} | ~1.27 |
| bottom | b | -\frac{1}{3} | ~4.18 |
| top | t | +\frac{2}{3} | ~173 |
Valence Quarks and Exotic Hadrons
Valence quarks represent the minimal number of quarks and antiquarks required to form a hadron, carrying the primary quantum numbers that define the particle's identity. For instance, the proton consists of two up quarks and one down quark (uud), while the positively charged pion is composed of an up quark and an anti-down quark (u\bar{d}).[6] Hadrons are classified into two main categories based on their valence quark content: baryons and mesons. Baryons, such as protons and neutrons, are fermions made of three valence quarks (qqq), resulting in a baryon number of +1 and half-integer spin. Mesons, like pions and kaons, are bosons formed from a quark-antiquark pair (q\bar{q}), with a baryon number of 0 and integer spin.[6] Beyond these conventional structures, exotic hadrons challenge the standard quark model by incorporating more complex valence quark configurations. Tetraquarks consist of four quarks (e.g., qq\bar{q}\bar{q}), pentaquarks have five (qqq q\bar{q}), and hybrids involve quarks bound with gluonic excitations. A prominent tetraquark candidate is the Z(4430)^+, observed in the \psi(2S) \pi^+ channel and confirmed as a resonant state with a mass of approximately 4430 MeV.[9] LHCb experiments at the Large Hadron Collider have discovered several pentaquarks, such as the P_c(4312)^+, P_c(4440)^+, and P_c(4457)^+, each with valence content uudc\bar{c} and masses around 4312 MeV, 4440 MeV, and 4457 MeV, respectively, observed in the J/\psi p system from \Lambda_b^0 decays.[10] These discoveries, along with tetraquark states like the T_{cc}(3875)^+ (cc\bar{u}\bar{d}), highlight multiquark bindings near heavy-light meson thresholds, often interpreted as molecular states.[11] The formation of hadrons, including exotics, adheres to fundamental conservation laws that govern quark combinations. Baryon number (B) is conserved, with quarks assigned B = +1/3 and antiquarks B = -1/3, ensuring baryons have B = 1 and mesons B = 0; this extends to exotics like pentaquarks (B = 1) and tetraquarks (B = 0). Strangeness (S), defined as S = -1 for the strange quark and S = +1 for its antiquark, is conserved in strong interactions, influencing flavor content in particles like kaons (e.g., K^+ = u\bar{s}, S = +1) and hyperons (e.g., \Lambda = uds, S = -1).[6][12] These observations of valence quark structures and exotic states provide strong validation for the quark model, demonstrating its predictive power for both ordinary and unconventional hadrons while prompting refinements to account for multiquark dynamics and gluonic contributions.[6][13]Historical Development
Proposal of the Quark Model
In the early 1960s, the rapid discovery of numerous hadrons through particle accelerator experiments created a complex "zoo" of particles that challenged existing theoretical frameworks in hadron spectroscopy. To organize these particles into coherent patterns, physicists developed symmetry-based classification schemes, notably the "eightfold way" proposed by Murray Gell-Mann in 1961, which utilized the SU(3) flavor symmetry group to group baryons and mesons into multiplets such as octets and decuplets based on their quantum numbers like strangeness and isospin. This approach successfully predicted mass relations and decay patterns but left unexplained how the underlying structure could account for the observed symmetries without invoking composite constituents. In 1964, Gell-Mann extended the eightfold way by proposing a model where hadrons are composite structures built from three fundamental triplet representations of SU(3), which he termed "quarks"—up, down, and strange—with fractional electric charges of +2/3, -1/3, and -1/3, respectively, arranged to yield integer charges for hadrons.[3] Independently, George Zweig at CERN formulated a similar idea in his internal reports, referring to the constituents as "aces" and emphasizing their role in explaining the additive quantum numbers of hadrons under SU(3) flavor symmetry, though he viewed them more as physical entities than mathematical tools.[14] Baryons were described as three-quark states (qqq) in the symmetric decuplet or mixed-symmetry octet representations, while mesons were quark-antiquark pairs (q\bar{q}), providing a unified explanation for the hadron multiplets observed in spectroscopy.[3][14] A key early success of the quark model was its prediction of a strangeness -3 baryon in the decuplet, the Ω⁻ (sss configuration), with a mass around 1680 MeV, which completed the SU(3) multiplet and was discovered shortly thereafter in August 1964 at Brookhaven National Laboratory using a 5 GeV proton beam on a beryllium target, confirming the model's symmetry structure.[3] Despite this validation, the quark model faced significant initial resistance from the physics community, primarily due to the counterintuitive fractional charges, which violated the long-held assumption of integral charges for fundamental particles, and the absence of free quarks in experiments, implying an unexplained confinement mechanism that prevented their isolation.[15] Gell-Mann himself initially regarded quarks as a calculational device rather than real particles, reflecting the skepticism, while the lack of a dynamical theory for confinement delayed broader acceptance until later developments in quantum chromodynamics.[16][15]Key Experimental Discoveries
The first compelling experimental evidence for quarks as point-like constituents within protons and neutrons came from deep inelastic scattering experiments conducted at the Stanford Linear Accelerator Center (SLAC) starting in 1968. In these experiments, high-energy electrons were scattered off hydrogen and deuterium targets, revealing a scaling behavior in the structure functions that indicated the nucleons contained fractionally charged, spin-1/2 partons—later identified as quarks—interacting electromagnetically like point particles.[17][5] This work, led by Jerome Friedman, Henry Kendall, and Richard Taylor at SLAC and MIT, earned them the 1990 Nobel Prize in Physics. The existence of a fourth quark flavor, charm, was confirmed in 1974 through the independent discovery of the J/ψ meson—a bound state of a charm quark and its antiquark—by two teams using different accelerators. Samuel Ting's group at Brookhaven National Laboratory observed it in proton-beryllium collisions at the Alternating Gradient Synchrotron (AGS), while Burton Richter's team at SLAC detected it in electron-positron annihilation at the SPEAR storage ring.[18][19] The J/ψ has a mass of approximately 3.1 GeV/c² and a narrow width, consistent with quark model predictions for a new flavor. Richter and Ting shared the 1976 Nobel Prize for this breakthrough, which resolved anomalies in hadron spectroscopy and solidified the quark model. Subsequent discoveries established the remaining heavier quarks. In 1977, Leon Lederman's E288 experiment at Fermilab's Proton Center observed the Υ meson in proton-beryllium collisions, signaling the bottom (or beauty) quark with a mass around 9.5 GeV/c².[20] This finding, using the Tevatron's predecessor infrastructure, completed the second generation of quarks and motivated further searches.[21] The top quark, the heaviest known elementary particle, was finally discovered in 1995 by the CDF and D0 collaborations at Fermilab's Tevatron proton-antiproton collider. Analyzing data from collisions at √s = 1.8 TeV, both experiments observed top-antitop quark pair production decaying into W bosons and bottom quarks, with a top mass of about 176 GeV/c² and evidence exceeding five standard deviations.[22][23] This completed the three generations of quarks in the Standard Model, leveraging the Tevatron's high luminosity after nearly two decades of searches.[24] Key evidence for the three color charges of quarks emerged from electron-positron annihilation experiments measuring the ratio R of hadronic to muonic cross sections above quark production thresholds. At energies between 2 and 5 GeV, R approached 3.67, aligning with the expectation of three colors per quark flavor after accounting for QCD corrections, as measured at SLAC's SPEAR and later PEP rings.[25][26] These accelerators played pivotal roles: SPEAR enabled precise e⁺e⁻ studies revealing quarkonium states, PEP provided higher-energy data confirming color dynamics, and the Tevatron delivered the proton-proton collision environment needed for top quark production.[5]Etymology and Terminology
Origin of the Term "Quark"
The term "quark" for the fundamental particles was coined by physicist Murray Gell-Mann in 1964, drawing directly from a line in James Joyce's 1939 novel Finnegans Wake: "Three quarks for Muster Mark! / Sure he hasn't got much of a bark / And sure any he has it's all beside the mark."[27][28] Gell-Mann selected the word because Joyce's novel is renowned for its inventive, nonsensical vocabulary, which he found apt for naming hypothetical subatomic constituents whose existence was not yet experimentally confirmed.[29] In a 1978 letter to the editor of the Oxford English Dictionary, Gell-Mann explained that he initially pronounced "quark" to rhyme with "cork" (as /kwɔːrk/), evoking a pun on "three quarts for Mister Mark" in a pub setting, while acknowledging Joyce's original likely rhymed with "bark" (/kwɑːrk/).[28] Gell-Mann kept the name secret during the early development of his quark model, first publicly revealing it in a 1963 lecture while on leave at MIT, where he discussed organizing the proliferation of known particles.[27] This revelation preceded the formal publication of the quark model in 1964, in which Gell-Mann proposed that hadrons are composites of three such particles (or quark-antiquark pairs for mesons), aligning with the "three quarks" phrase from Joyce.[1] Independently, George Zweig proposed a similar model in 1964 at CERN, referring to the particles as "aces" to evoke combinations like deuces and treys in hadrons, but Gell-Mann's evocative term from literature quickly became the universal standard in the field.[16][1] The choice of "quark" not only captured the playful yet profound nature of the discovery but also endured despite Zweig's alternative, reflecting the influence of Gell-Mann's presentation and publication.[29]Related Naming Conventions
The up and down quarks were named by Murray Gell-Mann in 1964 to reflect their roles in an isospin doublet, analogous to the spin-up and spin-down states of particles under the strong nuclear force. The strange quark, also proposed by Gell-Mann in 1964, received its name due to the unexpectedly long lifetimes of particles containing it, such as kaons, which decayed via the weak force rather than the strong force. The charm quark was predicted in 1964 by Sheldon Glashow and James Bjorken and named for the symmetry it restored in the subnuclear world, evoking the Latin term carmen meaning enchantment or song. The bottom and top quarks were proposed by Makoto Kobayashi and Toshihide Maskawa in 1973 to explain CP violation in weak interactions, with names coined by Haim Harari in 1975 to maintain sequential alphabetical symbols (t and b) while pairing them as counterparts to up and down; prior to standardization, they were sometimes referred to as "truth" and "beauty" respectively.[30] The bottom quark's existence was confirmed in 1977 through the discovery of the Υ meson—a bottom-antibottom quark bound state—at Fermilab, observed as a resonance in the dimuon spectrum around 9.4 GeV.[31] The top quark, predicted to complete the third generation, was discovered in 1995 at Fermilab's Tevatron collider via top-antitop pair production decaying into W bosons and bottom quarks. In particle physics notation, a generic quark is denoted by q, while specific flavors use lowercase symbols: u for up, d for down, s for strange, c for charm, b for bottom, and t for top.[32] Antiquarks are represented with an overline, such as \bar{u}, \bar{d}, \bar{s}, \bar{c}, \bar{b}, and \bar{t}, following the convention that flavor quantum numbers for antiquarks have opposite signs to those of quarks (e.g., strangeness S = -1 for s and +1 for \bar{s}).[32] These labels are standardized by the Particle Data Group (PDG), which establishes conventions for quark content in hadron nomenclature to ensure consistency in reporting experimental results and theoretical models.[32]Intrinsic Properties
Electric Charge and Color Charge
Quarks possess fractional electric charges, measured in units of the elementary charge e, which is the charge of the electron. The up-type quarks (up, charm, and top) each carry a charge of +\frac{2}{3}e, while the down-type quarks (down, strange, and bottom) each carry -\frac{1}{3}e.[33] Antiquarks have opposite charges to their corresponding quarks, so up-type antiquarks have -\frac{2}{3}e and down-type antiquarks have +\frac{1}{3}e.[33] The electric charge of a hadron is the algebraic sum of the charges of its valence quarks. For example, the proton, composed of two up quarks and one down quark (uud), has a total charge of \frac{2}{3}e + \frac{2}{3}e - \frac{1}{3}e = +e.[33] Similarly, the neutron (udd) has \frac{2}{3}e - \frac{1}{3}e - \frac{1}{3}e = 0.[33] This additive property ensures that observed hadrons have integer charges, consistent with experimental observations.[33] In addition to electric charge, quarks carry color charge, a quantum number associated with the strong nuclear force as described by quantum chromodynamics (QCD). Color charge comes in three types, conventionally labeled red, green, and blue, analogous to the primary colors but serving as the basis for SU(3) gauge symmetry in QCD.[34] Each quark carries a single color charge, while antiquarks carry the corresponding anticolor (antired, antigreen, antiblue).[34] The mediators of the strong force, gluons, carry a combination of one color and one anticolor, forming an octet of eight possible states under the SU(3) color group.[34] Unlike photons in electromagnetism, which are neutral, gluons are colored and thus interact with each other, leading to the complex dynamics of the strong force.[34] Hadrons must be color-neutral, or "white" in the color analogy, to comply with the principle of color confinement, where isolated quarks cannot be observed. Baryons, such as protons and neutrons, achieve this through a combination of three quarks carrying different colors (one red, one green, one blue), forming a color singlet.[34] Mesons, composed of a quark-antiquark pair, are color-neutral when the quark's color matches the antiquark's anticolor, also resulting in a singlet state.[34] This color neutrality ensures that the strong force binds quarks into colorless composites at low energies.[34]Spin and Weak Isospin
Quarks are fundamental fermions with an intrinsic spin of \frac{1}{2} \hbar, which dictates their behavior under quantum statistics and their role in composite particles.[3] This spin angular momentum ensures that quarks obey the Pauli exclusion principle, preventing identical fermions from occupying the same quantum state, a key feature that underlies the stability and diversity of hadronic matter.[35] In hadrons, the spins of constituent quarks combine to yield the total spin of the bound state; for instance, the ground-state baryons like the proton and neutron, which have total spin \frac{1}{2}, result from the symmetric or antisymmetric coupling of the spins of three spin-\frac{1}{2} quarks under the constraints of color and flavor symmetries.[35] Within the framework of electroweak theory, quarks carry weak isospin, a quantum number associated with the SU(2)_L gauge symmetry that governs weak interactions. Left-handed quark fields transform as doublets under this SU(2)_L, such as the up-down doublet \begin{pmatrix} u \\ d \end{pmatrix}_L for the first generation, with weak isospin components I_3 = +\frac{1}{2} for the up-type quark and I_3 = -\frac{1}{2} for the down-type.[36] In contrast, right-handed quark fields are weak isospin singlets, carrying I = 0, which reflects the chiral nature of the weak force where only left-handed chirality participates in charged current interactions.[36] This assignment extends analogously to higher generations, with doublets like \begin{pmatrix} c \\ s \end{pmatrix}_L and \begin{pmatrix} t \\ b \end{pmatrix}_L.[36] The weak charged currents involve transitions between up-type and down-type quarks across generations, parameterized by the Cabibbo-Kobayashi-Maskawa (CKM) matrix, a unitary 3×3 mixing matrix that introduces flavor-changing dynamics and a single phase responsible for CP violation in the Standard Model.[37] Originally proposed to accommodate the observed pattern of weak decays beyond the first generation, the CKM matrix quantifies the misalignment between weak and mass eigenstates, ensuring unitarity while allowing for non-trivial mixing angles and the CP-violating phase.[37] The relativistic description of quarks incorporates their spin through Dirac spinors, four-component objects that satisfy the Dirac equation, i \hbar \frac{\partial \psi}{\partial t} = \left( c \vec{\alpha} \cdot \vec{p} + \beta m c^2 \right) \psi, where \psi represents the quark field, \vec{\alpha} and \beta are matrices encoding spin and relativistic effects, and the equation unifies quantum mechanics with special relativity for massive spin-\frac{1}{2} particles.[38] This formulation captures the intrinsic spin degrees of freedom essential for quark dynamics in quantum field theory.[36]Mass and Size Estimates
Quark masses in the Standard Model are fundamental parameters, but their values are not directly measurable due to confinement. Instead, they are inferred from lattice QCD simulations, perturbative QCD analyses of experimental data, and global fits to electroweak precision observables. In the modified minimal subtraction (MS-bar) scheme, the current quark masses at a renormalization scale of μ = 2 GeV are estimated as follows for the light quarks: up quark (u) 2.16 ± 0.07 MeV/c², down quark (d) 4.70 ± 0.07 MeV/c², and strange quark (s) 93.5 ± 0.8 MeV/c². For the heavier quarks, the charm quark (c) mass is 1.273 ± 0.005 GeV/c² in the MS-bar scheme at μ = m_c, the bottom quark (b) mass is 4.183 ± 0.007 GeV/c² at μ = m_b, and the top quark (t) pole mass is 172.6 ± 0.3 GeV/c². These values reflect the 2025 Particle Data Group (PDG) averages, incorporating updates from collider experiments and lattice calculations.[39]| Quark | Flavor | MS-bar Mass (MeV/c²) | Scale μ (GeV) | Notes |
|---|---|---|---|---|
| u | Up | 2.16 ± 0.07 | 2 | Light quark |
| d | Down | 4.70 ± 0.07 | 2 | Light quark |
| s | Strange | 93.5 ± 0.8 | 2 | Light quark |
| c | Charm | 1273 ± 5 | ≈1.27 | Heavy quark |
| b | Bottom | 4183 ± 7 | ≈4.18 | Heavy quark |
| t | Top | 172600 ± 300 | Pole mass | Unstable, from tt̄ production |