Editing Lepton (section)

== Universality ==
{{See also|LHCb experiment#Lepton flavour universality}}

The coupling of leptons to all types of [[gauge boson]] are flavour-independent: The interaction between leptons and a gauge boson measures the same for each lepton.<ref name="MartinShaw" /> This property is called '''lepton universality'''<!--boldface per WP:R#PLA--> and has been tested in measurements of the [[muon]] and [[tau lepton|tau]] [[mean lifetime|lifetimes]] and of {{SubatomicParticle|link=yes|Z boson}} boson partial [[decay width]]s, particularly at the [[Stanford Linear Collider]] (SLC) and [[Large Electron–Positron Collider]] (LEP) experiments.<ref name="Cumalat1993">
{{cite book
 |last=Cumalat |first=J.P.
 |year=1993
 |title=Physics in Collision
 |volume=12
 |publisher=Atlantica Séguier Frontières
 |isbn=978-2-86332-129-4
}}</ref>{{rp|pages=241–243}}<ref name="Fraser1998">
{{cite book
 |last=Fraser |first=G.
 |date=1 January 1998
 |title=The Particle Century
 |publisher=CRC Press
 |isbn=978-1-4200-5033-2
 |url=https://books.google.com/books?id=pgasJfizmocC
 |via=Google Books
}}</ref>{{rp|page=138}}

The decay rate (<small><math>\Gamma</math></small>) of muons through the process {{nowrap|{{SubatomicParticle|link=yes|muon-}} → {{SubatomicParticle|link=yes|electron-}} + {{SubatomicParticle|link=yes|electron antineutrino}} + {{SubatomicParticle|link=yes|muon neutrino}}}} is approximately given by an expression of the form (see [[muon decay]] for more details)<ref name="MartinShaw" />
: <math>\Gamma \left ( \mu^- \rarr e^- + \bar{\nu_e} +\nu_\mu \right ) \approx K_2\,  G_\text{F}^2\,  m_\mu^5 ~,</math>
where {{mvar|K}}{{sub|2}} is some constant, and {{mvar|G}}{{sub|F}} is the [[Fermi coupling constant]]. The decay rate of tau particles through the process {{nowrap|{{SubatomicParticle|link=yes|tau-}} → {{SubatomicParticle|link=yes|electron-}} + {{SubatomicParticle|link=yes|electron antineutrino}} + {{SubatomicParticle|link=yes|tau neutrino}}}} is given by an expression of the same form<ref name="MartinShaw" />
: <math>\Gamma \left ( \tau^- \rarr e^- + \bar{\nu_e} +\nu_\tau \right ) \approx K_3\, G_\text{F}^2\, m_\tau^5 ~,</math>
where {{mvar|K}}{{sub|3}} is some other constant. Muon–tauon universality implies that {{nowrap|{{mvar|K}}{{sub|2}} ≈ {{mvar|K}}{{sub|3}}}}. On the other hand, electron–muon universality implies<ref name="MartinShaw" />
: <math>0.9726 \times \Gamma \left( \tau^- \rarr e^- + \bar{\nu_e} +\nu_\tau \right) = \Gamma \left( \tau^- \rarr \mu^- + \bar{\nu_\mu} +\nu_\tau \right) ~.</math>

The [[branching ratio]]s for the electronic mode (17.82%) and muonic (17.39%) mode of tau decay are not equal due to the mass difference of the final state leptons.<ref name="Tauon" />

Universality also accounts for the ratio of muon and tau lifetimes. The lifetime <math>\Tau_\ell</math> of a lepton <math>\ell</math> (with <math>\ell</math> = "{{math|μ}}" or "{{math|τ}}") is related to the decay rate by<ref name="MartinShaw" />
: <math>\Tau_\ell = \frac{\; \mathcal{B} \left( \ell^- \rarr e^- + \bar{\nu_e} +\nu_\ell \right) \; }{ \Gamma \left( \ell^- \rarr e^- + \bar{\nu_e} +\nu_\ell \right)}\,</math>,
where <math>\; \mathcal{B} (x \rarr y) \;</math> denotes the branching ratios and <math>\;\Gamma(x \rarr y) \;</math> denotes the [[decay width|resonance width]] of the process <math>\; x \rarr y ~,</math> with {{mvar|x}} and {{mvar|y}} replaced by two different particles from "{{math|e}}" or "{{math|μ}}" or "{{math|τ}}".

The ratio of tau and muon lifetime is thus given by<ref name="MartinShaw" />
: <math>\frac{\, \Tau_\tau \,}{\Tau_\mu} = \frac{\; \mathcal{B} \left( \tau^- \rarr e^- + \bar{\nu_e} +\nu_\tau \right) \;}{ \mathcal{B} \left( \mu^- \rarr e^- + \bar{\nu_e} +\nu_\mu \right) }\, \left(\frac{m_\mu}{m_\tau}\right)^5 ~.</math>

Using values from the 2008 ''[[Review of Particle Physics]]'' for the branching ratios of the muon<ref name="Muon" /> and tau<ref name="Tauon" /> yields a lifetime ratio of ~&nbsp;{{val|1.29|e=-7}}, comparable to the measured lifetime ratio of ~&nbsp;{{val|1.32|e=-7}}. The difference is due to {{mvar|K}}{{sub|2}} and {{mvar|K}}{{sub|3}} not ''actually'' being constants: They depend slightly on the mass of leptons involved.

Recent tests of lepton universality in [[B meson|{{Subatomic particle|B}} meson]] decays, performed by the [[LHCb]], [[BaBar experiment|BaBar]], and [[Belle experiment|Belle]] experiments, have shown consistent deviations from the Standard Model predictions. However the combined statistical and systematic significance is not yet high enough to claim an observation of [[new physics]].<ref name=Ciezarek2017>
{{cite journal
 |vauthors=Ciezarek G, Franco Sevilla M, Hamilton B, Kowalewski R, Kuhr T, Lüth V, Sato Y
 |year=2017
 |title=A challenge to lepton universality in B&nbsp;meson decays
 |journal=Nature
 |volume=546 |issue=7657 |pages=227–233
 |doi=10.1038/nature22346|pmid=28593973 |arxiv=1703.01766
 |bibcode=2017Natur.546..227C
 |s2cid=4385808
}}</ref>

In July 2021 results on lepton flavour universality have been published testing W decays, previous measurements by the LEP had given a slight imbalance but the new measurement by the [[ATLAS experiment|ATLAS]] collaboration have twice the precision and give a ratio of <math>R_W^{\tau/\mu}=\mathcal{B} (W\rarr \tau\nu_\tau)/\mathcal{B}( W\rarr \mu\nu_\mu)=0.992\pm0.013</math>, which agrees with the standard-model prediction of unity.<ref>{{Cite journal|last1=Aad|first1=G.|last2=Abbott|first2=B.|last3=Abbott|first3=D. C.|last4=Abud|first4=A. Abed|last5=Abeling|first5=K.|last6=Abhayasinghe|first6=D. K.|last7=Abidi|first7=S. H.|last8=AbouZeid|first8=O. S.|last9=Abraham|first9=N. L.|last10=Abramowicz|first10=H.|last11=Abreu|first11=H.|date=5 July 2021|title=Test of the universality of τ and μ lepton couplings in W-boson decays with the ATLAS detector|url=https://www.nature.com/articles/s41567-021-01236-w|journal=Nature Physics|language=en|volume=17|issue=7|pages=813–818|doi=10.1038/s41567-021-01236-w|issn=1745-2481|arxiv=2007.14040|bibcode=2021NatPh..17..813A|s2cid=220831347}}</ref><ref>{{Cite journal|last=Middleton|first=Christine|date=2021-07-09|title=ATLAS measurement supports lepton universality|journal=Physics Today|volume=2021|issue=1|pages=0709a|url=https://physicstoday.scitation.org/do/10.1063/PT.6.1.20210709a/abs/|language=EN|doi=10.1063/PT.6.1.20210709a|bibcode=2021PhT..2021a.709.|s2cid=242888088}}</ref><ref>{{Cite web|title=New ATLAS result addresses long-standing tension in the Standard Model|url=https://atlas.cern/updates/briefing/addressing-long-standing-tension-standard-model|access-date=2021-07-12|website=ATLAS|language=en}}</ref> In 2024 a preprint by the ATLAS collaboration has published a new value of <math>R_W^{\mu/e}=\mathcal{B} ( W\rarr \mu\nu_\mu)/\mathcal{B}( W\rarr e\nu_e)=0.9995\pm0.0045</math> the most precise ratio so far testing the lepton flavour universality.<ref>{{cite arXiv |last=ATLAS Collaboration |title=Precise test of lepton flavour universality in ''W''-boson decays into muons and electrons in ''pp'' collisions at &radic;''s'' = 13 TeV with the ATLAS detector |date=2024-03-04 | class=hep-ex |eprint=2403.02133}}</ref><ref>{{Cite web |date=2024-09-18 |title=The delicate balance of lepton flavours |url=https://home.cern/news/news/physics/delicate-balance-lepton-flavours |access-date=2024-09-20 |website=CERN |language=en}}</ref>