What are baryons and baryonic matter

Baryons (from Greek βαρύς (barys) = heavy) are elementary particles that each consist of three quarks (or Antibaryons from three antiquarks each). The class of baryons includes protons and neutrons (collective term: nucleons) and a number of other, heavier particles (so-called hyperons). The name is derived from the Greek word barys (difficult), in analogy to the "light" leptons and the "medium" mesons.

Baryons are strongly interacting fermions, that is, they are described by the Fermi-Dirac statistics, whereby they obey Pauli's exclusion principle, and they are subject to the strong interaction through the quarks of which they are made. In addition, baryons are subject to weak interaction, gravity and, if they are charged, also to electromagnetic force.

A related class of elementary particles, the mesons, are each composed of a quark and an antiquark. In contrast to baryons, mesons are bosons. Baryons, together with mesons, form the hadrons family, the strongly interacting elementary particles.

The only baryon that is stable as a free particle is the proton (or antiproton), since according to the standard model of elementary particle physics the baryon number is an absolute conservation quantity and the proton is the lightest baryon with the baryon number 1 (or -1). The neutron decays if it is not bound with other protons and neutrons in the atomic nucleus.

Baryon multiplets

In 1964, Murray Gell-Mann and Yuval Ne’eman succeeded in converting the known baryons into a schema (den Eightfold way, English: Eightfold way) classify. From today's perspective, your train of thought is as follows:

The baryons are made up of three fundamental particles each, which Gell-Mann called quarks. The original quark hypothesis was based on three different quarks, the up, down and strange quarks (u, d and s quarks). The up and down quarks are combined to form an isospin doublet due to their similar masses. The strange quark differs from u- and d-quark primarily in its larger mass and a property called strangeness. All quarks are fermions with spin 1/2. The charge of the u-quark is 2/3 times the elementary charge, the charge of the d- and s-quark is (-1/3) times the elementary charge.

The idea now is that every way to put the quarks together corresponds to a baryon. The properties of the quarks determine the properties of the baryon. First of all, the three spins of the quarks can be coupled to a total spin of 1/2 or a total spin of 3/2. In the first case there are eight possibilities, limited by the Pauli principle, in the second case there are ten. The eight baryons with spin 1/2 form that Baryon octetwho have favourited ten baryons with spin 3/2 that Baryon decuplet. Since it is assumed that the quarks in the ground state do not have a relative total orbital angular momentum, the parity of all baryons is positive.


Let's start with the baryon octet. First of all, we can combine u and d quarks to form the combinations uud and udd. The combinations uuu and ddd are forbidden by the Pauli principle. In fact, there are two non-strange spin 1/2 baryons in nature, the proton and the neutron. The combination uud has a total charge of 1, so we assign it to the proton, so that is the neutron uddParticles. The isospins of the three quarks couple to 1/2, so the proton and neutron form an isospin doublet. (Illustrative: Since both combinations ud contained, the isospin is inherited directly from the surplus third quark.)

The combinations represent the stranded baryons uus, uds and dds to disposal. The isospins of the two non-stranded quarks couple to form a triplet (the sigma particle) and a singlet, the lambda.

The decouplet can also be explained in a similar way, although symmetrical quark combinations are also allowed here, for example the Δ++ With uuu. The Pauli principle, however, requires the introduction of a further degree of freedom, the so-called colour. This can be seen as follows: The Pauli principle postulates that wave functions of fermions must be antisymmetric. In the case of the baryon, this means that the wave function receives a minus sign as soon as the quantum numbers of two of the three particles involved are swapped. The wave function of a baryon has parts in spatial space, in spin space and in isospin space. The spatial wave function is for the Δ++ symmetrical, since the three up quarks are indistinguishable. The three spins 1/2 of the quarks involved couple to a total spin 3/2, the spin wave function is therefore also symmetrical. This applies analogously to the isospin wave function. The previously composite wave function of the Δ++ so is symmetrical. Therefore, in order to fulfill the Pauli principle, we have to postulate another quantum number for the quarks. This is the color: It can take on the states "red", "green" and "blue". We now also postulate that in the color space the quarks always combine to form an antisymmetric wave function. This can be clearly formulated as follows: Quarks always combine in such a way that the resulting particle is "white", for example in the baryon "red", "green" and "blue" result together "white". The Pauli principle is then fulfilled.

The baryons can be classified according to the above in a scheme in which the x-axis is given by the third component of the isospin and the y-axis is given by the strangeness. Furthermore, the axes charge and hypercharge can be placed diagonally. The experimentally confirmed Gell-Mann-Nishijima relation can be read from the position of the axes.

Since the different rows of the multiplets differ in the number of strange quarks, the mass difference between the strange and non-stranded quarks provides a measure of the mass splitting of the individual isospin multiples. Furthermore, there is a fundamental split between the masses in octets and decupplets, which can be traced back to the (color-magnetic) spin-spin interaction. The quark combination (uus) has different masses, depending on the spin (e.g. Σ + with spin 1/2 has m = 1189.37 MeV / c ^ 2 and Σ * + with spin 3/2 has m = 1382.8 MeV / c ^ 2). Unfortunately, this distinction is not made in the adjacent illustration of the decouplet. The small mass splitting within the isospin multiples (e.g. proton-neutron splitting approx. 1.3 MeV) can be partly explained by the different charges of the quarks involved.

The omega particle (quark content: sss) was not yet known when the eightfold way was postulated. However, its properties could be predicted from the model. The discovery of this particle at the predicted mass is one of the early successes of the Quark model.

In addition to the basic states of the baryons described here, there is also a huge number of excitation states, the so-called baryon resonances.

Today it is known that in addition to the previously mentioned light quarks there are three other so-called heavier quarks (charm, bottom and Top) gives. With these heavy quarks further baryons can be created. For example, by looking at the lambda particle (uds) replacing the strange quark with a charm quark, you get the Λc with a mass about 1200 MeV greater.


Baryon N Δ Λ Σ Ξ Ω
number d-, uQuarks 3 2 1 0
number s-, c-, b-, tQuarks 0 1 2 3
Isospin I. 1/2 3/2 0 1 1/2 0
State of charge (= 2I. + 1) 2 4 1 3 2 1

The names of the baryons depend on their quark content and the isospin. Baryons from the light quarks (d, u, s) are depending on the isospin and quark composition with the letters N (Nucleon), Δ, Λ, Σ, Ξ and Ω. For baryons with heavy quarks (c, b, t) no new symbols were introduced; instead, one uses indices.

  • a baryon of three u- and or d-Quarks is called nucleon (N) if it has isospin 1/2, and Δ if it has isospin 3/2. The terms proton (p) and neutron (n).
  • a baryon with two u- and or d-Quarks and spin 1/2 is a Λ (isospin 0) or Σ (isospin 1). When the third curd a c, b or t it is given as an index. For spin 3/2 either an asterisk is added or the mass in MeV / c ^ 2 is given in brackets.
  • a baryon with a u- or d-Quark and Spin 1/2 is a Ξ. For spin 3/2 either an asterisk is added or the mass in MeV / c ^ 2 is given in brackets. Quarks heavier than s are again given as an index. (Example: a baryon of the composition usc is a Ξc.)
  • a baryon without u- and d-Quark is an Ω. Quarks heavier than s are again given as an index.
  • for baryons with isopine> 0 (i.e. N, Δ, Σ) there are several states of charge, depending on how many u- or dQuarks are involved. Therefore, the electrical charge is also given there. (Example: a baryon with the composition uss is a Ξ0.)

state of research

The above-mentioned model for the baryon composition is incomplete according to the current state of research. Today we suspect that the mass, spin and other properties of the baryons cannot be read directly from the properties of the quarks involved. The spin of the three quarks in the proton only accounts for about a quarter of its total spin. For about 30 years there has been a quantum field theory for the strong interaction, i.e. the interaction between the quarks, quantum chromodynamics (QCD). However, this theory is difficult to handle and, especially in wide energy ranges, cannot be treated in terms of perturbation theory. The biggest unsolved question is still how the previously only postulated color inclusion can be derived from the fundamentals of QCD. Confinement) can be derived. This is the above-described fact that particles observable in nature are always "white", which in particular results in the unobservability of free quarks.

For theoretical treatment, one is therefore dependent on effective theories or Quark models. A frequently observed peculiarity of such quark models is the prediction of far more baryon states than those previously observed. The search for such missing resonances missing resonances) is one of the main fields of activity of experimental research on baryons. In addition, research is carried out on the electroweak properties (e.g. form factors) and the decay of baryons.

Baryonic matter in cosmology

In cosmology and astrophysics, baryonic matter is the name given to matter made up of atoms in order to distinguish it from dark matter, dark energy and electromagnetic radiation. In the visible universe there are more baryons than antibaryons, this asymmetry is called baryon asymmetry.

Further information

The quark composition, masses and lifetimes of the light baryons can be found under List of Baryons.

Measured values ​​relating to elementary particles are taken from the Particle Data Group collected and analyzed (pdg.lbl.gov; English).


  • Bogdan Povh et al., Particles and nuclei, 6th edition. Springer-Verlag GmbH, 2004, ISBN 3-540-21065-2

Category: elementary particles