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((Short description|Quantum number relating the quantity of quarks and antiquarks in a system))
((more citations needed|date=July 2013))
((Flavour_quantum_numbers))

In [[particle physics]], the '''baryon number''' is a [[Conservation law (physics)|strictly conserved]]<!--No processes ever observed violate baryon number--> additive [[quantum number]] of a [[Quantum mechanics|system]]. It is defined as
<math display="block">B = \frac{1}{3}(n_\text{q} - n_{\rm \overline q}), </math>
where ((tmath|n_{\rm q} )) is the number of [[quark]]s, and ((tmath|n_{\rm \overline q} )) is the number of [[antiquark]]s. [[Baryon]]s (three quarks) have a baryon number of +1, [[meson]]s (one quark, one antiquark) have a baryon number of 0, and antibaryons (three antiquarks) have a baryon number of &minus;1. [[Exotic hadron]]s like [[pentaquark]]s (four quarks, one antiquark) and [[tetraquark]]s (two quarks, two antiquarks) are also classified as baryons and mesons depending on their baryon number.

== Baryon number vs. quark number ==
((See also|Color charge))

Quarks carry not only [[electric charge]], but also [[charge (physics)|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".<ref name="hyerphys">((cite web |last=Nave |first=R. |author-link=Rod Nave |title=The Color Force |url=http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/color.html |access-date=May 29, 2021))</ref>

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 &minus;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 hadron]]s 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|LHCb collaboration]] at [[CERN]] reported results consistent with pentaquark states in the decay of [[bottom Lambda baryon]]s (((nowrap|Λ((su|p=0|b=b))))).<ref name="LHCb2015">
((cite journal
 |author=R. Aaij et al. ([[LHCb|LHCb collaboration]])
 |year=2015
 |title=Observation of J/ψp resonances consistent with pentaquark states in Λ((su|p=0|b=b))→J/ψK<sup>−</sup>p decays
 |journal=[[Physical Review Letters]]
 |volume=115 |issue=7
 |pages=072001
 |doi=10.1103/PhysRevLett.115.072001
 |pmid=26317714
 |arxiv = 1507.03414 |bibcode = 2015PhRvL.115g2001A |s2cid=119204136
))</ref>

== Particles not formed of quarks ==

Particles without any quarks have a baryon number of zero. Such particles are
* [[lepton]]s – the [[electron]], [[muon]], [[tau (particle)|tauon]], and their corresponding [[neutrino]]s
* [[vector boson]]s – the [[photon]], [[W and Z bosons]], [[gluons]]
* [[scalar boson]] – the [[Higgs boson]] 
* second-order tensor [[boson]] – the hypothetical [[graviton]]

== Conservation ==
((See also|Conservation law (physics)))

The baryon number is conserved in all the [[fundamental force|interactions]] of the [[Standard Model]], with one possible exception. The conservation is due to <math>U(1)_V</math> global symmetry of the QCD Lagrangian.<ref>((Cite web |last=Tong |first=David |author-link=David Tong (physicist) |title=David Tong: Lectures on Gauge Theory - DAMTP |url=http://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf |website=DAMTP |page=244 |format=PDF))</ref> '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 interaction]]s;<ref>((Cite journal |last='t Hooft |first=G. |author-link=Gerard 't Hooft |date=1976-07-05 |title=Symmetry Breaking through Bell-Jackiw Anomalies |url=http://dx.doi.org/10.1103/physrevlett.37.8 |journal=Physical Review Letters |volume=37 |issue=1 |pages=8–11 |doi=10.1103/physrevlett.37.8 |issn=0031-9007))</ref> however, [[sphaleron]]s are not all that common and could occur at high energy and temperature levels and can explain electroweak baryogenesis and [[leptogenesis (physics)|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 [[lepton]]s  and antiquarks (see [[B − L|''B'' − ''L'']]), thus violating the conservation of both baryon and [[lepton number]]s.<ref>((cite book |last=Griffiths |first=David |authorlink=David Griffiths (physicist) |title=Introduction to Elementary Particles |edition=2nd |year=2008 |publisher=John Wiley & Sons |location=New York |isbn=9783527618477 |url=https://books.google.com/books?id=Wb9DYrjcoKAC&q=%22In+the+grand+unified+theories+new+interactions+are+contemplated%2C+permitting+decays+such+as%22+%22in+which+baryon+number+and+lepton+number+change.%22&pg=PA77 |page=77 |quote=In the grand unified theories new interactions are contemplated, permitting decays such as ((SubatomicParticle|link=yes|Proton+)) → ((SubatomicParticle|link=yes|Positron)) + ((SubatomicParticle|link=yes|Pion0)) or ((SubatomicParticle|link=yes|Proton+)) → ((SubatomicParticle|link=yes|muon antineutrino)) + ((SubatomicParticle|link=yes|Pion+)) in which baryon number and lepton number change.))</ref>  [[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]].<ref>Harlow, Daniel and Ooguri, Hirosi", "Symmetries in quantum field theory and quantum gravity", hep-th 1810.05338 (2018)</ref> It is expected in general that quantum gravitational effects violate the conservation of all charges associated to global symmetries.<ref>Kallosh, Renata and Linde, Andrei D. and Linde, Dmitri A. and Susskind, Leonard", "Gravity and global symmetries", Phys. Rev. D 52 (1995) 912-935</ref> The violation of conservation of baryon number led [[John Archibald Wheeler]] to speculate on a [[mutability|principle of mutability]] for all physical properties.<ref>((citation| title=John Archibald Wheeler: A Few Highlights of His Contributions to Physics| editor=[[Kip S. Thorne]]| date=October 28, 1985| work=Between Quantum and Cosmos|pages=9))</ref>

== See also ==
((cols))
* [[Lepton number]]
* [[Flavour (particle physics)]]
* [[Isospin]]
* [[Hypercharge]]
* [[Proton decay]]
* [[B − L|''B'' − ''L'']]
((colend))

== References ==
((Reflist))

((Authority control))

[[Category:Baryons]]
[[Category:Conservation laws]]
[[Category:Nuclear physics]]
[[Category:Quantum chromodynamics]]
[[Category:Quarks]]
[[Category:Standard Model]]
[[Category:Flavour (particle physics)]]

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