nLab baryon



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 the standard model of particle physics (specifically in QCD), a baryon is bound state of three quarks via the strong nuclear force. Baryons are the “heavy” types of hadrons, the other being the mesons.

Examples of baryons are the nucleons: protons and neutrons. Other examples are Lambda baryons.

Also pentaquarks are counted as baryons.


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



Baryons as 3-constituent quark bound states:

  • Gernot Eichmann, Helios Sanchis-Alepuz, Richard Williams, Reinhard Alkofer, Christian S. Fischer, Baryons as relativistic three-quark bound states, Progress in Particle and Nuclear Physics Volume 91, November 2016, Pages 1-100 (arXiv:1606.09602, doi:10.1016/j.ppnp.2016.07.001)

Baryons as quark/diquark bound states:


  • Eberhard Klempt, Jean-Marc Richard, Baryon spectroscopy, Rev. Mod. Phys. 82:1095-1153, 2010 (arXiv:0901.2055

See also

  • Wikipedia, Baryon

  • Aarts, Baryons at finite temperature (pdf)

Baryon chiral perturbation theory

Discussion of baryon chiral perturbation theory, i.e of chiral perturbation theory with explicit effective (as opposed to or in addition to implicit skyrmionic) baryon fields included (see also Walecka model and quantum hadrodynamics):


Original articles:

  • Elizabeth Jenkins, Aneesh V. Manohar, Baryon chiral perturbation theory using a heavy fermion lagrangian, Physics Letters B Volume 255, Issue 4, 21 February 1991, Pages 558-562 (doi:10.1016/0370-2693(91)90266-S)

  • Robert Baur, Joachim Kambor, Generalized Heavy Baryon Chiral Perturbation Theory, Eur. Phys. J. C7:507-524, 1999 (arXiv:hep-ph/9803311)

Higher order terms:

See also:

  • Lisheng Geng, Recent developments in SU(3)SU(3) covariant baryon chiral perturbation theory, Front. Phys., 2013, 8(3): 328-348 (arXiv:1301.6815)

Baryons as Skyrmions

The Skyrmion-model for baryons (see there for more references):

Hadrons as KK-modes of 5d Yang-Mills theory

The suggestion that the tower of observed vector mesons – when regarded as gauge fields of hidden local symmetries of chiral perturbation theory – is reasonably modeled as a Kaluza-Klein tower of D=5 Yang-Mills theory:

That the pure pion-Skyrmion-model of baryons is approximately the KK-reduction of instantons in D=5 Yang-Mills theory is already due to:

with a hyperbolic space-variant in:

Further discussion of this approximation:

The observation that the result of Atiyah-Manton 89 becomes an exact Kaluza-Klein construction of Skyrmions/baryons from D=5 instantons when the full KK-tower of vector mesons as in Son-Stephanov 03 is included into the Skyrmion model (see also there) is due to:

In the Sakai-Sugimoto model of holographic QCD the D=5 Yang-Mills theory of this hadron Kaluza-Klein theory is identified with the worldvolume-theory of D8-flavour branes intersected with D4-branes in an intersecting D-brane model:

Extensive review of this holographic/KK-theoretic-realization of quantum hadrodynamics from D=5 Yang-Mills theory is in:

Via the realization of D4/D8 brane bound states as instantons in the D8-brane worldvolume-theory (see there and there), this relates also to the model of baryons as wrapped D4-branes, originally due to

and further developed in the nuclear matrix model:

In relation to Yang-Mills monopoles:

Discussion, in this context, of D-term effects affecting hadron stability:

More on baryons in the Sakai-Sugimoto model of holographic QCD:

More on mesons in holographic QCD:

An alternative scenario of derivation of 4d Skyrmions by KK-compactification of D=5 Yang-Mills theory, now on a closed interval, motivated by M5-branes instead of by D4/D8-brane intersections as in the Sakai-Sugimoto model, is discussed in:


See also:

  • Y. H. Ahn, Sin Kyu Kang, Hyun Min Lee, Towards a Model of Quarks and Leptons (arXiv:2112.13392)

In the large NN limit

In the large N limit:

Last revised on May 8, 2020 at 08:11:35. See the history of this page for a list of all contributions to it.