nLab hadron



Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)


in grand unified theory

minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields



In QCD a bound state of quarks via the strong nuclear force.

Binding two quarks: meson,

Binding three quarks: baryon,

Binding four quarks: tetraquark.


Computation via lattice QCD

Comparison of light hadron masses as seen in accelertator experiment and in lattice QCD-computer simulation (from Fodor-Hoelbling 12)

Conceptualization and computation in AdS/QCD

In the Witten-Sakai-Sugimoto model for strongly coupled QCD via an intersecting D-brane model, the hadrons in QCD correspond to string-theoretic-phenomena in an ambient bulk field theory on an approximately anti de Sitter spacetime:

  1. the mesons (bound states of 2 quarks) correspond to open strings in the bulk, whose two endpoints on the asymptotic boundary correspond to the two quarks;

  2. baryons (bound states of N cN_c quarks) appear in two different but equivalent (Sugimoto 16, 15.4.1) guises:

    1. as wrapped D4-branes with N cN_c open strings connecting them to the D8-brane

      (Witten 98b, Gross-Ooguri 98)

    2. as skyrmions

      (Sakai-Sugimoto 04, section 5.2, Sakai-Sugimoto 05, section 3.3, see Bartolini 17).

For review see Sugimoto 16, also Rebhan 14, around (18).

graphics grabbed from Sugimoto 16

This produces baryon mass spectra with moderate quantitative agreement with experiment (HSSY 07):

graphics grabbed from Sugimoto 16

For more see at hadron Kaluza-Klein theory.



  • Claude Amsler, The Quark Structure of Hadrons: An Introduction to the Phenomenology and Spectroscopy, Lecture Notes in Physics 949 (doi:10.1007/978-3-319-98527-5)

See also:

Discussion in a general context of bound states:

  • Paul Hoyer, Bound states – from QED to QCD, Lectures at “Mini-school on theoretical methods in particle physics” at the Higgs Centre for Theoretical Physics, University of Edinburgh on 30 September to 4 October 2013 (arXiv:1402.5005)

  • Paul Hoyer, Journey to the Bound States (arXiv:2101.06721)

On the issue of hadron mass (confinement):

  • Minghui Ding, Craig D. Roberts, Sebastian M. Schmidt, Emergence of Hadron Mass and Structure lbrack;arXiv:2211.07763]

List of hadrons discovered at the LHC experiment:

Walecka hadrodynamics with nucleon fields

On quantum hadrodynamics (relativivist effective field theory of nuclear physics, coupling mesons and nucleons) in the sense of the Walecka model, hence with nucleons appearing as explicit fields (as opposed to being solitonic Skyrmions in the pion field as in chiral perturbation theory).


The original Walecka model (QHD-I model), with nucleons coupled to sigma-mesons and omega-mesons:

Inclusion into the Walecka model also of the pion and the rho-meson (the QHD-II model):

Further discussion of these models:

Further inclusion of electromagnetism (photon field):

  • A. Yu. Korchin, D. Van Neck, M. Waroquier, Electromagnetic interaction in chiral quantum hadrodynamics and decay of vector and axial-vector mesons, Phys. Rev. C67 (2003) 015207 (arXiv:nucl-th/0302042)

Relation to quark-meson coupling model:

  • Koichi Saito, Relationship between Quark-Meson Coupling Model and Quantum Hadrodynamics, Prog. Theor. Phys. 108 (2002) 609-614 (arXiv:nucl-th/0207053)

Hadrodynamics via Light-front QCD

On light-front QCD for quantum hadrodynamics:

Skyrme hadrodynamics with vector mesons (π\pi-ω\omega-ρ\rho-model)

Inclusion of vector mesons (omega-meson and rho-meson/A1-meson) into the Skyrmion model of quantum hadrodynamics, in addition to the pion:

First, on the equivalence between hidden local symmetry- and massive Yang-Mills theory-description of Skyrmion quantum hadrodynamics:

  • Atsushi Hosaka, H. Toki, Wolfram Weise, Skyrme Solitons With Vector Mesons: Equivalence of the Massive Yang-Mills and Hidden Local Symmetry Scheme, 1988, Z. Phys. A332 (1989) 97-102 (spire:24079)

See also

  • Marcelo Ipinza, Patricio Salgado-Rebolledo, Meron-like topological solitons in massive Yang-Mills theory and the Skyrme model (arXiv:2005.04920)

Inclusion of the ω\omega-meson

Original proposal for inclusion of the ω-meson in the Skyrme model:

Relating to nucleon-scattering:

  • J. M. Eisenberg, A. Erell, R. R. Silbar, Nucleon-nucleon force in a skyrmion model stabilized by omega exchange, Phys. Rev. C 33, 1531 (1986) (doi:10.1103/PhysRevC.33.1531)

Combination of the omega-meson-stabilized Skyrme model with the bag model for nucleons:

Discussion of nucleon phenomenology for the ω\omega-stabilized Skyrme model:

Inclusion of the ρ\rho-meson

Original proposal for inclusion of the ρ-meson:

Discussion for phenomenology of light atomic nuclei:

Inclusion of the ω\omega- and ρ\rho-meson

The resulting π\pi-ρ\rho-ω\omega model:

See also

  • Ki-Hoon Hong, Ulugbek Yakhshiev, Hyun-Chul Kim, Modification of hyperon masses in nuclear matter, Phys. Rev. C 99, 035212 (2019) (arXiv:1806.06504)


Combination of the omega-rho-Skyrme model with the bag model of quark confinement:

  • H. Takashita, S. Yoro, H. Toki, Chiral bag plus skyrmion hybrid model with vector mesons for nucleon, Nuclear Physics A Volume 485, Issues 3–4, August 1988, Pages 589-605 (doi:10.1016/0375-9474(88)90555-6)

Inclusion of the σ\sigma-meson

Inclusion of the sigma-meson:

  • Thomas D. Cohen, Explicit σ\sigma meson, topology, and the large-NN limit of the Skyrmion, Phys. Rev. D 37 (1988) (doi:10.1103/PhysRevD.37.3344)

For analysis of neutron star equation of state:

  • David Alvarez-Castillo, Alexander Ayriyan, Gergely Gábor Barnaföldi, Hovik Grigorian, Péter Pósfay, Studying the parameters of the extended σ\sigma-ω\omega model for neutron star matter (arXiv:2006.03676)

Skyrme hadrodynamics with heavy quarks/mesons

Inclusion of heavy flavors into the Skyrme model for quantum hadrodynamics:

Inclusion of strange quarks/kaons

Inclusion of strange quarks/kaons into the Skyrme model:


Inclusion of charm quarks/D-mesons

Inclusion of charm quarks/D-mesons into the Skyrme model:

Inclusion of bottom quarks/B-mesons

Inclusion of further heavy flavors beyond strange quark/kaons, namely charm quarks/D-mesons and bottom quarks/B-mesons, into the Skyrme model:

  • Mannque Rho, D. O. Riska, Norberto Scoccola, The energy levels of the heavy flavour baryons in the topological soliton model, Zeitschrift für Physik A Hadrons and Nuclei volume 341, pages 343–352 (1992) (doi:10.1007/BF01283544)

  • Arshad Momen, Joseph Schechter, Anand Subbaraman, Heavy Quark Solitons: Strangeness and Symmetry Breaking, Phys. Rev. D49:5970-5978, 1994 (arXiv:hep-ph/9401209)

  • Yongseok Oh, Byung-Yoon Park, Dong-Pil Min, Heavy Baryons as Skyrmion with 1/m Q1/m_Q Corrections, Phys. Rev. D49 (1994) 4649-4658 (arXiv:hep-ph/9402205)



Observation of hadrons at LHC:

  • Maria Vasileiou on behalf of the ALICE Collaboration, Measurement of the Hadronic Resonance Production with ALICE at the CERN LHC, Universe 2019, 5(1), 6 (doi:10.3390/universe5010006)

In lattice QCD

Computation of the mass of hadrons using lattice QCD (see also confinement and mass gap problem) is discussed in

  • S. Durr, Z. Fodor, J. Frison, C. Hoelbling, R. Hoffmann, S.D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K.K. Szabo, G. Vulvert,

    Ab-initio Determination of Light Hadron Masses,

    Science 322:1224-1227,2008 (arXiv:0906.3599)

    conclusion on p. 4:

our study strongly suggests that QCD is the theory of the strong interaction, at low energies as well

  • Zoltan Fodor, Christian Hoelbling, Light Hadron Masses from Lattice QCD, Rev. Mod. Phys. 84, 449, (arXiv:1203.4789)

  • S. Aoki et. al. Review of lattice results concerning low-energy particle physics (arXiv:1607.00299)

In Witten-Sakai-Sugimoto model for AdS-QCD

QCD hadrons realized in the Witten-Sakai-Sugimoto model of holographic QCD:


Last revised on November 16, 2022 at 04:08:56. See the history of this page for a list of all contributions to it.