Baryon number#Conservation

{{See also|Color charge}}

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".{{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 }}

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.

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 ({{nowrap|Λ{{su|p=0|b=b}}}}).

{{cite journal

|author=R. Aaij et al. (LHCb collaboration)

|year=2015

|title=Observation of J/ψp resonances consistent with pentaquark states in Λ{{su|p=0|b=b}}→J/ψK⁻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

}}

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

• leptons – the electron, muon, tauon, and their corresponding neutrinos
• vector bosons – the photon, W and Z bosons, gluons
• scalar boson – the Higgs boson
• second-order tensor boson – the hypothetical graviton

{{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.{{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 }} However, neither Baryon number nor lepton number can from theory be shown to be conserved quantities due to nonperturbative effects in the Standard Model.{{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}} These effects are, for example, sphalerons and instantons. The hypothesized Adler–Bell–Jackiw anomaly in electroweak interactions{{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 }} is an example of an electroweak sphaleron. These reactions are massively suppressed at low energies/temperatures.{{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 }}{{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 }} At high temperatures, in for example the early universe, they could explain electroweak baryogenesis and 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) is a conserved quantity in the standard model.{{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 }}

The hypothetical concepts of grand unified theory (GUT) models and supersymmetry allows for the changing of a baryon into leptons and antiquarks (see B − L), thus violating the conservation of both baryon and lepton numbers.{{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 }} 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.

The conservation of baryon number is not consistent with the physics of black hole evaporation via Hawking radiation.Harlow, Daniel and Ooguri, Hirosi", "Symmetries in quantum field theory and quantum gravity", hep-th 1810.05338 (2018) It is expected in general that quantum gravitational effects violate the conservation of all charges associated to global symmetries.Kallosh, Renata and Linde, Andrei D. and Linde, Dmitri A. and Susskind, Leonard", "Gravity and global symmetries", Phys. Rev. D 52 (1995) 912-935 The violation of conservation of baryon number led John Archibald Wheeler to speculate on a principle of mutability for all physical properties.{{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}}

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

• Kamiokande in 1985{{Cite web |title=INSPIRE |url=https://inspirehep.net/literature/216055 |access-date=2025-03-18 |website=inspirehep.net}}
• ILL experiment in 1994{{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}}
• Super-Kamiokande in 1999{{Cite web |title=INSPIRE |url=https://inspirehep.net/literature/512073 |access-date=2025-03-18 |website=inspirehep.net}}

Two planned experiments are:

• Hyper-Kamiokande{{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.}}
• HIBEAM/NNBAR{{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}}

{{cols}}

• Lepton number
• Flavour (particle physics)
• Isospin
• Hypercharge
• Proton decay
• B − L
• Neutrinoless double beta decay{{colend}}

{{Reflist}}

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Category:Baryons

Category:Conservation laws

Category:Nuclear physics

Category:Quantum chromodynamics

Category:Quarks

Category:Standard Model

Category:Flavour (particle physics)