Editing Lepton (section)

== Properties ==

=== Spin and chirality ===
[[File:Right left helicity.svg|thumb|200px|right|Left-handed and right-handed helicities]]

Leptons are [[Spin (physics)|spin]]&nbsp;{{sfrac|1|2}} particles. The [[spin-statistics theorem]] thus implies that they are [[fermion]]s and thus that they are subject to the [[Pauli exclusion principle]]: no two leptons of the same species can be in the same state at the same time. Furthermore, it means that a lepton can have only two possible spin states, namely up or down.

A closely related property is [[chirality (physics)|chirality]], which in turn is closely related to a more easily visualized property called [[helicity (particle physics)|helicity]]. The helicity of a particle is the direction of its spin relative to its [[momentum]]; particles with spin in the same direction as their momentum are called ''right-handed'' and they are otherwise called ''left-handed''. When a particle is massless, the direction of its momentum relative to its spin is the same in every reference frame, whereas for massive particles it is possible to 'overtake' the particle by choosing a faster-moving [[Lorentz transformation|reference frame]]; in the faster frame, the helicity is reversed. Chirality is a technical property, defined through transformation behaviour under the [[Poincaré group]], that does not change with reference frame. It is contrived to agree with helicity for massless particles, and is still well defined for particles with mass.

In many [[quantum field theories]], such as [[quantum electrodynamics]] and [[quantum chromodynamics]], left- and right-handed fermions are identical. However, the Standard Model's [[weak interaction]] treats left-handed and right-handed fermions differently: only left-handed fermions (and right-handed anti-fermions) participate in the weak interaction. This is an example of [[parity violation]] explicitly written into the model. In the literature, left-handed fields are often denoted by a capital <small>L</small> subscript (e.g. the normal electron e{{su|b=L|p=−}}) and right-handed fields are denoted by a capital <small>R</small> subscript (e.g. a positron e{{su|b=R|p=+}}).

Right-handed neutrinos and left-handed anti-neutrinos have no possible interaction with other particles (see ''[[Sterile neutrino]]'') and so are not a functional part of the Standard Model, although their exclusion is not a strict requirement; they are sometimes listed in particle tables to emphasize that they would have no active role if included in the model. Even though electrically charged right-handed particles (electron, muon, or tau) do not engage in the weak interaction specifically, they can still interact electrically, and hence still participate in the [[Electroweak unification|combined electroweak force]], although with different strengths ([[Weak hypercharge|{{math|''Y''}}<sub>W</sub>]]).
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=== Electromagnetic interaction ===
[[File:Lepton-interaction-vertex-eeg.svg|thumb|right|Lepton–photon interaction]]
One of the most prominent properties of leptons is their [[electric charge]], {{mvar|Q}}. The electric charge determines the strength of their [[electromagnetic interaction]]s. It determines the strength of the [[electric field]] generated by the particle (see [[Coulomb's law]]) and how strongly the particle reacts to an external electric or magnetic field (see [[Lorentz force]]). Each generation contains one lepton with {{nowrap|1={{math|''Q''}} = −1 [[elementary charge|''e'']]}} and one lepton with zero electric charge. The lepton with electric charge is commonly simply referred to as a ''charged lepton'' while a neutral lepton is called a ''neutrino''. For example, the first generation consists of the electron {{SubatomicParticle|electron}} with a negative electric charge and the electrically neutral electron neutrino {{SubatomicParticle|electron neutrino}}.

In the language of quantum field theory, the electromagnetic interaction of the charged leptons is expressed by the fact that the particles interact with the quantum of the electromagnetic field, the [[photon]]. The [[Feynman diagram]] of the electron–photon interaction is shown on the right.

Because leptons possess an intrinsic rotation in the form of their spin, charged leptons generate a magnetic field. The size of their [[magnetic dipole moment]] {{mvar|μ}} is given by
: <math>\mu = g\, \frac{\; Q \hbar \;}{4 m} \ ,</math>
where {{mvar|m}} is the mass of the lepton and {{mvar|g}} is the so-called [[g-factor (physics)|"{{mvar|g}}&nbsp;factor"]] for the lepton. First-order quantum mechanical approximation predicts that the {{mvar|g}}&nbsp;factor is 2 for all leptons. However, higher-order quantum effects caused by loops in Feynman diagrams introduce corrections to this value. These corrections, referred to as the ''[[anomalous magnetic dipole moment]]'', are very sensitive to the details of a quantum field theory model, and thus provide the opportunity for precision tests of the Standard Model. The theoretical and measured values for the ''electron'' anomalous magnetic dipole moment are within agreement within eight significant figures.<ref>{{harvnb|Peskin|Schroeder|1995|p=197}}</ref> The results for the ''muon'', however, [[Muon g-2|are problematic]], hinting at a small, persistent discrepancy between the Standard Model and experiment.

=== Weak interaction ===
{|  style="float:right; margin: 0em 0em 1em 1em "
|-
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{|class=wikitable style="font-size:90%;"
|[[File:Lepton-interaction-vertex-evW.svg|frameless|upright=.7]]
|[[File:Lepton-interaction-vertex-pvW.svg|frameless|upright=.7]]
|[[File:Lepton-interaction-vertex-eeZ.svg|frameless|upright=.7]]
|-
|colspan=3|{{center|The [[weak interaction]]s of the first generation leptons.}}
|}
|}
In the Standard Model, the left-handed charged lepton and the left-handed neutrino are arranged in [[Doublet (physics)|doublet]] {{nowrap||(ν{{sub|e {{sc|L}}}}, e{{small|{{su|p=−|b={{sc|L}} }} }})}} that transforms in the [[spinor]] representation ({{nowrap|{{math|''T''}} {{=}} {{sfrac| 1 |2}}}}) of the [[weak isospin]] [[SU(2)]] gauge symmetry. This means that these particles are eigenstates of the isospin projection {{math|''T''}}{{sub|3}} with eigenvalues {{sfrac|+| 1 |2}} and {{sfrac|−| 1 |2}} respectively. In the meantime, the right-handed charged lepton transforms as a weak isospin scalar ({{nowrap|{{math|''T''}} {{=}} 0}}) and thus does not participate in the [[weak interaction]], while there is no evidence that a right-handed neutrino exists at all.

The [[Higgs mechanism]] recombines the gauge fields of the weak isospin SU(2) and the [[weak hypercharge]] U(1) symmetries to three massive vector bosons ({{SubatomicParticle|W boson+}}, {{SubatomicParticle|W boson-}}, {{SubatomicParticle|Z boson0}}) mediating the [[weak interaction]], and one massless vector boson, the photon (&gamma;), responsible for the electromagnetic interaction. The electric charge {{mvar|Q}} can be calculated from the isospin projection {{mvar|T}}{{sub|3}} and weak hypercharge {{math|''Y''}}{{sub|W}} through the [[Gell-Mann–Nishijima formula]],
: {{nowrap|{{math|''Q'' {{=}} ''T''{{sub|3}} + {{sfrac| 1 |2}} ''Y''{{sub|W}}}}.}}

To recover the observed electric charges for all particles, the left-handed weak isospin doublet {{nowrap|(ν{{sub|eL}}, e{{su|p=−|b=L}})}} must thus have {{nowrap|''Y''{{sub|W}} {{=}} −1}}, while the right-handed isospin scalar {{nowrap|e{{su|p=−|b=R}}}} must have {{nowrap|{{math|''Y''}}{{sub|W}} {{=}} −2}}. The interaction of the leptons with the massive weak interaction vector bosons is shown in the figure on the right.

=== Mass ===
In the [[Standard Model]], each lepton starts out with no intrinsic mass. The charged leptons (i.e. the electron, muon, and tau) obtain an effective mass through interaction with the [[Higgs field]], but the neutrinos remain massless. For technical reasons, the masslessness of the neutrinos implies that there is no mixing of the different generations of charged leptons as [[CKM matrix|there is for quarks]]. The zero mass of neutrino is in close agreement with current direct experimental observations of the mass.<ref>{{harvnb|Peskin|Schroeder|1995|p=27}}</ref>

However, it is known from indirect experiments—most prominently from observed [[neutrino oscillation]]s<ref>{{harvnb|Fukuda|1998}}</ref>—that neutrinos have to have a nonzero mass, probably less than {{val|2|ul=eV/c2}}.<ref name="Neutrino" /> This implies the existence of physics [[beyond the Standard Model]]. The currently most favoured extension is the so-called [[seesaw mechanism]], which would explain both why the left-handed neutrinos are so light compared to the corresponding charged leptons, and why we have not yet seen any right-handed neutrinos.

=== Lepton flavor quantum numbers ===
{{Main|Lepton number}}
The members of each generation's [[weak isospin]] [[doublet (physics)|doublet]] are assigned [[lepton number|leptonic numbers]] that are conserved under the Standard Model.<ref name="MartinShaw">{{harvnb|Martin|Shaw|1992}}</ref> Electrons and electron neutrinos have an ''electronic number'' of {{nowrap|{{math|''L''}}<sub>e</sub> {{=}} 1}}, while muons and muon neutrinos have a ''muonic number'' of {{nowrap|{{math|''L''}}<sub>μ</sub> {{=}} 1}}, while tau particles and tau neutrinos have a ''tauonic number'' of {{nowrap|{{math|''L''<sub>τ</sub>}} {{=}} 1}}. The antileptons have their respective generation's leptonic numbers of&nbsp;−1.

Conservation of the leptonic numbers means that the number of leptons of the same type remains the same, when particles interact. This implies that leptons and antileptons must be created in pairs of a single generation. For example, the following processes are allowed under conservation of leptonic numbers:
[[File:Lepton isodoublets fixed.png|thumb|right|Each generation forms a [[weak isospin]] [[Doublet (physics)|doublet]].]]
: {{SubatomicParticle|link=yes|Photon}} &nbsp; &nbsp;→&nbsp;&nbsp; {{SubatomicParticle|link=yes|Electron}} + {{SubatomicParticle|link=yes|Antielectron}},
: {{SubatomicParticle|link=yes|Z boson0}} &nbsp;→&nbsp;&nbsp; {{SubatomicParticle|link=yes|Tau}} + {{SubatomicParticle|link=yes|Antitau}},
but none of these:
: {{SubatomicParticle|link=yes|Photon}} &nbsp; &nbsp; &nbsp;→&nbsp;&nbsp; {{SubatomicParticle|link=yes|Electron}} + {{SubatomicParticle|link=yes|Antimuon}},
: {{SubatomicParticle|link=yes|W boson-}} &nbsp;→&nbsp;&nbsp; {{SubatomicParticle|link=yes|Electron}} + {{SubatomicParticle|link=yes|Tau neutrino}},
: {{SubatomicParticle|link=yes|Z boson0}} &nbsp;&nbsp; →&nbsp;&nbsp; {{SubatomicParticle|link=yes|Muon}} + {{SubatomicParticle|link=yes|Antitau}}.

However, [[neutrino oscillation]]s are known to violate the conservation of the individual leptonic numbers. Such a violation is considered to be smoking gun evidence for [[physics beyond the Standard Model]]. A much stronger conservation law is the conservation of the total number of leptons ({{mvar|L}} {{small|with ''no'' subscript}}), conserved even in the case of neutrino oscillations, but even it is still violated by a tiny amount by the [[chiral anomaly]].