Definitions

c quark

List of baryons

This list is of all known and predicted baryons. See list of particles for a more detailed list of particles found in particle physics.

Baryons, being composed of quarks, are part of the subatomic particle family called the hadrons. Baryons are the sub-family of hadrons with a baryon number of 1, as opposed to the mesons which are the sub-family of hadrons with a baryon number of 0. Since baryons are composed of quarks they participate in the strong interaction, in contrast to leptons which are not composed of quarks and as such do not participate in the strong interaction. The protons and neutrons that make up most of the mass of the visible matter in the universe are both baryons, whereas electrons (the other major component of atoms) are leptons.

Traditionally, baryons were believed to be composed of only three quarks (triquarks) (quarks have a baryon number of and antiquarks have a baryon number of −). Recently, physicists have reported the existence of pentaquarks – "exotic" baryons made of four quarks and one antiquark – but their existence is not generally accepted within the particle physics community. Each baryon has a corresponding antiparticle (antibaryon) where quarks are replaced by their corresponding antiquarks and vice versa. For example, a proton is made of two up quarks and one down quark; thus, the antiproton is made of two up antiquarks and one down antiquark.

Overview

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  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, therefore does not appear anywhere.

Quarks are fermionic particles of spin (S = ). Because spin projections varies in increments of 1 (that is 1 ħ), a single quark has a spin vector of length , and has two spin projections (Sz = + and Sz = −). 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 =  which has four spin projections (Sz = +, Sz = +, Sz = −, and Sz = −), or a vector of length S =  with two spin projections (Sz = +, and Sz = −).

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

Particles physicists are most interested in baryons with no orbital angular momentum (L = 0), therefore the two groups of baryons most studied are the S = ; L = 0 and S = ; L = 0, which corresponds to J =  and J = , although they are not the only ones. It is also possible to obtain J =  particles from S =  and L = 1. How to distinguish between the S = , L = 0 and S = , L = 1 baryons is an active area of research in baryon spectroscopy.

Parity

Parity refers to whether the wavefunction of a particle is even or odd. A positive parity (P = +) means that the wavefunction is even, while a negative (P = −) means the wavefunction is odd.

Psi(x) = x^3e^{-x^2} is an odd 1-dimensional wavefunction because Psi(x)=-Psi(-x).
Psi(x) = x^4e^{-x^2} is an even 1-dimensional wavefunction because Psi(x)=Psi(-x).

For baryons, the parity is related to the orbital angular momentum by the relation:

P=(-1)^L.

Physicists are often particularly interested in baryons with no orbital angular momentum (L = 0), which are of even parity (P = +).

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. Although they had different electric charges, their masses were so similar that physicists believed they were actually 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.

This belief lasted until Murray Gell-Mann proposed the quark model in 1964 (containing originally only the u, d, and s quarks). The success of the isospin model is now understood to be the result of the similar masses of the u and d quarks. Since the 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 + while d quarks carry charge −. For example the four Deltas all have different charges ((uuu), (uud), (udd), (ddd)), but have similar masses (~1,232 MeV/c2) as they are each made of a total of three u and 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 "chared state". Since the "Delta particle" had four "charged states", it was said to be of isospin I = . Its "charged states" , , , and , corresponded to the isospin projections Iz = +, Iz = +, Iz = −, and Iz = − respectively. Another example is the "nucleon particle". As there were two nucleon "charged states", it was said to be of isospin . The positive nucleon (proton) was identified with Iz = + and the neutral nucleon (neutron) with Iz = −. It was later noted that the isospin projections were related to the up and down quark content of particles by the relation:

I_z=frac{1}{2}[(n_u-n_bar{u})-(n_d-n_bar{d})],
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 numbers

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 where 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 only works well 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 exactly the same way with respect 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 (Iz), the baryon number (B) and flavour quantum numbers (S, C, B′, T) by the Gell-Mann–Nishijima formula:

Q=I_z+frac{1}{2}(B+S+C+B^prime+T),

where S, C, B′, and T represent the strangeness, charmness, 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:

S=-(n_s-n_bar{s})
C=+(n_c-n_bar{c})
B^prime=-(n_b-n_bar{b})
T=+(n_t-n_bar{t}),

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

Q=frac{2}{3}[(n_u-n_bar{u})+(n_c-n_bar{c})+(n_t-n_bar{t})]-frac{1}{3}[(n_d-n_bar{d})+(n_s-n_bar{s})+(n_b-n_bar{b})].

Particle classification

Baryons are classified into groups according to their isospin (I) values and quark (q) content. There are six groups of triquarks – nucleon Delta Lambda Sigma Xi and Omega (). The rules for classification are defined by the Particle Data Group. These rules consider the up down and strange quarks to be light and the charm bottom and top to be heavy. The rules cover all the particles that can be made from three of each of the six quarks, even though baryons made of t quarks are not expected to exist because of the t quark's short lifetime. The rules do not cover pentaquarks.

  • Baryons with three and/or quarks are 's (I = ) or 's (I = ).
  • Baryons with two and/or quarks are 's (I = 0) or 's (I = 1). If the third quark is heavy, its identity is given by a subscript.
  • Baryons with one or quark are 's (I = ). One or two subscripts are used if one or both of the remaining quarks are heavy.
  • Baryons with no or quarks are 's (I = 0), and subscripts indicate any heavy quark content.
  • Baryons that decay strongly have their masses as part of their names. For example, Σ0 does not decay strongly, but Δ++(1232) does.

It is also a widespread (but not universal) practice to follow some additional rules when distinguishing between some states which would otherwise have the same symbol.

  • Baryons in total angular momentum J =  configuration which have the same symbols as their J =  counterparts are denoted by an asterisk ( * ).
  • Two baryons can be made of three different quarks in J =  configuration. In this case, a prime ( ′ ) is used to distinguish between them.

* Exception: When two of the three quarks are one up and one down quark, one baryon is dubbed Λ while the other is dubbed Σ.

Quarks carry charge, so knowing the charge of a particle indirectly gives the quark content. For example, the rules above say that a contains a c quark and some combination of two u and/or d quarks. The c quark as a charge of (Q = +), therefore the other two must be a u quark (Q = +), and a d quark (Q = −) to have the correct total charge (Q = 1).

Lists of baryons

These lists detail all known and predicted triquark baryons in total angular momentum J =  and J =  configurations with positive parity, as well as all the reported pentaquark baryons.

The symbols encountered in these lists are: I (isospin), J (total angular momentum), P (parity), u (up quark), d (down quark), s (strange quark), c (charm quark), b (bottom), Q (charge), B (baryon number), S (strangeness), C (charmness), B′ (bottomness), as well as a wide array of subatomic particles (hover for name).

Antiparticles are not listed in the tables; however, they simply would have all quarks changed to antiquarks (and antiquarks changed to quarks), and Q, B, S, C, B′, would be of opposite signs. Particles with next to their names have been predicted by the standard model but not yet observed. I, J, and P values marked with *'s have not been firmly established by experiments, but are predicted by the quark model and are consistent with the measurements.

JP = + baryons (triquarks)

JP = + baryons (triquarks)
Particle name Symbol Quark
content
Rest mass (MeV/c2) I JP Q (e) S C B' Mean lifetime (s) Commonly decays to
nucleon/proton / / 0,938.272 029 ± 0.000 080 + +1 0 0 0 Stable Unobserved
nucleon/neutron / / 0,939.565 360 ± 0.000 081 + 0 0 0 0 885.7 ± 0.8
Lambda 1,115.683 ± 0.006 0 + 0 −1 0 0 2.631 ± 0.020 × 10−10
charmed Lambda 2,286.46 ± 0.14 0 + +1 0 +1 0 2.00 ± 0.06 × 10−13 See decay modes
bottom Lambda 5,620.2 ± 1.6 0* +* 0 0 0 −1  × 10−12 See decay modes
Sigma 1,189.37 ± 0.07 1 + +1 −1 0 0 8.018 ± 0.026 × 10−11
Sigma 1,192.642 ± 0.024 1 + 0 −1 0 0 7.4 ± 0.7 × 10−20
Sigma 1,197.449 ± 0.030 1 + −1 −1 0 0 1.479 ± 0.011 × 10−10
charmed Sigma (2455) 2,454.02 ± 0.18 1 +* +2 0 +1 0 Unknown
charmed Sigma (2455) 2,452.9 ± 0.4 1 +* +1 0 +1 0 Unknown
charmed Sigma (2455) 2,453.76 ± 0.18 1 +* 0 0 +1 0 Unknown
bottom Sigma (?) 1* +* +1 0 0 −1 Unknown
bottom Sigma (?) Unknown 1* +* 0 0 0 −1 Unknown Unknown
bottom Sigma (?) 5,815.2 ± 2.7 1* +* −1 0 0 −1 Unknown
Xi 1,314.86 ± 0.20 +* 0 −2 0 0 2.90 ± 0.09 × 10−10
Xi 1,321.71 ± 0.07 +* −1 −2 0 0 1.639 ± 0.015 × 10−10
charmed Xi 2,467.9 ± 0.4 +* +1 −1 +1 0 4.42 ± 0.26 × 10−13 See decay modes
charmed Xi 2,471.0 ± 0.4 +* 0 −1 +1 0  × 10−13 See decay modes
charmed Xi prime 2,575.7 ± 3.1 +* +1 −1 +1 0 Unknown
charmed Xi prime 2,578.0 ± 2.9 +* +1 −1 +1 0 Unknown
double charmed Xi Unknown * +* +2 0 +2 0 Unknown Unknown
double charmed Xi 3,518.9 ± 0.9 * +* +1 0 +2 0 < 3.3 × 10−14 or
bottom Xi
(or Cascade B)
Unknown * +* 0 −1 0 −1  × 10−12 See decay modes
bottom Xi
(or Cascade B)
5,792.9 ± 4.2 * +* −1 −1 0 −1  × 10−12 See decay modes
(
bottom Xi prime Unknown 0* +* 0 −1 0 −1 Unknown Unknown
bottom Xi prime Unknown 0* +* 0 −1 0 −1 Unknown Unknown
double bottom Xi Unknown * +* 0 0 0 −2 Unknown Unknown
double bottom Xi Unknown * +* −1 0 0 −2 Unknown Unknown
charmed bottom Xi Unknown * + +1 0 +1 −1 Unknown Unknown
charmed bottom Xi Unknown * +* 0 0 +1 −1 Unknown Unknown
charmed bottom Xi prime Unknown 0* + +1 0 +1 −1 Unknown Unknown
charmed bottom Xi prime Unknown 0* + +1 0 +1 −1 Unknown Unknown
charmed Omega 2,697.5 ± 2.6 0 +* 0 −2 +1 0 6.9 ± 1.2 × 10−14 See decay modes
bottom Omega 6,165 ± 16 0* +* −1 −2 0 −1 Unknown (
double charmed Omega Unknown 0* +* +1 −1 +2 0 Unknown Unknown
charmed bottom Omega Unknown 0* +* 0 −1 +1 −1 Unknown Unknown
charmed bottom Omega prime Unknown 0* +* 0 −1 +1 −1 Unknown Unknown
double bottom Omega Unknown 0* +* −1 −1 0 −2 Unknown Unknown
double charmed bottom Omega Unknown 0* +* +1 0 +2 −1 Unknown Unknown
charmed double bottom Omega Unknown 0* +* 0 0 +1 −2 Unknown Unknown
[a] The masses of the proton and neutron are known with much better precision in atomic mass units (u) than in Electron volt/c2, due to the relatively poorly known value of the elementary charge. In atomic mass unit, the mass of the proton is 1.007 276 466 88(13) u while that of the neutron is 1.008 664 915 60(55) u.
[b] At least 1035 years. See proton decay.
[c] For free neutrons; in most common nuclei, neutrons are stable.
[d] The specific values of the name has not been decided yet, but will likely be close to (5810).
[e] Some controversy exists about this data.
[f] This is actually a measurement of the average lifetime of b-baryons that decay to a jet containing a same sign pair. Presumably the mix is mainly , with some .

JP = + baryons (triquarks)

JP = + baryons (triquarks)
Particle name Symbol Quark
content
Rest mass (MeV/c2) I JP Q (e) S C B' Mean lifetime (s) Commonly decays to
Delta (1232) 1,232 ± 1 + +2 0 0 0 6 × 10−24
Delta (1232) 1,232 ± 1 + +1 0 0 0 6 × 10−24
Delta (1232) 1,232 ± 1 + 0 0 0 0 6 × 10−24
Delta (1232) 1,232 ± 1 + −1 0 0 0 6 × 10−24
Sigma (1385) 1,382.8 ± 0.4 1 + +1 −1 0 0 Unknown

Sigma (1385) 1,383.7 ± 1.0 1 + 0 −1 0 0 Unknown

Sigma (1385) 1,387.2 ± 0.5 1 + −1 −1 0 0 Unknown

charmed Sigma (2520) 2,518.4 ± 0.6 1 +* +2 0 +1 0 Unknown
charmed Sigma (2520) 2,517.5 ± 2.3 1 +* +1 0 +1 0 Unknown
charmed Sigma (2520) 2,518.0 ± 0.5 1 +* 0 0 +1 0 Unknown
bottom Sigma Unknown 1* +* +1 0 0 −1 Unknown Unknown
bottom Sigma Unknown 1* +* 0 0 0 −1 Unknown Unknown
bottom Sigma Unknown 1* +* −1 0 0 −1 Unknown Unknown
Xi (1530) 1,531.80 ± 0.32 + 0 −2 0 0 Unknown
Xi (1530) 1,535.0 ± 0.6 + −1 −2 0 0 Unknown
charmed Xi (2645) 2,646.6 ± 1.4 +* +1 −1 +1 0 Unknown
charmed Xi (2645) 2,646.1 ± 1.2 +* 0 −1 +1 0 Unknown
double charmed Xi Unknown * +* +2 0 +2 0 Unknown Unknown
double charmed Xi Unknown * +* +1 0 +2 0 Unknown Unknown
bottom Xi Unknown * +* 0 −1 0 −1 Unknown Unknown
bottom Xi Unknown * +* −1 −1 0 −1 Unknown Unknown
double bottom Xi Unknown * +* 0 0 0 −2 Unknown Unknown
double bottom Xi Unknown * +* −1 0 0 −2 Unknown Unknown
charmed bottom Xi Unknown * +* +1 0 +1 −1 Unknown Unknown
charmed bottom Xi Unknown * +* 0 0 +1 −1 Unknown Unknown
Omega 1,672.45 ± 0.29 0 + −1 −3 0 0 8.21 ± 0.11 × 10−11 or
or

charmed Omega (2770) 2,768.3 ± 1.5 0 +* 0 −2 +1 0 Unknown
bottom Omega Unknown 0* +* −1 −2 0 −1 Unknown Unknown
double charmed Omega Unknown 0* +* +1 −1 +2 0 Unknown Unknown
charmed bottom Omega Unknown 0* +* 0 −1 +1 −1 Unknown Unknown
double bottom Omega Unknown 0* +* −1 −1 0 −2 Unknown Unknown
triple charmed Omega Unknown 0* +* +2 0 +3 0 Unknown Unknown
double charmed bottom Omega Unknown 0* +* +1 0 +2 −1 Unknown Unknown
charmed double bottom Omega Unknown 0* +* 0 0 +1 −2 Unknown Unknown
triple bottom Omega Unknown 0 +* −1 0 0 −3 Unknown Unknown

Exotic baryons (pentaquarks)

This lists details pentaquarks reported to exist. However, other groups have looked for them and reported to have found nothing. Data is controversial to the point that the existence of pentaquarks is not generally accepted.

Exotic baryons (pentaquarks)
Particle name Symbol Quark
content
Rest mass (MeV/c2) I JP Q (e) S C B' Mean lifetime (s) Commonly decays to
Theta (1540) 1,533.6 ± 2.4 0 Unknown +1 +1 0 0 Unknown or
charmed Theta (3100) 3,099 ± 8 0 Unknown 0 0 −1 0 Unknown Unknown
Phi (1860) 1,862 ± 2 Unknown 0 −2 0 0 Unknown Unknown

See also

References

References

Further reading

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