# Baryon number

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In particle physics, the baryon number is a strictly conserved additive quantum number of a system. It is defined as

## Contents

${\displaystyle B={\frac {1}{3}}\left(n_{\text{q}}-n_{\bar {\text{q}}}\right),}$

where nq is the number of quarks, and nq is the number of antiquarks. Baryons (three quarks) have a baryon number of +1, mesons (one quark, one antiquark) have a baryon number of 0, and antibaryons (three antiquarks) have a baryon number of 1. Exotic hadrons like pentaquarks (four quarks, one antiquark) and tetraquarks (two quarks, two antiquarks) are also classified as baryons and mesons depending on their baryon number.

## Baryon number vs. quark number

Quarks carry not only electric charge, but also charges such as color charge and weak isospin. Because of a phenomenon known as color confinement , a hadron cannot have a net color charge; that is, the total color charge of a particle has to be zero ("white"). A quark can have one of three "colors", dubbed "red", "green", and "blue"; while an antiquark may be either "anti-red", "anti-green" or "anti-blue".

For normal hadrons, a white color can thus be achieved in one of three ways:

• A quark of one color with an antiquark of the corresponding anticolor, giving a meson with baryon number 0,
• Three quarks of different colors, giving a baryon with baryon number +1,
• Three antiquarks of different anticolors, giving an antibaryon with baryon number 1.

The baryon number was defined long before the quark model was established, so rather than changing the definitions, particle physicists simply gave quarks one third the baryon number. Nowadays it might be more accurate to speak of the conservation of quark number.

In theory, exotic hadrons can be formed by adding pairs of quarks and antiquarks, provided that each pair has a matching color/anticolor. For example, a pentaquark (four quarks, one antiquark) could have the individual quark colors: red, green, blue, blue, and antiblue. In 2015, the LHCb collaboration at CERN reported results consistent with pentaquark states in the decay of bottom Lambda baryons (Λ0
b
). [1]

## Particles not formed of quarks

Particles without any quarks have a baryon number of zero. Such particles are

## Conservation

The baryon number is conserved in all the interactions of the Standard Model, with one possible exception. 'Conserved' means that the sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction. The one exception is the hypothesized Adler–Bell–Jackiw anomaly in electroweak interactions; [2] however, sphalerons are not all that common and could occur at high energy and temperature levels and can explain electroweak baryogenesis and leptogenesis. Electroweak sphalerons can only change the baryon and/or lepton number by 3 or multiples of 3 (collision of three baryons into three leptons/antileptons and vice versa). No experimental evidence of sphalerons has yet been observed.

The hypothetical concepts of grand unified theory (GUT) models and supersymmetry allows for the changing of a baryon into leptons and antiquarks (see BL), thus violating the conservation of both baryon and lepton numbers. [3] Proton decay would be an example of such a process taking place, but has never been observed.

The conservation of baryon number is not consistent with the physics of black hole evaporation via Hawking radiation. [4] It is expected in general that quantum gravitational effects violate the conservation of all charges associated to global symmetries. [5] The violation of conservation of baryon number led John Archibald Wheeler to speculate on a principle of mutability for all physical properties. [6]

## Related Research Articles

In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks. 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.

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In particle physics, a hadron is a subatomic composite particle made of two or more quarks held together by the strong force in a similar way as molecules are held together by the electromagnetic force. Most of the mass of ordinary matter comes from two hadrons: the proton and the neutron.

In particle physics, mesons are hadronic subatomic particles composed of an equal number of quarks and antiquarks, usually one of each, bound together by strong interactions. Because mesons are composed of quark subparticles, they have a meaningful physical size, a diameter of roughly one femtometer (1×10−15 m), which is about 1.2 times the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond. Heavier mesons decay to lighter mesons and ultimately to stable electrons, neutrinos and photons.

A quark is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly observable matter is composed of up quarks, down quarks and electrons. Owing to a phenomenon known as color confinement, quarks are never found in isolation; they can be found only within hadrons, which include baryons and mesons, or in quark–gluon plasmas. For this reason, much of what is known about quarks has been drawn from observations of hadrons.

Color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics (QCD).

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In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons. The total energy and momentum of the initial pair are conserved in the process and distributed among a set of other particles in the final state. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of such an original pair are zero. Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy and conservation of momentum are obeyed.

The W and Z bosons are together known as the weak or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are
W+
,
W
, and
Z0
. The
W±
bosons have either a positive or negative electric charge of 1 elementary charge and are each other's antiparticles. The
Z0
boson is electrically neutral and is its own antiparticle. The three particles have a spin of 1. The
W±
bosons have a magnetic moment, but the
Z0
has none. All three of these particles are very short-lived, with a half-life of about 3×10−25 s. Their experimental discovery was pivotal in establishing what is now called the Standard Model of particle physics.

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Exotic hadrons are subatomic particles composed of quarks and gluons, but which - unlike "well-known" hadrons such as protons, neutrons and mesons - consist of more than three valence quarks. By contrast, "ordinary" hadrons contain just two or three quarks. Hadrons with explicit valence gluon content would also be considered exotic. In theory, there is no limit on the number of quarks in a hadron, as long as the hadron's color charge is white, or color-neutral.

In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU(3)", or the Eightfold Way, the successful classification scheme organizing the large number of lighter hadrons that were being discovered starting in the 1950s and continuing through the 1960s. It received experimental verification beginning in the late 1960s and is a valid effective classification of them to date. The model was independently proposed by physicists Murray Gell-Mann, who dubbed them "quarks" in a concise paper, and George Zweig, who suggested "aces" in a longer manuscript. André Petermann also touched upon the central ideas from 1963 to 1965, without as much quantitative substantiation. Today, the model has essentially been absorbed as a component of the established quantum field theory of strong and electroweak particle interactions, dubbed the Standard Model.

The timeline of particle physics lists the sequence of particle physics theories and discoveries in chronological order. The most modern developments follow the scientific development of the discipline of particle physics.

In particle physics, the X and Y bosons are hypothetical elementary particles analogous to the W and Z bosons, but corresponding to a new type of force predicted by the Georgi–Glashow model, a grand unified theory.

## References

1. R. Aaij et al. (LHCb collaboration) (2015). "Observation of J/ψp resonances consistent with pentaquark states in Λ0
b
→J/ψKp decays". Physical Review Letters . 115 (7): 072001. arXiv:. Bibcode:2015PhRvL.115g2001A. doi:10.1103/PhysRevLett.115.072001. PMID   26317714. S2CID   119204136.
2. G. ’t Hooft, "Symmetry breaking through Bell-Jackiw anomalies", Phys. Rev. Lett. 37 (1976) 8
3. Griffiths, David (2008). Introduction to Elementary Particles (2nd ed.). New York: John Wiley & Sons. p. 77. ISBN   9783527618477. In the grand unified theories new interactions are contemplated, permitting decays such as
p+

e+
+
π0
or
p+

ν
μ
+
π+
in which baryon number and lepton number change.
4. Harlow, Daniel and Ooguri, Hirosi", "Symmetries in quantum field theory and quantum gravity", hep-th 1810.05338 (2018)
5. Kallosh, Renata and Linde, Andrei D. and Linde, Dmitri A. and Susskind, Leonard", "Gravity and global symmetries", Phys. Rev. D 52 (1995) 912-935
6. Kip S. Thorne, ed. (October 28, 1985), "John Archibald Wheeler: A Few Highlights of His Contributions to Physics", Between Quantum and Cosmos, p. 9