Editing Baryon number (section)

== 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>