Editing Baryon number

{{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 (B)''' is an <!--Baryon number violation has never been observed. Despite there being much theoretical support--> 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 '''B''' = +1, [[meson]]s (one quark, one antiquark) have '''B''' = 0, and antibaryons (three antiquarks) have '''B''' = &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. In the [[Standard Model|standard model]] '''B''' conservation is an accidental symmetry<ref>{{Citation |last1=Altmannshofer |first1=Wolfgang |title=Gauging the accidental symmetries of the standard model, and implications for the flavor anomalies |date=2019-09-18 |url=https://arxiv.org/abs/1909.02021 |access-date=2025-03-18 |arxiv=1909.02021 |last2=Davighi |first2=Joe |last3=Nardecchia |first3=Marco|journal=Physical Review D |volume=101 |page=015004 |doi=10.1103/PhysRevD.101.015004 }}</ref> which means that it appears in the [[Standard Model|standard model]] but is often violated when going beyond it. [[Physics beyond the Standard Model]] theories that contain baryon number violation are, for example, Standard Model with extra dimensions,<ref name=":0">{{Cite journal |last1=Addazi |first1=A |last2=Anderson |first2=K |last3=Ansell |first3=S |last4=Babu |first4=K S |last5=Barrow |first5=J L |last6=Baxter |first6=D V |last7=Bentley |first7=P M |last8=Berezhiani |first8=Z |last9=Bevilacqua |first9=R |last10=Biondi |first10=R |last11=Bohm |first11=C |last12=Brooijmans |first12=G |last13=Broussard |first13=L J |last14=Cedercäll |first14=J |last15=Crawford |first15=C |date=2021-07-01 |title=New high-sensitivity searches for neutrons converting into antineutrons and/or sterile neutrons at the HIBEAM/NNBAR experiment at the European Spallation Source |url=https://iopscience.iop.org/article/10.1088/1361-6471/abf429 |journal=Journal of Physics G: Nuclear and Particle Physics |volume=48 |issue=7 |pages=070501 |doi=10.1088/1361-6471/abf429 |arxiv=2006.04907 |bibcode=2021JPhG...48g0501A |issn=0954-3899}}</ref> [[Supersymmetry]], [[Grand Unified Theory]] and [[String theory]]. 

== 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 |archive-date=August 20, 2007 |archive-url=https://web.archive.org/web/20070820075205/http://hyperphysics.phy-astr.gsu.edu/hbase/forces/color.html |url-status=live }}</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.

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)}}

Baryon number is a 'conserved' quantity in the sense that for perturbutative reactions in the [[Standard Model]] the total baryon number of the incoming particles is equal to the baryon number of the outgoing particles. Baryon number violation has never been observed experimentally.<ref>{{Cite journal |last1=Navas |first1=S. |last2=Amsler |first2=C. |last3=Gutsche |first3=T. |last4=Hanhart |first4=C. |last5=Hernández-Rey |first5=J. J. |last6=Lourenço |first6=C. |last7=Masoni |first7=A. |last8=Mikhasenko |first8=M. |last9=Mitchell |first9=R. E. |last10=Patrignani |first10=C. |last11=Schwanda |first11=C. |last12=Spanier |first12=S. |last13=Venanzoni |first13=G. |last14=Yuan |first14=C. Z. |last15=Agashe |first15=K. |date=2024-08-01 |title=Review of Particle Physics |url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.110.030001 |journal=Physical Review D |volume=110 |issue=3 |pages=030001 |doi=10.1103/PhysRevD.110.030001|hdl=20.500.11850/695340 |hdl-access=free }}</ref> However, neither Baryon number nor [[lepton number]] can from theory be shown to be conserved quantities due to nonperturbative effects in the [[Standard Model]].<ref>{{Cite journal |last=Kobach |first=Andrew |date=2016-07-10 |title=Baryon number, lepton number, and operator dimension in the Standard Model |url=https://linkinghub.elsevier.com/retrieve/pii/S0370269316301976 |journal=Physics Letters B |volume=758 |pages=455–457 |doi=10.1016/j.physletb.2016.05.050 |arxiv=1604.05726 |bibcode=2016PhLB..758..455K |issn=0370-2693}}</ref> These effects are, for example, [[Sphaleron|sphalerons]] and [[Instanton|instantons]]. 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 |bibcode=1976PhRvL..37....8T |issn=0031-9007|url-access=subscription }}</ref> is an example of an electroweak [[sphaleron]]. These reactions are massively suppressed at low energies/temperatures.<ref>{{Cite journal |last1=Klinkhamer |first1=F. R. |last2=Manton |first2=N. S. |date=1984-11-15 |title=A saddle-point solution in the Weinberg-Salam theory |url=https://doi.org/10.1103/physrevd.30.2212 |journal=Physical Review D |volume=30 |issue=10 |pages=2212–2220 |doi=10.1103/physrevd.30.2212 |bibcode=1984PhRvD..30.2212K |issn=0556-2821|url-access=subscription }}</ref><ref>{{Cite journal |last1=Klinkhamer |first1=F. R. |last2=Nagel |first2=P. |date=2017-07-12 |title=$SU(3)$ sphaleron: Numerical solution |url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.016006 |journal=Physical Review D |volume=96 |issue=1 |pages=016006 |doi=10.1103/PhysRevD.96.016006|arxiv=1704.07756 |bibcode=2017PhRvD..96a6006K }}</ref> At high temperatures, in for example the early universe, they could explain electroweak baryogenesis and [[leptogenesis (physics)|leptogenesis]]. Sphalerons can only change the baryon and lepton number by 3 or multiples of 3 (the reactions create 3 leptons and 3 baryons or the corresponding antiparticles). This is because the sum of baryon and lepton number (see [[B − L|''B'' − ''L'']]) is a conserved quantity in the standard model.<ref>{{Cite journal |last1=Beringer |first1=J. |last2=Arguin |first2=J. -F. |last3=Barnett |first3=R. M. |last4=Copic |first4=K. |last5=Dahl |first5=O. |last6=Groom |first6=D. E. |last7=Lin |first7=C. -J. |last8=Lys |first8=J. |last9=Murayama |first9=H. |last10=Wohl |first10=C. G. |last11=Yao |first11=W. -M. |last12=Zyla |first12=P. A. |last13=Amsler |first13=C. |last14=Antonelli |first14=M. |last15=Asner |first15=D. M. |date=2012-07-20 |title=Review of Particle Physics |url=https://link.aps.org/doi/10.1103/PhysRevD.86.010001 |journal=Physical Review D |language=en |volume=86 |issue=1 |page=010001 |doi=10.1103/PhysRevD.86.010001 |bibcode=2012PhRvD..86a0001B |issn=1550-7998|hdl=10481/34377 |hdl-access=free }}</ref>  

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. |access-date=2020-10-12 |archive-date=2024-04-28 |archive-url=https://web.archive.org/web/20240428045336/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#v=snippet&q=%22In%20the%20grand%20unified%20theories%20new%20interactions%20are%20contemplated%2C%20permitting%20decays%20such%20as%22%20%22in%20which%20baryon%20number%20and%20lepton%20number%20change.%22&f=false |url-status=live }}</ref>  [[Proton decay]] would be an example of such a process taking place, but has never been observed. [[Neutrinoless double beta decay]] is a reaction that would violate lepton number and neutron-to-antineutron oscillation would violate baryon number by −2 units.<ref name=":0" />

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>

Searches for baryon number violation have been conducted in the following ways:

* [[Kamiokande]] in 1985<ref>{{Cite web |title=INSPIRE |url=https://inspirehep.net/literature/216055 |access-date=2025-03-18 |website=inspirehep.net}}</ref> 
* ILL experiment in 1994<ref>{{Cite journal |last1=Cogswell |first1=B. K. |last2=Ernst |first2=D. J. |last3=Ufheil |first3=K. T. L. |last4=Gaglione |first4=J. T. |last5=Malave |first5=J. M. |date=2019-03-12 |title=Neutrino oscillations: The ILL experiment revisited |url=https://link.aps.org/doi/10.1103/PhysRevD.99.053003 |journal=Physical Review D |language=en |volume=99 |issue=5 |page=053003 |doi=10.1103/PhysRevD.99.053003 |arxiv=1802.07763 |bibcode=2019PhRvD..99e3003C |issn=2470-0010}}</ref>
* [[Super-Kamiokande]] in 1999<ref>{{Cite web |title=INSPIRE |url=https://inspirehep.net/literature/512073 |access-date=2025-03-18 |website=inspirehep.net}}</ref>

Two planned experiments are:

* [[Hyper-Kamiokande]]<ref>{{Citation |last1=Proto-Collaboration |first1=Hyper-Kamiokande |title=Hyper-Kamiokande Design Report |date=2018-11-28 |url=https://arxiv.org/abs/1805.04163 |access-date=2025-03-18 |arxiv=1805.04163 |last2=Abe |first2=K. |last3=Abe |first3=Ke |last4=Aihara |first4=H. |last5=Aimi |first5=A. |last6=Akutsu |first6=R. |last7=Andreopoulos |first7=C. |last8=Anghel |first8=I. |last9=Anthony |first9=L. H. V.}}</ref>
* HIBEAM<ref name=":0" />/NNBAR<ref>{{Cite journal |last1=Santoro |first1=V. |last2=Abou El Kheir |first2=O. |last3=Acharya |first3=D. |last4=Akhyani |first4=M. |last5=Andersen |first5=K.H. |last6=Barrow |first6=J. |last7=Bentley |first7=P. |last8=Bernasconi |first8=M. |last9=Bertelsen |first9=M. |last10=Beßler |first10=Y. |last11=Bianchi |first11=A. |last12=Brooijmans |first12=G. |last13=Broussard |first13=L. |last14=Brys |first14=T. |last15=Busi |first15=M. |date=2024-05-03 |title=HighNESS conceptual design report: Volume II. The NNBAR experiment. |url=https://journals.sagepub.com/doi/10.3233/JNR-230951 |journal=Journal of Neutron Research |language=en |volume=25 |issue=3–4 |pages=315–406 |doi=10.3233/JNR-230951 |issn=1023-8166}}</ref>

== See also ==
{{cols}}
* [[Lepton number]]
* [[Flavour (particle physics)]]
* [[Isospin]]
* [[Hypercharge]]
* [[Proton decay]]
* [[B − L|''B'' − ''L'']]
* [[Neutrinoless double beta decay]]{{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)]]