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Hadron
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| Standard Model of particle physics |
|---|
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In particle physics, a hadron is a composite subatomic particle made of two or more quarks held together by the strong nuclear force. Pronounced /ˈhædrɒn/ ⓘ, the name is derived from Ancient Greek ἁδρός (hadrós) 'stout, thick'. They are analogous to molecules, which are held together by the electric force. Most of the mass of ordinary matter comes from two hadrons: the proton and the neutron, while most of the mass of the protons and neutrons is in turn due to the binding energy of their constituent quarks, due to the strong force.
Hadrons are categorized into two broad families: baryons, made of an odd number of quarks (usually three), and mesons, made of an even number of quarks (usually two: one quark and one antiquark).[1] Protons and neutrons (which make the majority of the mass of an atom) are examples of baryons; pions are an example of a meson. A tetraquark state (an exotic meson), named the Z(4430)−, was discovered in 2007 by the Belle Collaboration[2] and confirmed as a resonance in 2014 by the LHCb collaboration.[3] Two pentaquark states (exotic baryons), named P+
c(4380) and P+
c(4450), were discovered in 2015 by the LHCb collaboration.[4] There are several other "Exotic" hadron candidates and other colour-singlet quark combinations that may also exist.
Almost all "free" hadrons and antihadrons (meaning, in isolation and not bound within an atomic nucleus) are believed to be unstable and eventually decay into other particles. The only known possible exception is free protons, which appear to be stable, or at least, take immense amounts of time to decay (order of 1034+ years). By way of comparison, free neutrons are the longest-lived unstable particle, and decay with a half-life of about 611 seconds, and have a mean lifetime of 879 seconds,[a][5] see free neutron decay.
Hadron physics is studied by colliding hadrons, e.g. protons, with each other or the nuclei of dense, heavy elements, such as lead (Pb) or gold (Au), and detecting the debris in the produced particle showers. A similar process occurs in the natural environment, in the extreme upper-atmosphere, where muons and mesons such as pions are produced by the collisions of cosmic rays with rarefied gas particles in the outer atmosphere.[6]
Terminology and etymology
[edit]The term "hadron" is a new Greek word introduced by L. B. Okun in a plenary talk at the 1962 International Conference on High Energy Physics at CERN.[7] He opened his talk with the definition of a new category term:
Notwithstanding the fact that this report deals with weak interactions, we shall frequently have to speak of strongly interacting particles. These particles pose not only numerous scientific problems, but also a terminological problem. The point is that "strongly interacting particles" is a very clumsy term which does not yield itself to the formation of an adjective. For this reason, to take but one instance, decays into strongly interacting particles are called "non-leptonic". This definition is not exact because "non-leptonic" may also signify photonic. In this report I shall call strongly interacting particles "hadrons", and the corresponding decays "hadronic" (the Greek ἁδρός signifies "large", "massive", in contrast to λεπτός which means "small", "light"). I hope that this terminology will prove to be convenient. — L. B. Okun (1962)[7]
Properties
[edit]
According to the quark model,[8] the properties of hadrons are primarily determined by their so-called valence quarks. For example, a proton is composed of two up quarks (each with electric charge ++2⁄3, for a total of +4⁄3 together) and one down quark (with electric charge −+1⁄3). Adding these together yields the proton charge of +1. Although quarks also carry color charge, hadrons must have zero total color charge because of a phenomenon called color confinement. That is, hadrons must be "colorless" or "white". The simplest ways for this to occur are with a quark of one color and an antiquark of the corresponding anticolor, or three quarks of different colors. Hadrons with the first arrangement are a type of meson, and those with the second arrangement are a type of baryon.
Massless virtual gluons compose the overwhelming majority of particles inside hadrons, as well as the major constituents of its mass (with the exception of the heavy charm and bottom quarks; the top quark vanishes before it has time to bind into a hadron). The strength of the strong-force gluons which bind the quarks together has sufficient energy (E) to have resonances composed of massive (m) quarks (E ≥ mc2). One outcome is that short-lived pairs of virtual quarks and antiquarks are continually forming and vanishing again inside a hadron. Because the virtual quarks are not stable wave packets (quanta), but an irregular and transient phenomenon, it is not meaningful to ask which quark is real and which virtual; only the small excess is apparent from the outside in the form of a hadron. Therefore, when a hadron or anti-hadron is stated to consist of (typically) two or three quarks, this technically refers to the constant excess of quarks versus antiquarks.
Like all subatomic particles, hadrons are assigned quantum numbers corresponding to the representations of the Poincaré group: JPC (m), where J is the spin quantum number, P the intrinsic parity (or P-parity), C the charge conjugation (or C-parity), and m is the particle's mass. Note that the mass of a hadron has very little to do with the mass of its valence quarks; rather, due to mass–energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction. Hadrons may also carry flavor quantum numbers such as isospin (G-parity), and strangeness. All quarks carry an additive, conserved quantum number called a baryon number (B), which is ++1⁄3 for quarks and −+1⁄3 for antiquarks. This means that baryons (composite particles made of three, five or a larger odd number of quarks) have B = 1 whereas mesons have B = 0.
Hadrons have excited states known as resonances. Each ground state hadron may have several excited states; several hundred different resonances have been observed in experiments. Resonances decay extremely quickly (within about 10−24 seconds) via the strong nuclear force.
In other phases of matter the hadrons may disappear. For example, at very high temperature and high pressure, unless there are sufficiently many flavors of quarks, the theory of quantum chromodynamics (QCD) predicts that quarks and gluons will no longer be confined within hadrons, "because the strength of the strong interaction diminishes with energy". This property, which is known as asymptotic freedom, has been experimentally confirmed in the energy range between 1 GeV (gigaelectronvolt) and 1 TeV (teraelectronvolt).[9] All free hadrons except (possibly) the proton and antiproton are unstable.
Baryons
[edit]Baryons are hadrons containing an odd number of valence quarks (at least 3).[1] Most well-known baryons such as the proton and neutron have three valence quarks, but pentaquarks with five quarks—three quarks of different colors, and also one extra quark-antiquark pair—have also been proven to exist. Because baryons have an odd number of quarks, they are also all fermions, i.e., they have half-integer spin. As quarks possess baryon number B = 1⁄3, baryons have baryon number B = 1. Pentaquarks also have B = 1, since the extra quark's and antiquark's baryon numbers cancel.
Each type of baryon has a corresponding antiparticle (antibaryon) in which quarks are replaced by their corresponding antiquarks. For example, just as a proton is made of two up quarks and one down quark, its corresponding antiparticle, the antiproton, is made of two up antiquarks and one down antiquark.
As of August 2015, there are two known pentaquarks, P+
c(4380) and P+
c(4450), both discovered in 2015 by the LHCb collaboration.[4]
Mesons
[edit]Mesons are hadrons containing an even number of valence quarks (at least two).[1] Most well known mesons are composed of a quark-antiquark pair, but possible tetraquarks (four quarks) and hexaquarks (six quarks, comprising either a dibaryon or three quark-antiquark pairs) may have been discovered and are being investigated to confirm their nature.[10] Several other hypothetical types of exotic meson may exist which do not fall within the quark model of classification. These include glueballs and hybrid mesons (mesons bound by excited gluons).
Because mesons have an even number of quarks, they are also all bosons, with integer spin, i.e., 0, +1, or −1. They have baryon number B = 1/3 − 1/3 = 0 . Examples of mesons commonly produced in particle physics experiments include pions and kaons. Pions also play a role in holding atomic nuclei together via the residual strong force.
See also
[edit]- Exotic hadron
- Hadron therapy, a.k.a. particle therapy
- Hadronization, the formation of hadrons out of quarks and gluons
- Large Hadron Collider (LHC)
- List of particles
- List of baryons
- List of mesons
- Standard Model
- Subatomic particle
Footnotes
[edit]- ^ The proton and neutrons' respective antiparticles are expected to follow the same pattern, but they are difficult to capture and study, because they immediately annihilate on contact with ordinary matter.
References
[edit]- ^ a b c Gell-Mann, M. (1964). "A schematic model of baryons and mesons". Physics Letters. 8 (3): 214–215. Bibcode:1964PhL.....8..214G. doi:10.1016/S0031-9163(64)92001-3.
- ^
Choi, S.-K.; et al. (Belle Collaboration) (2008). "Observation of a resonance-like structure in the π±
Ψ′ mass distribution in exclusive B→Kπ±
Ψ′ decays". Physical Review Letters. 100 (14) 142001. arXiv:0708.1790. Bibcode:2008PhRvL.100n2001C. doi:10.1103/PhysRevLett.100.142001. PMID 18518023. S2CID 119138620. - ^ Aaij, R.; et al. (LHCb collaboration) (2014). "Observation of the Resonant Character of the Z(4430)− State". Physical Review Letters. 112 (22) 222002. arXiv:1404.1903. Bibcode:2014PhRvL.112v2002A. doi:10.1103/PhysRevLett.112.222002. PMID 24949760. S2CID 904429.
- ^ a b
Aaij, R.; et al. (LHCb collaboration) (2015). "Observation of J/ψp resonances consistent with pentaquark states in Λ0
b → J/ψK−p decays". Physical Review Letters. 115 (7) 072001. arXiv:1507.03414. Bibcode:2015PhRvL.115g2001A. doi:10.1103/PhysRevLett.115.072001. PMID 26317714. S2CID 119204136. - ^ Zyla, P. A. (2020). "n MEAN LIFE". PDG Live: 2020 Review of Particle Physics. Particle Data Group. Retrieved 3 February 2022.
- ^ Martin, B. R. (2017). Particle physics (Fourth ed.). Chichester, West Sussex, UK. ISBN 978-1-118-91190-7.
{{cite book}}: CS1 maint: location missing publisher (link) - ^ a b Okun, L. B. (1962). "The theory of weak interaction". Proceedings of 1962 International Conference on High-Energy Physics at CERN. International Conference on High-Energy Physics (plenary talk). CERN, Geneva, CH. p. 845. Bibcode:1962hep..conf..845O.
- ^ Amsler, C.; et al. (Particle Data Group) (2008). "Quark Model" (PDF). Physics Letters B. Review of Particle Physics. 667 (1): 1–6. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594.
- ^ Bethke, S. (2007). "Experimental tests of asymptotic freedom". Progress in Particle and Nuclear Physics. 58 (2): 351–386. arXiv:hep-ex/0606035. Bibcode:2007PrPNP..58..351B. doi:10.1016/j.ppnp.2006.06.001. S2CID 14915298.
- ^ Mann, Adam (2013-06-17). "Mysterious subatomic particle may represent exotic new form of matter". Science. Wired. Retrieved 2021-08-27. — News story about Z(3900) particle discovery.
External links
[edit]
The dictionary definition of hadron at Wiktionary
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Hadron
View on Grokipediafrom Grokipedia
Introduction
Definition
A hadron is a composite subatomic particle made up of two or more quarks bound together by the strong nuclear force, distinguishing it from leptons, which do not experience this interaction.[12] These particles are the building blocks of atomic nuclei and play a central role in the strong interaction described by quantum chromodynamics (QCD). Hadrons are characterized by their participation in the strong force, mediated by gluons, and they exhibit a rich spectrum of masses and quantum numbers arising from the confinement of quarks within them.[6] Hadrons are broadly classified into two families: baryons and mesons. Baryons consist of three quarks (or three antiquarks), obeying the Pauli exclusion principle due to their fermionic nature, with protons (two up quarks and one down quark) and neutrons (one up quark and two down quarks) serving as the most stable and familiar examples.[13] Mesons, in contrast, are composed of one quark and one antiquark, making them bosons capable of occupying the same quantum state, as exemplified by pions, which mediate the nuclear force between protons and neutrons.[14][15] Beyond these conventional hadrons, exotic states such as tetraquarks (four quarks) and pentaquarks (four quarks and one antiquark) have been observed, challenging earlier models but still fitting within the broader definition as color-neutral bound states under QCD. All hadrons are color singlets, meaning their constituent quarks' color charges neutralize to confine the strong force internally, preventing free quarks from existing in isolation.[6]Classification
Hadrons are classified primarily according to their valence quark content and the resulting quantum numbers, such as spin, parity, and flavor, within the framework of the quark model. The two fundamental categories are mesons and baryons, distinguished by their composition and statistics: mesons consist of a quark-antiquark pair (q\bar{q}), making them bosons with integer spin, while baryons comprise three quarks (qqq), rendering them fermions with half-integer spin. This dichotomy arises from the color confinement in quantum chromodynamics (QCD), where quarks combine to form color-neutral states.[3][16] Further subclassification relies on flavor symmetry groups, such as SU(3) for light quarks (up, down, strange) or SU(4) including charm, which organize hadrons into multiplets based on isospin (I), hypercharge (Y), and strangeness (S). For instance, baryons form octets and decuplets in the SU(3) flavor scheme, exemplified by the nucleon (I=1/2, S=0) and the Delta resonances (I=3/2, S=0), while mesons form nonets with pseudoscalar (J^{PC}=0^{-+}) and vector (J^{PC}=1^{--}) states, such as the pion triplet (I=1, S=0) and the eta singlet (I=0, S=0). Heavy-flavor hadrons, involving charm or bottom quarks, follow similar patterns but with reduced symmetry due to mass differences.[6][17] The Particle Data Group (PDG) maintains a standardized naming convention for hadrons, driven by their minimal quark content, quantum numbers, and spectroscopic assignments, ensuring consistent identification across experiments. For baryons, names like "proton" (uud) or "Lambda" (uds) reflect historical and flavor-based designations, while mesons use symbols like π for pions or K for kaons, with superscripts denoting charge and subscripts for excited states. This scheme extends to heavier quarks, such as D mesons (c\bar{u}, etc.) and bottom baryons like Λ_b (udb). Exotic hadrons, such as tetraquarks or pentaquarks, challenge the conventional q\bar{q} or qqq paradigm but are classified separately when their quark content deviates.[18][19]Historical Development
Early Discoveries
The proton, the first known hadron, was identified in 1919 by Ernest Rutherford during experiments at the University of Manchester, where alpha particles from radioactive sources bombarded nitrogen gas, resulting in the ejection of hydrogen nuclei—later named protons in 1920 for their positive charge.[20] This discovery established the proton as a fundamental constituent of atomic nuclei, with a mass approximately 1836 times that of the electron.[21] The neutron, a neutral hadron with nearly the same mass as the proton, was discovered in 1932 by James Chadwick at the Cavendish Laboratory in Cambridge. Chadwick interpreted penetrating neutral radiation produced by bombarding beryllium with alpha particles as arising from neutrons, resolving discrepancies in nuclear binding energies and enabling models of stable nuclei composed of protons and neutrons.[22] This finding, confirmed through scattering experiments, earned Chadwick the 1935 Nobel Prize in Physics and marked the beginning of nuclear fission research.[23] In the 1930s, the need for a force mediating the strong nuclear interaction between protons and neutrons prompted Hideki Yukawa to propose in 1935 a massive particle, the meson, with a mass around 200 times that of the electron to explain the short-range nature of the force. The predicted π meson (pion) was discovered in 1947 by Cecil F. Powell and colleagues at the University of Bristol using photographic emulsions exposed to cosmic rays on the Jungfraujoch, observing tracks consistent with charged pions decaying into muons.[24] Neutral pions were identified shortly after in 1950 via their decay into two photons. The pion's role as the primary mediator of the strong force was confirmed through subsequent scattering experiments, validating Yukawa's theory and earning him the 1949 Nobel Prize. The late 1940s brought surprises with the discovery of "strange" particles exhibiting unexpectedly long lifetimes despite strong interaction production, challenging existing models. In 1947, George D. Rochester and Clifford C. Butler at the University of Manchester observed V-shaped tracks in a cloud chamber exposed to cosmic rays, indicating neutral particles decaying into proton-pion (later identified as the Λ hyperon) and two-pion (neutral kaon, K⁰) final states.[25] These findings, published in 1949, initiated the study of strangeness, a new quantum number conserved in strong interactions but violated in weak decays. Charged kaons (K⁺ and K⁻) were observed in 1948–1949 through cloud chamber and emulsion experiments, resolving the τ–θ puzzle where particles with the same mass decayed differently—later explained by parity violation in weak interactions in 1956.[26] By the early 1950s, accelerator experiments revealed further hadrons, expanding the "particle zoo." The Δ(1232) baryon resonance, the first excited state of the nucleon, was discovered in 1952 at the University of Chicago's cyclotron through pion-proton scattering, showing a broad peak at 1232 MeV indicating a short-lived state decaying strongly into nucleon-pion.[27] Cosmic ray and early accelerator data from Berkeley and Brookhaven uncovered additional hyperons (Σ, Ξ) and mesons (K*, ρ) between 1953 and 1959, with lifetimes suggesting associated production to conserve strangeness. By 1960, over 100 hadron species had been identified, prompting theoretical frameworks to classify their properties and interactions.[28]Quark Model Proposal
In the early 1960s, the rapid discovery of numerous hadrons through particle accelerator experiments created a need for a systematic classification to explain their diverse properties, such as masses, charges, and decay patterns. Building on the SU(3) flavor symmetry framework known as the Eightfold Way, developed by Murray Gell-Mann and Yuval Ne'eman in 1961, physicists sought a underlying physical mechanism to account for the observed multiplet structures in baryons and mesons.[29] In 1964, Murray Gell-Mann proposed the quark model as a schematic representation of hadrons as composite particles formed from fundamental building blocks. In his concise paper "A Schematic Model of Baryons and Mesons," Gell-Mann introduced three types of quarks—up (u), down (d), and strange (s)—with electric charges of , , and in units of the elementary charge , respectively. He posited that baryons consist of three-quark combinations in symmetric states under the strong interaction, while mesons are quark-antiquark pairs; this structure naturally reproduced the Eightfold Way multiplets, including the decuplet containing the resonances and the octet with protons and neutrons. The quark model, building on the Eightfold Way, predicted the existence of the Ω⁻ baryon (composed of three strange quarks), which was discovered in August 1964 at Brookhaven National Laboratory by a team led by Nicholas Samios, confirming the model's validity shortly after its proposal.[30][31] Independently, George Zweig developed a nearly identical model in his CERN preprint "An SU(3) Model for Strong Interaction Symmetry and its Breaking," where he termed the constituents "aces" and emphasized their role in both preserving and spontaneously breaking SU(3) symmetry to match observed hadron masses and interactions. Zweig's formulation highlighted the additivity of quantum numbers like isospin, hypercharge, and strangeness across the fundamental triplets, providing a predictive tool for hadron spectroscopy.[32][32] The quark model gained traction for its elegance in unifying the hadron zoo under a minimal set of three quarks, though Gell-Mann's whimsical name, drawn from James Joyce's Finnegans Wake, became the standard. Initially treated as a mathematical device rather than literal particles—due to the puzzling fractional charges and Pauli exclusion principle challenges for identical quarks in baryons—the proposal marked a paradigm shift from viewing hadrons as elementary.[7][7] This framework laid the groundwork for later experimental validations and the development of quantum chromodynamics.[7]Theoretical Description
Quark Composition
Hadrons are composite particles composed of quarks, which are fundamental fermions held together by the strong nuclear force mediated by gluons. There are six known flavors of quarks—up (u), down (d), strange (s), charm (c), bottom (b), and top (t)—each with distinct masses, electric charges, and other quantum numbers. The up and down quarks are the lightest and most common in everyday matter, while the heavier flavors (s, c, b, t) appear in high-energy processes or exotic states. Quarks carry fractional electric charges: +2/3 e for u and c, -1/3 e for d, s, and b, and +2/3 e for t. Additionally, quarks possess color charge (red, green, or blue), and hadrons form as color-neutral (singlet) combinations to satisfy quantum chromodynamics (QCD) confinement.[6] In the standard quark model, mesons consist of a quark-antiquark pair (q\bar{q}), where the antiquark has opposite quantum numbers to its quark counterpart. This pairing ensures overall integer electric charge and color neutrality. Light mesons, such as the pion (\pi^+ = u\bar{d}), are formed from up and down quarks, while strange mesons like the kaon (K^+ = u\bar{s}) incorporate the strange quark. Charmed mesons, such as the D^0 (c\bar{u}), involve the charm quark, and bottom mesons like the B^0 (b\bar{d}) feature the bottom quark. The top quark, due to its extremely short lifetime (\tau_t \approx 5 \times 10^{-25} s), does not form stable hadrons, as it decays before binding. Antiquarks in mesons carry opposite flavor, strangeness, charm, etc., allowing for a rich spectrum of states classified by total angular momentum and parity.[6][33] Baryons, in contrast, are composed of three quarks (qqq), resulting in half-integer spin and fermionic statistics, with examples including protons (uud) and neutrons (udd) from the first generation of quarks. The delta resonances, such as \Delta^{++} (uuu), further illustrate combinations of up and down quarks. Baryons with strangeness, like the lambda (\Lambda^0 = uds), include the strange quark, while charmed baryons such as \Lambda_c^+ (udc) incorporate charm. Bottom and double-bottom baryons, e.g., \Lambda_b^0 (udb), have been observed at accelerators. Antibaryons are made of three antiquarks (\bar{q}\bar{q}\bar{q}). The minimal quark content dominates the model's description, though higher Fock states with gluons or sea quarks contribute at higher orders in QCD.[6][33] The foundational quark model was proposed by Murray Gell-Mann in 1964, postulating three quark flavors (u, d, s) to explain the observed hadron spectrum and symmetries, with baryons as triplets or octets in SU(3) flavor symmetry and mesons as nonets. Independently, George Zweig suggested a similar model using "aces," but the term "quarks" prevailed. Subsequent discoveries extended the model: charm in 1974, bottom in 1977, and top in 1995, completing the three-generation structure aligned with leptons. This framework successfully predicts hadron masses and decays via flavor SU(3) and higher symmetries, though QCD provides the underlying dynamics. Exotic hadrons, such as tetraquarks (qq\bar{q}\bar{q}) or pentaquarks (qqq\bar{q}\bar{q}), deviate from the simple q\bar{q} or qqq paradigm but are still quark-based.[34][6]Strong Interaction and QCD
The strong interaction, responsible for binding quarks and antiquarks to form hadrons, is fundamentally described by Quantum Chromodynamics (QCD), a quantum field theory that models the strong nuclear force as a non-Abelian gauge theory invariant under the SU(3)c color group.[35] In QCD, quarks possess an intrinsic property called color charge, analogous to electric charge in electromagnetism but with three types—conventionally labeled red, green, and blue—while antiquarks carry anticolors.[35] The force is mediated by gluons, massless vector bosons that carry both color and anticolor, enabling them to interact with quarks and among themselves, unlike photons in quantum electrodynamics (QED).[36] This self-interaction of gluons introduces nonlinearities in the theory, profoundly affecting its behavior across different energy scales. A cornerstone of QCD is asymptotic freedom, the phenomenon where the effective strength of the strong coupling constant αs decreases as the energy scale (or inverse distance between quarks) increases. This property was independently discovered in 1973 by David Gross and Frank Wilczek, and by David Politzer, through calculations showing that the beta function governing the running of the coupling has a negative sign for the number of quark flavors nf < 16.5. The leading-order beta function is given by where g is the QCD coupling, confirming that αs ≈ 0.118 at the Z boson mass scale but grows at lower energies.[35] Asymptotic freedom allows perturbative QCD (pQCD) calculations for high-energy processes, such as deep inelastic scattering, where quarks behave as nearly free particles inside hadrons, validating the parton model.[37] At low energies, corresponding to typical hadron scales (~1 fm), the strong coupling becomes large, leading to color confinement: isolated quarks or gluons cannot exist as free particles, but are perpetually bound into color-singlet combinations like mesons (quark-antiquark pairs) and baryons (three quarks).[35] Confinement arises non-perturbatively from the growth of the quark-antiquark potential, which is linear at large distances, V(r) ≈ σ r, with string tension σ ≈ 420 MeV/fm, as evidenced by lattice QCD simulations that reproduce the hadron spectrum and exclude free colored states in the vacuum.[38] This mechanism ensures that all observed strongly interacting particles are hadrons with zero net color charge, explaining the absence of free quarks in nature despite their role as fundamental constituents.Physical Properties
Intrinsic Properties
Hadrons are characterized by intrinsic quantum numbers that define their composition and behavior under strong interactions, including baryon number, electric charge, spin, parity, and flavor quantum numbers. These properties emerge from the additive contributions of their valence quarks (and antiquarks for mesons), as described in the quark model. Baryon number distinguishes the two main classes: for baryons composed of three quarks and for mesons made of a quark-antiquark pair, with where and are the numbers of quarks and antiquarks.[39] Electric charge is the sum of the fractional charges of constituent quarks: for up () and charm () quarks, for down (), strange (), and bottom () quarks, for top (), and opposite signs for antiquarks. Flavor quantum numbers quantify the content of heavier quarks beyond the light , , and : strangeness per quark (and per ), charm per (and per ), bottomness per (and per ), and topness per (and per ). These are conserved in strong and electromagnetic processes but violated in weak decays.[39][39] Isospin and its third component arise from approximate SU(2) symmetry treating and quarks as a doublet with , for and for ; heavier quarks have . For light hadrons, SU(3) flavor symmetry extends this to include quarks (), organizing ground-state mesons into an octet plus singlet and baryons into an octet and decuplet. Hypercharge combines baryon number with flavor numbers for symmetry classifications.[39][6] Spin and parity derive from the spins and relative motions of quarks, each with intrinsic spin . For mesons, total spin or combines with orbital angular momentum to yield ; parity is , and for neutral mesons, charge conjugation , restricting allowed states (e.g., , , for in , ). Baryons, with three quarks, have from coupling two quark spins to or , then with the third spin and total ; parity is , with flavor-spin couplings yielding symmetric wavefunctions under SU(6).[6][6]Spectroscopic Properties
Hadron spectroscopy examines the energy levels, or mass spectrum, of hadrons along with their associated quantum numbers, providing crucial insights into quark binding mechanisms and the dynamics of quantum chromodynamics (QCD). These properties include the total angular momentum , parity , and for mesons, charge conjugation or -parity (where for neutral systems with isospin ). Flavor-related quantum numbers such as isospin , hypercharge (with baryon number and strangeness ), and third component of isospin further classify states into symmetry multiplets. Measurements of these quantities, primarily from scattering experiments and decays, allow identification of hadron resonances and test theoretical models like the constituent quark model.[6][39] In the quark model, light hadrons ( quarks) organize into SU(3)-flavor multiplets reflecting approximate symmetry. Ground-state mesons form nonets of nine particles: the pseudoscalar octet plus singlet with , exemplified by the (mass ≈ 140 MeV, ), (≈ 495 MeV, ), (≈ 548 MeV, ), and (≈ 958 MeV, ); and the vector nonet with , including the (≈ 775 MeV, ), (≈ 892 MeV, ), (≈ 782 MeV, ), and (≈ 1020 MeV, ). Baryons comprise an octet of states, such as the proton (, mass ≈ 938 MeV, ) and (, ≈ 1116 MeV, ), and a decuplet of states, including the (≈ 1232 MeV, ) and (≈ 1385 MeV, ). These groupings arise from combining quark spins and orbital angular momenta, with masses influenced by quark masses and hyperfine splitting proportional to .[6][39] Excited states reveal richer structure, with radial and orbital excitations leading to higher masses and varied quantum numbers. For instance, the scalar mesons around 1-2 GeV may mix and glueball components, while tensor mesons like the have . Baryon excitations include the with (negative parity from ). The spectrum follows approximate Regge trajectories, where with , yielding linear relations with slope GeV for mesons and similar for baryons, indicative of flux-tube models for quark confinement. Deviations from linearity at high highlight QCD non-perturbative effects. Selection rules from conservation of angular momentum, parity, and flavor dictate allowed decays, such as (S-wave, strong decay).[6][40]| Hadron Type | Multiplet | Example Quantum Numbers | Representative Masses (MeV) |
|---|---|---|---|
| Pseudoscalar Mesons | Nonet | , | |
| Vector Mesons | Nonet | , | |
| Baryon Octet | Proton: 938, | ||
| Baryon Decuplet | , |
Baryons
Stable Baryons
Stable baryons are the fundamental constituents of ordinary atomic matter, consisting solely of the proton and the neutron, both belonging to the nucleon family with spin . These particles are composed of up and down quarks bound by the strong nuclear force mediated by gluons, as described by quantum chromodynamics (QCD). Unlike other baryons, which decay rapidly via the strong or weak interactions, the proton and neutron exhibit exceptional longevity, making them the only baryons observed in stable form in nature. The proton (uud quark content) carries a positive electric charge of +1 e, a rest mass of 938.272 MeV/, and is absolutely stable, with experimental lower limits on its lifetime exceeding years (90% CL) for the decay mode .[41] This stability arises because the proton is the lightest baryon, and baryon number conservation prohibits its decay into lighter particles without violating energy conservation or other quantum numbers. Its magnetic moment is measured at nuclear magnetons, reflecting the intrinsic spins and orbital motions of its constituent quarks.[42] The neutron (udd quark content) is electrically neutral, with a rest mass of 939.565 MeV/, slightly heavier than the proton by about 1.293 MeV/. Free neutrons decay via the weak interaction with a mean lifetime of 878.4 ± 0.5 seconds, primarily through the channel , releasing approximately 0.782 MeV of kinetic energy. However, neutrons become stable within atomic nuclei, where the binding energy difference prevents decay due to the Pauli exclusion principle and nuclear stability constraints. The neutron's magnetic moment is nuclear magnetons, opposite in sign to the proton's despite its neutrality, a consequence of the quark flavor asymmetry in the nucleon wave function.[42]| Property | Proton (p) | Neutron (n) |
|---|---|---|
| Quark content | uud | udd |
| Charge (e) | +1 | 0 |
| Mass (MeV/) | 938.272 | 939.565 |
| Spin | ||
| Mean lifetime | > years (90% CL) | 878.4 ± 0.5 s (free) |
| Magnetic moment () | +2.7928 | -1.9130 |
| Baryon number (B) | +1 | +1 |
Unstable Baryons
Unstable baryons, often referred to as baryon resonances, represent excited states of three-quark systems that decay predominantly through the strong interaction, resulting in extremely short lifetimes on the order of 10^{-23} to 10^{-24} seconds. These particles are not constituents of stable matter but are transiently produced in high-energy collisions, such as pion-nucleon scattering, photoproduction, or heavy-ion interactions, and detected via their decay products. Their properties, including masses, widths, and branching ratios, are compiled and analyzed by the Particle Data Group (PDG), providing a standardized reference for experimental and theoretical studies. The investigation of unstable baryons is essential for probing the confinement regime of quantum chromodynamics (QCD), where quarks and gluons form color-neutral hadrons, and for testing models of baryon structure beyond the simple quark model. In the sector of light quarks (u, d, s), unstable baryons are organized into multiplets based on SU(3) flavor symmetry, with quantum numbers specifying isospin (I), strangeness (S), and spin-parity (J^P). The lowest-lying excitations above the ground-state nucleon octet and decuplet are overwhelmingly unstable, decaying into stable baryons plus mesons like pions or kaons. A seminal example is the Δ(1232) resonance (I=3/2, S=0, J^P=3/2^+), discovered in the 1950s through pion-nucleon scattering at Brookhaven National Laboratory; it has a mass of 1232 MeV/c² and a width of 117 MeV, primarily decaying to a nucleon and a pion (Nπ) with nearly 100% branching ratio. This resonance exemplifies the spin-flip excitation in the quark model, where orbital angular momentum between quarks contributes to the total spin. Similarly, the N(1535) resonance (I=1/2, S=0, J^P=1/2^-) at ≈1535 MeV/c² (1515–1545 MeV) and width ≈150 MeV (125–175 MeV) favors decays to Nη (30–55%) and Nπ (32–52%), highlighting negative parity states arising from p-wave quark orbitals.[42] Strange unstable baryons, incorporating the s quark, reveal additional complexities due to flavor symmetry breaking. The Λ(1405) (I=0, S=-1, J^P=1/2^-) at 1405 MeV/c² and narrow width of 50 MeV is particularly intriguing, as it lies below the K̄N threshold and is often interpreted as a K̄N quasi-bound state rather than a pure three-quark state, influencing our understanding of strangeness in QCD. The Σ(1385) (I=1, S=-1, J^P=3/2^+) at 1387-1394 MeV/c² (depending on charge state) and width 36 MeV decays mainly to Λπ (88%) or Σπ (12%), serving as the strange partner to the Δ(1232) in the decuplet. Higher-mass states, such as the N(1720) (3/2^+) or Ξ(1530) (3/2^+), exhibit multi-pion decays and broader widths, reflecting increased phase space and possible hybrid or molecular contributions. These resonances are observed at accelerators like Jefferson Lab and CERN's COMPASS experiment through partial-wave analysis of production reactions.[45][46] The spectrum of unstable baryons remains incomplete, with quark models predicting more states than experimentally confirmed—a phenomenon known as the "missing resonances" problem—potentially due to their coupling to multi-meson continua or suppression in certain production channels. Lattice QCD simulations and effective field theories are advancing predictions, while recent data from facilities like BESIII and GlueX continue to refine masses and couplings. For heavy-flavor unstable baryons (charmed or bottom), such as the Λ_c(2595) (J^P=1/2^-, mass 2592 MeV/c², decaying to Λ_c π), strong decays dominate for excited states, testing heavy-quark effective theories, though these are addressed in dedicated sections. Representative examples of light unstable baryons are summarized below, with properties from the PDG 2025 edition:| Resonance | Quark Content (example) | I, S | J^P | Mass (MeV/c²) | Width (MeV) | Primary Decay Modes |
|---|---|---|---|---|---|---|
| Δ(1232) | uud (for Δ++) | 3/2, 0 | 3/2^+ | 1230–1234 (≈1232) | 114–120 (≈117) | Nπ (~100%) |
| N(1535) | uud (for N*) | 1/2, 0 | 1/2^- | 1515–1545 (≈1535) | 125–175 (≈150) | Nη (30–55%), Nπ (32–52%) |
| Λ(1405) | uds | 0, -1 | 1/2^- | 1405.1^{+1.3}_{-1.0} | 50.5 ± 2.0 | Σπ (~100%), coupled to K̄N |
| Σ(1385) | uus (for Σ*+) | 1, -1 | 3/2^+ | 1382.8–1394 (varies by charge) | 36–39 (varies) | Λπ (~88%), Σπ (~12%) |
| Ξ(1530) | uss (for Ξ*) | 1/2, -2 | 3/2^+ | 1531.8–1535.0 (varies) | 9.1–9.9 | Ξπ (~100%) |
Mesons
Pseudoscalar Mesons
Pseudoscalar mesons are a class of mesons characterized by total angular momentum J=0 and negative parity P=-1, resulting in J^P=0^-. They represent the ground state in the quark-antiquark (q\bar{q}) spectrum under the strong interaction and are pivotal in quantum chromodynamics (QCD) as approximate Goldstone bosons arising from the spontaneous breaking of approximate chiral SU(3)_L × SU(3)_R symmetry.[6] These particles mediate the residual strong force between nucleons and exhibit nearly massless behavior in the chiral limit, where up (u) and down (d) quark masses are negligible compared to the QCD scale.[6] In the constituent quark model, light pseudoscalar mesons form a nonet under the approximate SU(3) flavor symmetry, comprising an octet and a singlet. The octet includes the isovector pions (π) and the strangeness-carrying kaons (K), while the isoscalars η and η' arise from mixing between the SU(3) octet and singlet states. The pion states are π^+ = u\bar{d}, π^- = d\bar{u}, and π^0 = (u\bar{u} - d\bar{d})/√2, with isospin I=1. Kaons form an I=1/2 doublet: K^+ = u\bar{s}, K^0 = d\bar{s}, \bar{K}^0 = s\bar{d}, and K^- = s\bar{u}. The η and η' mixing is described by the angle θ ≈ -15.4°, where η ≈ cosθ |η_8\rangle - sinθ |η_1\rangle and η' ≈ sinθ |η_8\rangle + cosθ |η_1\rangle, with |η_8\rangle = (u\bar{u} + d\bar{d} - 2s\bar{s})/√6 and |η_1\rangle = (u\bar{u} + d\bar{d} + s\bar{s})/√3; this mixing resolves the U(1)_A anomaly, explaining the heavier η' mass despite the light quark content.[6] Key physical properties of these mesons are summarized in the table below, based on precision measurements. Charged pions and kaons decay primarily via the weak interaction, with lifetimes on the order of 10^{-8} s, corresponding to widths of ~2.5 × 10^{-14} MeV for π and ~5.3 × 10^{-14} MeV for K. Neutral pions decay electromagnetically to two photons with a width of 7.73 ± 0.18 eV, while η and η' decay via strong and electromagnetic modes, with dominant channels η → γγ (38.7%) and η' → ηπ^0π^0 (42.5%). These decays provide probes for CKM matrix elements and chiral perturbation theory predictions.[48][49]| Particle | Quark Content | Mass (MeV) | Width (MeV) | Dominant Decays |
|---|---|---|---|---|
| π^+ | u\bar{d} | 139.57039 ± 0.00018 | (2.53 ± 0.004) × 10^{-14} (lifetime 2.6033 × 10^{-8} s) | μ^+ ν_μ (99.9877%) |
| π^0 | (u\bar{u} - d\bar{d})/√2 | 134.9768 ± 0.0005 | (7.73 ± 0.18) × 10^{-6} | γγ (98.823%) |
| K^+ | u\bar{s} | 493.677 ± 0.016 | (5.32 ± 0.01) × 10^{-14} (lifetime 1.2380 × 10^{-8} s) | μ^+ ν_μ (63.55%), π^+ π^0 (20.66%) |
| η | ≈ (u\bar{u} + d\bar{d} - 2s\bar{s})/√6 | 547.862 ± 0.018 | (1.275 ± 0.018) × 10^{-3} | γγ (38.7%), 3π^0 (32.2%) |
| η' | ≈ (u\bar{u} + d\bar{d} + s\bar{s})/√3 | 957.78 ± 0.06 | 0.197 ± 0.016 | ηπ^+π^- (22.2%), ηπ^0π^0 (42.5%) |
Vector Mesons
Vector mesons constitute a subclass of mesons with total angular momentum quantum number , negative parity , and, for their neutral members, negative charge conjugation , denoted as . These particles are quark-antiquark () bound states held together by the strong force, as described within quantum chromodynamics (QCD), where the vector nature arises from the orbital and spin angular momentum alignment of the quark pair. Unlike pseudoscalar mesons, vector mesons exhibit a richer decay spectrum due to their higher spin, often decaying electromagnetically or via strong interactions into lighter hadrons or dileptons. Their study provides insights into non-perturbative QCD dynamics, as their masses and widths reflect the confinement scale of approximately 1 GeV.[51] The lightest vector mesons, known as the vector nonet in the quark model, include the isovector mesons, the isoscalar and , forming an SU(3) flavor octet and singlet. The mesons, discovered in 1961 through pion-nucleon scattering experiments at Brookhaven National Laboratory, have a mass of about 775 MeV and predominantly decay into two pions via the strong interaction, with a width of roughly 150 MeV indicating short lifetimes on the order of seconds. The meson, observed in 1963 in pion-proton interactions, is a light-quark isoscalar state with a mass of 782 MeV and decays primarily to three pions, suppressed for two-pion modes by isospin and G-parity conservation. The meson, identified in 1962 in antiproton-proton annihilations, is nearly a pure strange quark-antiquark pair with a mass of 1020 MeV and favors kaon pair decays, highlighting the role of flavor mixing in the vector nonet. These properties align with the quark model predictions, where ideal mixing separates the (mostly ) from the ().| Meson | Quark Content | Mass (MeV/c²) | Width (MeV) | Primary Decay Mode |
|---|---|---|---|---|
| (and charge conjugates) | 775.26 ± 0.05 | 149.1 ± 0.8 | (≈100%) | |
| 782.65 ± 0.12 | 8.49 ± 0.08 | (≈89%) | ||
| 1019.461 ± 0.016 | 4.249 ± 0.014 | (≈49%) |
Exotic Hadrons
Pentaquarks
Pentaquarks are exotic hadrons composed of four quarks and one antiquark, representing a multiquark configuration beyond the conventional three-quark baryons. Unlike standard baryons, pentaquarks challenge the quark model by suggesting tightly bound or loosely associated states involving additional quark-antiquark pairs. Theoretical predictions for pentaquarks date back to the 1960s, but experimental confirmation remained elusive until recent high-energy collider data revealed hidden-charm candidates. These states are typically interpreted as having a minimal quark content of three light quarks (uud or similar) plus a heavy charm quark-antiquark pair (c\bar{c}), forming structures like uudc\bar{c}. Early searches for pentaquarks focused on light-flavor states, such as the proposed Θ^+ (uudd\bar{s}) with a mass around 1540 MeV, claimed in 2003 by several experiments including LEPS and DIANA. However, subsequent high-statistics analyses by other facilities, including CLAS and HERMES, failed to confirm these signals, attributing them to statistical fluctuations or background effects. No undisputed light pentaquarks have been observed to date, and the Particle Data Group lists no established candidates in this category. The breakthrough came from the LHCb experiment at CERN, which reported evidence for hidden-charm pentaquarks in 2015 through an amplitude analysis of Λ_b^0 → J/ψ K^- p decays. Two broad structures were identified in the J/ψ p invariant mass spectrum: P_c(4380)^+ with mass 4380 ± 8 ± 29 MeV and width 205 ± 18 ± 86 MeV, and P_c(4450)^+ with mass 4449.8 ± 1.7 ± 2.5 MeV and width 39 ± 5 ± 19 MeV, observed with a combined statistical significance exceeding 9σ. These states decay primarily to J/ψ p, consistent with a minimal quark content of uudc\bar{c} and positive charge.[52][53] A reanalysis in 2019 using the full Run 1 dataset (3 fb^{-1}) refined these observations, resolving the higher-mass structure into two narrow peaks and discovering a new state. The updated spectrum showed P_c(4312)^+ with mass 4311.9 ± 0.7^{+0.6}{-0.0} MeV and width 9.8 ± 2.7 ± 4.5 MeV (significance 7.3σ), alongside P_c(4440)^+ at 4440.3 ± 1.3^{+4.1}{-4.4} MeV and width 20.6 ± 4.9 ^{+10.0}{-5.3} MeV (significance 5.3σ), and P_c(4457)^+ at 4457.3 ± 0.6^{+4.1}{-1.7} MeV and width 6.4 ± 2.0 ± 1.9 MeV (combined significance > 5σ for the pair). The overall significance for all three states reached 13σ, favoring a three-peak model over previous interpretations. These narrow widths suggest tightly bound configurations.[54] LHCb also reported evidence for a hidden-charm strange pentaquark P_{cs}(4459)^0 in 2019 from Ξ_b^- → J/ψ Λ \bar{K}^- decays, with mass 4459 ± 2.6 ± 3.0 MeV, width < 23 MeV (95% CL), and significance 3.1σ, consistent with quark content udsc\bar{c} and J^P = 1/2^-. In 2022, LHCb extended the search, observing a narrow resonance P_{cs}(4338)^0 in the J/ψ Λ spectrum from B^- → J/ψ Λ \bar{p} decays, with mass 4338.2 ± 0.7 ± 0.4 MeV, width 7.0 ± 1.2 ± 1.3 MeV, statistical significance 15σ (model-dependent 5.5σ), and preferred J^P = 1/2^-. Additionally, evidence for a doubly charmed pentaquark candidate P_{cc}(4337)^+ was found in 2022 from B_s^0 → J/ψ p \bar{p} decays, with mass ~4337 MeV and width ~30 MeV (significance ~6σ), possibly a compact state or cusp effect.[55][56][57] Theoretical interpretations of these P_c states fall into two primary categories: compact five-quark models and hadronic molecular models. In the compact picture, the states arise from diquark-triquark clustering, such as [ud][uc]\bar{d}\bar{c} or similar color-connected configurations, predicted by lattice QCD and potential models to have masses aligning with observations. However, these models struggle with the narrow widths without fine-tuning. The molecular interpretation, supported by proximity to thresholds like Σ_c \bar{D}^*, views the pentaquarks as loosely bound S-wave states of a charmed baryon and anticharmed meson, explaining the narrow decays via short-range forces and explaining the mass splittings through binding energies of a few MeV. For the strange candidates, a Λ_c \bar{D}^{*s} molecule is favored for P_{cs}(4338)^0, with binding consistent with heavy-quark symmetry. Ongoing debates center on spin-parity assignments, with amplitude analyses suggesting mixed J^P = 3/2^-, 5/2^- for the non-strange states.[58][59] Further searches continue at LHCb and other facilities, including for bottom-analog states and fully heavy pentaquarks, with ongoing analyses as of 2025 providing additional constraints but no new confirmations beyond evidence-level candidates. The observed pentaquarks provide crucial tests for quantum chromodynamics in the non-perturbative regime, highlighting the role of heavy quarks in stabilizing exotic configurations.Tetraquarks and Hybrids
Tetraquarks are exotic hadrons composed of two quarks and two antiquarks (qq¯q¯q), distinct from conventional mesons (q¯q) due to their multiquark configuration.[39] Theoretical models interpret them as compact diquark-antidiquark states, hadronic molecules of meson pairs bound by residual strong forces, or mixtures thereof, with lattice QCD simulations supporting stable bound states in heavy flavor sectors.[60] The Particle Data Group updated its naming scheme in 2023 to formally include tetraquarks, particularly heavy ones observed in collider experiments.[61] Seminal discoveries began with the X(3872) in 2003 by the Belle Collaboration, observed in B meson decays, marking the first clear evidence for charmonium-like exotics near the D¯0D*0 threshold. Subsequent observations confirmed charged and neutral tetraquarks, primarily involving charm quarks, produced in e⁺e⁻ annihilations, B decays, or proton-proton collisions. The Z_c(3900)⁺, discovered by BESIII in 2013, is a charged state with I=1, decaying to π⁺J/ψ, providing evidence for hidden-charm tetraquarks. LHCb's observation of the T_{cc}^+(3875) in 2022, a doubly charmed isosinglet state, demonstrated a loosely bound molecule-like structure just below the D^D threshold, with a binding energy of 0.34 ± 0.20 MeV, stable against strong decay.[62] In 2023, LHCb reported evidence for strange doubly charmed tetraquarks T_{ccs1}(4000)^+ and T_{ccs1}(4220)^+, observed in D^0 K^- π^+ invariant mass from B^+ decays, with masses ~4015 MeV and ~4220 MeV, widths ~300 MeV and ~250 MeV, respectively (significances ~4σ each), interpreted as compact or molecular states with quark content c c u \bar s \bar d. Additionally, in 2024, LHCb observed the open-charm tetraquark candidate T_{c \bar s}^0 (2900) in further channels like B^- → D^- D_s^+ K^-, confirming its scalar nature (J^P=0^+) near the D^ K threshold. Recent fully charmed candidates, such as the X(6600), X(6900), and X(7100) triplet decaying to J/ψ J/ψ, suggest axial-vector states (J^{PC}=1^{++}) in proton-proton collisions at the LHC, supporting compact tetraquark interpretations over pure quarkonia; these were confirmed by ATLAS in 2025.[63][64][65][66] These states probe non-perturbative QCD dynamics, with molecular models favored for near-threshold bindings and diquark models for compact cores.[67]| State | Flavor Content | Mass (MeV/c²) | J^{PC} | Key Decay | Discovery Experiment | Interpretation |
|---|---|---|---|---|---|---|
| X(3872) | c¯c u¯u (or similar) | 3871.69 ± 0.17 | 1^{++} | J/ψ π⁺π⁻ | Belle (2003) | D¯^0 D^{*0} molecule or tetraquark |
| Z_c(3900)^+ | c¯c u¯d | 3886.6 ± 2.4 | 1^{+-} | π^+ J/ψ | BESIII (2013) | Charged hidden-charm tetraquark |
| T_{cc}^+(3875) | ccu d¯ | 3874.10 ± 0.16 | 1^+ | D^0 D^0 π^+ | LHCb (2022) | Doubly charmed molecule |
| T_{ccs1}(4000)^+ | c c u \bar s \bar d | ~4015 | ? | D^0 K^- π^+ | LHCb (2023) | Strange doubly charmed tetraquark |
| T_{c \bar s}^0 (2900) | c u \bar s \bar s (or similar) | ~2900 | 0^+ | D^0 K^- | LHCb (2020/2024) | Open-charm tetraquark |
| X(6900) | c c \bar c \bar c | ~6900 | 0^{++} or 2^{++} | J/ψ J/ψ | LHCb (2020) | Fully charmed tetraquark |
| State | Flavor | Mass (MeV/c²) | Width (MeV) | J^{PC} | Key Decays | Key Experiments | Status |
|---|---|---|---|---|---|---|---|
| π_1(1400) | u¯u, d¯d | ~1400 | ~300 | 1^{-+} | ηπ | VES, E852 | Tentative hybrid candidate |
| π_1(1600) | u¯u, d¯d | 1593 ± 8 | 168 ± 20 | 1^{-+} | ηπ, b_1 π | E852, COMPASS | Strong evidence for exotic hybrid |