Editing Neutrino (section)

=== Mass <span type="anchor" id="neutrino_mass_anchor"></span> ===
{{unsolved|physics|Can we measure the neutrino masses? Do neutrinos follow [[Fermi–Dirac statistics|Dirac]] or [[Majorana fermion|Majorana]] statistics?}}
[[File:NeutrinoMassTimeline2022.webp|thumb|upright=1.4|left|Timeline of neutrino mass measurements by different experiments<ref name=KATRIN-2022-NatPhys/>]]

The Standard Model of particle physics assumed that neutrinos are massless.<ref>
{{cite book
 |last1=Cottingham |first1=W.N.
 |last2=Greenwood |first2=D.A.
 |date=2007
 |title=An Introduction to the Standard Model of Particle Physics
 |edition=2nd
 |publisher=Cambridge University Press
}}
</ref> The experimentally established phenomenon of neutrino oscillation, which mixes neutrino flavor states with neutrino mass states (analogously to [[Cabibbo–Kobayashi–Maskawa matrix|CKM mixing]]), requires neutrinos to have nonzero masses.<ref>
{{cite journal
 |last1=Schechter |first1=Joseph
 |last2=Valle |first2=José W.F.
 |year=1980
 |title=Neutrino masses in SU(2) ⊗ U(1) theories
 |journal=Physical Review D
 |volume=22 |issue=9 |pages=2227–2235
 |bibcode=1980PhRvD..22.2227S |doi=10.1103/PhysRevD.22.2227
}}
</ref> Massive neutrinos were originally conceived by [[Bruno Pontecorvo]] in the 1950s. Enhancing the basic framework to accommodate their mass is straightforward by adding a right-handed Lagrangian.<ref>{{cite book |last1=Terranova |first1=Francesco |title=A Modern Primer in Particle and Nuclear Physics. |date=2021 |publisher=Oxford Univ. Press |isbn=978-0-19-284525-2}}</ref>

Providing for neutrino mass can be done in two ways, and some proposals use both:
* If, like other fundamental Standard Model fermions, mass is generated by the [[Dirac fermion|Dirac mechanism]], then the framework would require an additional right-chiral component which is an [[Special unitary group#The group SU(2)|SU(2) singlet]]. This component would have the conventional [[Yukawa interaction]]s with the neutral component of the [[Higgs boson|Higgs doublet]]; but, otherwise, would have no interactions with Standard Model particles. 
* Or, else, mass can be generated by the [[Majorana mass|Majorana mechanism]], which would require the neutrino and antineutrino to be the same particle.

A hard upper limit on the masses of neutrinos comes from [[physical cosmology|cosmology]]: the [[Big Bang]] model predicts that there is a fixed ratio between the number of neutrinos and the number of [[photon]]s in the [[cosmic microwave background radiation|cosmic microwave background]]. If the total mass of all three types of neutrinos exceeded an average of {{val|50|ul=eV/c2}} per neutrino, there would be so much mass in the universe that it would collapse.<ref>
{{cite journal
 |last1=Hut |first1=Piet |author-link1=Piet Hut
 |last2=Olive |first2=Keith A.
 |year=1979
 |title=A cosmological upper limit on the mass of heavy neutrinos
 |journal=Physics Letters B
 |volume=87 |issue=1–2 |pages=144–146
 |doi=10.1016/0370-2693(79)90039-X |bibcode=1979PhLB...87..144H
}}
</ref> This limit can be circumvented by assuming that the neutrino is unstable, but there are limits within the Standard Model that make this difficult. A much more stringent constraint comes from a careful analysis of cosmological data, such as the cosmic microwave background radiation, [[galaxy survey]]s, and the [[Lyman-alpha forest]]. Analysis of data from the WMAP microwave space telescope found that the sum of the masses of the three neutrino species must be less than {{val|0.3|u=eV/c2}}.<ref>
{{cite journal
 |last1=Goobar |first1=Ariel |last2=Hannestad |first2=Steen
 |last3=Mörtsell |first3=Edvard |last4=Tu |first4=Huitzu
 |year=2006
 |title=The neutrino mass bound from WMAP 3&nbsp;year data, the baryon acoustic peak, the SNLS supernovae and the Lyman-α forest
 |journal=Journal of Cosmology and Astroparticle Physics
 |volume=2006 |issue=6 |page=019
 |arxiv=astro-ph/0602155 |bibcode=2006JCAP...06..019G
 |s2cid=119535760 |doi=10.1088/1475-7516/2006/06/019
}}
</ref> In 2018, the [[Planck (spacecraft)|Planck collaboration]] published a stronger bound of {{val|0.11|u=eV/c2}}, which was derived by combining their CMB total intensity, polarization and gravitational lensing observations with Baryon-Acoustic oscillation measurements from galaxy surveys and supernova measurements from Pantheon.<ref name=planck_2018>
{{cite journal
 |author=Planck Collaboration
 |journal=Astronomy & Astrophysics
 |year=2020
 |title=Planck 2018 results. VI. Cosmological parameters
 |volume=641 |issue=A6
 |pages=A6
 |arxiv=1807.06209 |doi=10.1051/0004-6361/201833910
 |bibcode=2020A&A...641A...6P
 |s2cid=119335614
}}</ref> A 2021 reanalysis that adds redshift space distortion measurements from the SDSS-IV eBOSS survey gets an even tighter upper limit of {{val|0.09|u=eV/c2}}.<ref>
{{cite journal
 |last1=Di Valentino |first1=Eleonora
 |last2=Gariazzo |first2=Stefano
 |last3=Mena |first3=Olga
 |journal=Physical Review D
 |arxiv=2106.15267
 |doi=10.1103/PhysRevD.104.083504
 |year=2021
 |title=On the most constraining cosmological neutrino mass bounds
 |volume=104
 |issue=8
 |page=083504
 |s2cid=235669844
}}</ref> However, several ground-based telescopes with similarly sized error bars as Planck prefer higher values for the neutrino mass sum, indicating some tension in the data sets.<ref>
{{cite journal
 |last1=Di Valentino |first1=Eleonora
 |last2=Melchiorri |first2=Alessandro
 |arxiv=2112.02993
 |title=Neutrino Mass Bounds in the Era of Tension Cosmology
 |journal=The Astrophysical Journal Letters
 |year=2022
 |volume=931
 |issue=2
 |pages=L18
 |doi=10.3847/2041-8213/ac6ef5
 |bibcode=2022ApJ...931L..18D
 |s2cid=244909022
 |doi-access=free
}}</ref>

The Nobel prize in Physics 2015 was awarded to Takaaki Kajita and Arthur B. McDonald for their experimental discovery of neutrino oscillations, which demonstrates that neutrinos have mass.<ref>
{{cite press release
 |title=Nobel physics laureates
 |date=2015-10-06
 |publisher=The Royal Swedish Academy of Sciences
 |url=https://www.nobelprize.org/nobel_prizes/physics/laureates/2015/press.html
 |access-date=14 June 2017
 |archive-date=6 October 2015
 |archive-url=https://web.archive.org/web/20151006172856/http://www.nobelprize.org/nobel_prizes/physics/laureates/2015/press.html
 |url-status=live
}}</ref><ref>
{{cite news
 |first=Charles |last=Day
 |date=7 October 2015
 |title=Takaaki Kajita and Arthur McDonald share 2015 Physics Nobel
 |journal=[[Physics Today]]
 |issue=10
 |issn=0031-9228 |doi=10.1063/PT.5.7208
}}
</ref>

In 1998, research results at the [[Super-Kamiokande]] neutrino detector determined that neutrinos can oscillate from one flavor to another, which requires that they must have a nonzero mass.<ref name=Fukuda-Hayakawa-Ichihara-Inoue-etal-1998/> While this shows that neutrinos have mass, the absolute neutrino mass scale is still not known. This is because neutrino oscillations are sensitive only to the difference in the squares of the masses.<ref name=Mohapatra-Antusch-Babu-Barenboim-etal-2007/> As of 2020,<ref name=Esteban-GonzlzGarc-Maltoni-Schwetz-Zhou-2020/> the best-fit value of the difference of the squares of the masses of mass eigenstates 1 and 2 is {{nowrap|{{abs|Δ''m''{{Su|b=21|p=2}}}} {{=}} {{val|0.000074|u=(eV/''c''<sup>2</sup>)<sup>2</sup>}}}}, while for eigenstates 2 and 3 it is {{nowrap|{{abs|Δ''m''{{Su|b=32|p=2}}}} {{=}} {{val|0.00251|u=(eV/''c''<sup>2</sup>)<sup>2</sup>}}}}. Since {{nowrap|{{abs|Δ''m''{{Su|b=32|p=2}}}}}} is the difference of two squared masses, at least one of them must have a value that is at least the square root of this value. Thus, there exists at least one neutrino mass eigenstate with a mass of at least {{val|0.05|u=eV/c2}}.<ref name=Amsler-Doser-Antnli-etal-2008/>

A number of efforts are under way to directly determine the absolute neutrino mass scale in laboratory experiments, especially using nuclear beta decay. Upper limits on the effective electron neutrino masses come from beta decays of tritium. The Mainz Neutrino Mass Experiment set an upper limit of {{nowrap|''m'' < {{val|2.2|u=eV/c2}}}} at 95% confidence level.<ref>
{{cite press release
 |title=The Mainz Neutrino Mass Experiment
 |url=http://www.physik.uni-mainz.de/exakt/neutrino/en_experiment.html
 |archive-url=https://web.archive.org/web/20160303220947/http://www.physik.uni-mainz.de/exakt/neutrino/en_experiment.html
 |archive-date=2016-03-03
}}</ref> Since June&nbsp;2018 the [[KATRIN]] experiment searches for a mass between {{val|0.2|u=eV/c2}} and {{val|2|u=eV/c2}} in tritium decays.<ref name=KATRIN-2018-06-12-pr/> The February 2022 upper limit is ''m''<sub>ν</sub> < {{val|0.8|u=eV/c2}} at 90% CL in combination with a previous campaign by KATRIN from 2019.<ref name="KATRIN-2022-NatPhys">
{{cite journal |last1=Aker |first1=M. |last2=Mertens |first2=S. |last3=Schlösser |first3=M. |display-authors=etal |date=February 2022 |title=Direct neutrino-mass measurement with sub-electronvolt sensitivity |journal=[[Nature Physics]] |volume=18 |issue=2 |pages=160–166 |bibcode=2022NatPh..18..160K |doi=10.1038/s41567-021-01463-1 |issn=1745-2473 |doi-access=free |collaboration=KATRIN Collaboration|hdl=1721.1/141776 |hdl-access=free }} {{ISSN|1745-2481}}&nbsp;(online)
</ref><ref>
{{cite journal
 |last=Castelvecchi
 |first=Davide
 |date=2022-02-14
 |title=How light is a neutrino? The answer is closer than ever
 |journal=[[Nature (journal)|Nature]]
 |language=en
 |doi=10.1038/d41586-022-00430-x
 |pmid=35165410
 |s2cid=246827702
 |url=https://www.nature.com/articles/d41586-022-00430-x
 |access-date=18 February 2022
 |archive-date=7 August 2023
 |archive-url=https://web.archive.org/web/20230807134612/https://www.nature.com/articles/d41586-022-00430-x
 |url-status=live
}}</ref>

On 31 May 2010, [[OPERA experiment|OPERA]] researchers observed the first tau neutrino candidate event in a muon neutrino beam, the first time this transformation in neutrinos had been observed, providing further evidence that they have mass.<ref name=Agafnva-Aleksndrv-Altinok-etal-2010/>

If the neutrino is a [[Majorana particle]], the mass may be calculated by finding the [[half-life]] of [[Neutrinoless double beta decay|neutrinoless double-beta decay]] of certain nuclei. The current lowest upper limit on the Majorana mass of the neutrino has been set by [[KamLAND]]-Zen: {{val|0.060|–|0.161|u=eV/c2}}.<ref>
{{cite journal
 |collaboration=KamLAND-Zen Collaboration
 |last1=Gando |first1=Azusa
 |date=11 May 2016
 |title=Search for Majorana neutrinos near the inverted mass hierarchy region with KamLAND-Zen
 |journal=Physical Review Letters
 |volume=117 |issue=8 |page=082503
 |doi=10.1103/PhysRevLett.117.082503 |bibcode=2016PhRvL.117h2503G
 |pmid=27588852 |arxiv=1605.02889
 |s2cid=204937469
}}</ref>