Definition [1]

​

In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3).[1] Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classified as fermions because they have half-integer spin.

​

The name "baryon", introduced by Abraham Pais,[2] comes from the Greek word for "heavy" (βαρύς, barýs), because, at the time of their naming, most known elementary particles had lower masses than the baryons. Each baryon has a corresponding antiparticle (antibaryon) where their corresponding antiquarks replace quarks. For example, a proton is made of two up quarks and one down quark; and its corresponding antiparticle, the antiproton, is made of two up antiquarks and one down antiquark.

​

Because they are composed of quarks, baryons participate in the strong interaction, which is mediated by particles known as gluons. The most familiar baryons are protons and neutrons, both of which contain three quarks, and for this reason they are sometimes called triquarks. These particles make up most of the mass of the visible matter in the universe and compose the nucleus of every atom. (Electrons, the other major component of the atom, are members of a different family of particles called leptons; leptons do not interact via the strong force.) Exotic baryons containing five quarks, called pentaquarks, have also been discovered and studied.

​

A census of the Universe's baryons indicates that 10% of them could be found inside galaxies, 50 to 60% in the circumgalactic medium,[3] and the remaining 30 to 40% could be located in the warm–hot intergalactic medium (WHIM).[4]

​

Isospin and charge

​

The concept of isospin was first proposed by Werner Heisenberg in 1932 to explain the similarities between protons and neutrons under the strong interaction.[11] Although they had different electric charges, their masses were so similar that physicists believed they were the same particle. The different electric charges were explained as being the result of some unknown excitation similar to spin. This unknown excitation was later dubbed isospin by Eugene Wigner in 1937. [5]

​

This belief lasted until Murray Gell-Mann proposed the quark model in 1964 (containing originally only the u, d, and s quarks). [6]  The success of the isospin model is now understood to be the result of the similar masses of u and d quarks. Since u and d quarks have similar masses, particles made of the same number then also have similar masses. The exact specific u and d quark composition determines the charge, as u quarks carry charge +2/3 while d quarks carry charge −1/3. For example, the four Deltas all have different charges (Δ++(uuu), 
Δ+(uud), Δ0(udd), Δ−(ddd)), but have similar masses (~1,232 MeV/c2) as they are each made of a combination of three u or d quarks. Under the isospin model, they were considered to be a single particle in different charged states.

​

The mathematics of isospin was modeled after that of spin. Isospin projections varied in increments of 1 just like those of spin, and to each projection was associated a "charged state". Since the "Delta particle" had four "charged states", it was said to be of isospin I = 3/2. Its "charged states" Δ++, Δ+, Δ0, and Δ−, corresponded to the isospin projections I3 = +3/2, I3 = +1/2, I3 = −1/2, and I3 = −3/2, respectively. Another example is the "nucleon particle". As there were two nucleon "charged states", it was said to be of isospin 1/2. The positive nucleon N+(proton) was identified with I3 = +1/2 and the neutral nucleon N0(neutron) with I3 = −1/2. [7]  It was later noted that the isospin projections were related to the up and down quark content of particles by the relation:

​

​

​

​

​

​

where the n's are the number of up and down quarks and antiquarks.

In the "isospin picture", the four Deltas and the two nucleons were thought to be the different states of two particles. However, in the quark model, Deltas are different states of nucleons (the N++ or N− are forbidden by Pauli's exclusion principle). Isospin, although conveying an inaccurate picture of things, is still used to classify baryons, leading to unnatural and often confusing nomenclature.

​

Flavour quantum number

​

The strangeness flavour quantum number S (not to be confused with spin) was noticed to go up and down along with particle mass. The higher the mass, the lower the strangeness (the more s quarks). Particles could be described with isospin projections (related to charge) and strangeness (mass) (see the uds octet and decuplet figures on the right). As other quarks were discovered, new quantum numbers were made to have similar description of udc and udb octets and decuplets. Since only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers works well only for octet and decuplet made of one u, one d, and one other quark, and breaks down for the other octets and decuplets (for example, ucb octet and decuplet). If the quarks all had the same mass, their behaviour would be called symmetric, as they would all behave in the same way to the strong interaction. Since quarks do not have the same mass, they do not interact in the same way (exactly like an electron placed in an electric field will accelerate more than a proton placed in the same field because of its lighter mass), and the symmetry is said to be broken.

​

It was noted that charge (Q) was related to the isospin projection (I3), the baryon number (B) and flavour quantum numbers (S, C, B′, T) by the Gell-Mann–Nishijima formula :  [7]

​

​

​

​

​

​

where S, C, B′, and T represent the strangeness, charm, bottomness and topness flavour quantum numbers, respectively. They are related to the number of strange, charm, bottom, and top quarks and antiquark according to the relations:

​

​

​

​

​

​

​

​

​

meaning that the Gell-Mann–Nishijima formula is equivalent to the expression of charge in terms of quark content:

​

​

​

​

​

​

Spin, orbital angular momentum, and total angular momentum

​

Spin (quantum number S) is a vector quantity that represents the "intrinsic" angular momentum of a particle. It comes in increments of 1/2 ħ (pronounced "h-bar"). The ħ is often dropped because it is the "fundamental" unit of spin, and it is implied that "spin 1" means "spin 1 ħ". In some systems of natural units, ħ is chosen to be 1, and therefore does not appear anywhere.

​

Quarks are fermionic particles of spin 1/2 (S = 1/2). Because spin projections vary in increments of 1 (that is 1 ħ), a single quark has a spin vector of length 1/2, and has two spin projections (Sz = +1/2 and Sz = −1/2). Two quarks can have their spins aligned, in which case the two spin vectors add to make a vector of length S = 1 and three spin projections (Sz = +1, Sz = 0, and Sz = −1). If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and has only one spin projection (Sz = 0), etc. Since baryons are made of three quarks, their spin vectors can add to make a vector of length S = 3/2, which has four spin projections (Sz = +3/2, Sz = +1/2, Sz = −1/2, and Sz = −3/2), or a vector of length S = 1/2 with two spin projections (Sz = +1/2, and Sz = −1/2).[8]

​

There is another quantity of angular momentum, called the orbital angular momentum (azimuthal quantum number L), that comes in increments of 1 ħ, which represent the angular moment due to quarks orbiting around each other. The total angular momentum (total angular momentum quantum number J) of a particle is therefore the combination of intrinsic angular momentum (spin) and orbital angular momentum. It can take any value from J = |L − S| to J = |L + S|, in increments of 1.

​

​

​

​

​