Editing Pion (section)

== Basic properties ==
Pions, which are [[meson]]s with zero [[Spin (physics)|spin]], are composed of first-[[generation (particle physics)|generation]] [[quark]]s. In the [[quark model]], an [[up quark]] and an anti-[[down quark]] make up a {{math|{{SubatomicParticle|Pion+}}}}, whereas a [[down quark]] and an anti-[[up quark]] make up the {{math|{{SubatomicParticle|Pion-}}}}, and these are the [[antiparticle]]s of one another. The neutral pion {{math|{{SubatomicParticle|Pion0}}}} is a combination of an up quark with an anti-up quark, or a down quark with an anti-down quark. The two combinations have identical [[quantum number]]s, and hence they are only found in [[quantum superposition|superposition]]s. The lowest-energy superposition of these is the {{SubatomicParticle|Pion0}}, which is its own antiparticle. Together, the pions form a triplet of [[isospin]]. Each pion has overall [[isospin]] ({{math|''I'' {{=}} 1}}) and third-component [[Gell-Mann–Nishijima formula|isospin equal to its charge]] ({{math|''I''{{sub|z}} {{=}} +1, 0, −1}}).

=== Charged pion decays ===
[[Image:PiPlus muon decay.svg|right|thumb|[[Feynman diagram]] of the dominant leptonic pion decay.]]
[[File:K meson decay.jpg|thumb|[[Kaon]] decay in a [[nuclear emulsion]]. The positively-charged kaon enters at the top of the image and decays into a {{SubatomicParticle|Pion-}} meson (''a'') and two {{math|{{SubatomicParticle|Pion+}}}} mesons (''b'' and ''c''). The {{math|{{SubatomicParticle|Pion-}}}} meson interacts with a [[Atomic nucleus|nucleus]] in the emulsion at ''B''.]]
The {{math|{{SubatomicParticle|Pion+-}}}} mesons have a [[mass]] of {{val|139.6|ul=MeV/c2}} and a [[mean life]]time of {{val|2.6033|e=-8|ul=s}}. They decay due to the [[weak force|weak interaction]]. The primary decay mode of a pion, with a [[branching fraction]] of 0.999877, is a [[lepton]]ic decay into a [[muon]] and a [[muon neutrino]]:
<math display=block>\begin{align}
  \pi^+ &\longrightarrow \mu^+ + \nu_\mu \\[2pt]
  \pi^- &\longrightarrow \mu^- + \overline\nu_\mu
\end{align}</math>

The second most common decay mode of a pion, with a branching fraction of 0.000123, is also a leptonic decay into an [[electron]] and the corresponding [[electron antineutrino]]. This "electronic mode" was discovered at [[CERN]] in 1958:<ref>{{cite journal | last1 = Fazzini | first1 = T. | last2 = Fidecaro | first2 = G. | last3 = Merrison | first3 = A. | last4 = Paul | first4 = H. | last5 = Tollestrup | first5 = A. | year = 1958 | title = Electron Decay of the Pion | journal = Physical Review Letters | volume = 1 | issue = 7 | pages = 247–249 | bibcode=1958PhRvL...1..247F | doi = 10.1103/PhysRevLett.1.247 | url = https://cds.cern.ch/record/342714}}</ref>
<math display=block>\begin{align}
  \pi^+ &\longrightarrow {\rm e}^+ + \nu_e \\[2pt]
  \pi^- &\longrightarrow {\rm e}^- + \overline\nu_e
\end{align}</math>

The suppression of the electronic decay mode with respect to the muonic one is given approximately (up to a few percent effect of the radiative corrections) by the ratio of the half-widths of the pion–electron and the pion–muon decay reactions,
<math display="block"> R_\pi = \left(\frac{m_e}{m_\mu}\right)^2 \left(\frac{m_\pi^2 - m_e^2}{m_\pi^2 - m_\mu^2}\right)^2 = 1.283 \times 10^{-4}</math>
and is a [[Spin (physics)|spin]] effect known as [[helicity (particle physics)|helicity]] suppression.

Its mechanism is as follows: The negative pion has spin zero; therefore the lepton and the antineutrino must be emitted with opposite spins (and opposite linear momenta) to preserve net zero spin (and conserve linear momentum). However, because the weak interaction is sensitive only to the left [[Chirality (physics)|chirality]] component of fields, the antineutrino has always left chirality, which means it is right-handed, since for massless anti-particles the helicity is opposite to the chirality. This implies that the lepton must be emitted with spin in the direction of its linear momentum (i.e., also right-handed). If, however, leptons were massless, they would only interact with the pion in the left-handed form (because for massless particles helicity is the same as chirality) and this decay mode would be prohibited. Therefore, suppression of the electron decay channel comes from the fact that the electron's mass is much smaller than the muon's. The electron is relatively massless compared with the muon, and thus the electronic mode is greatly suppressed relative to the muonic one, virtually prohibited.<ref>{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/particles/hadron.html |title=Mesons |website=Hyperphysics |publisher=Georgia State U.}}</ref>

Although this explanation suggests that parity violation is causing the helicity suppression, the fundamental reason lies in the vector-nature of the interaction which dictates a different handedness for the neutrino and the charged lepton. Thus, even a parity conserving interaction would yield the same suppression.

Measurements of the above ratio have been considered for decades to be a test of [[lepton universality]]. Experimentally, this ratio is {{val|1.233|(2)|e=-4}}.<ref name=pdg/>

Beyond the purely leptonic decays of pions, some structure-dependent radiative leptonic decays (that is, decay to the usual leptons plus a gamma ray) have also been observed.

Also observed, for charged pions only, is the very rare "pion [[beta decay]]" (with branching fraction of about {{10^|−8}}) into a neutral pion, an electron and an electron antineutrino (or for positive pions, a neutral pion, a positron, and electron neutrino).
<math display=block>\begin{align}
  \pi^+ &\longrightarrow \pi^0 + {\rm e}^+ + \nu_e \\[2pt]
  \pi^- &\longrightarrow \pi^0 + {\rm e}^- + \overline\nu_e
\end{align}</math>

The rate at which pions decay is a prominent quantity in many sub-fields of particle physics, such as [[chiral perturbation theory]]. This rate is parametrized by the [[pion decay constant]] ({{math|''f''{{sub|&pi;}}}}), related to the [[wave function]] overlap of the quark and antiquark, which is about {{val|130|u=MeV}}.<ref>{{cite report |first1=J.L. |last1=Rosner |first2=S. |last2=Stone |collaboration=[[Particle Data Group]] |date=18 December 2013 |title=Leptonic decays of charged pseudo- scalar mesons |website=pdg.lbl.gov |place=Lawrence, CA |publisher=[[Lawrence Berkeley Lab]] |url=http://pdg.lbl.gov/2014/reviews/rpp2014-rev-pseudoscalar-meson-decay-cons.pdf}}</ref>

=== Neutral pion decays ===
The {{math|{{SubatomicParticle|Pion0}}}} meson has a mass of {{val|135.0|u=MeV/c2}} and a mean lifetime of {{val|8.5|e=-17|u=s}}.<ref name=pdg/> It decays via the [[electromagnetism|electromagnetic force]], which explains why its mean lifetime is much smaller than that of the charged pion (which can only decay via the [[weak force]]). 
[[Image:Anomalous-pion-decay.png |right|thumb| [[Chiral anomaly#Calculation|Anomaly]]-induced  neutral pion decay.]]
The dominant {{math|{{SubatomicParticle|Pion0}}}} decay mode, with a [[branching fraction|branching ratio]] of {{nowrap|1=BR{{sub|γγ}} = 0.98823}}, is into two [[photon]]s:
<math display=block>\pi^0 \longrightarrow 2\ \gamma</math>

The decay {{nobr|{{math| {{SubatomicParticle|Pion0}} → 3 {{SubatomicParticle|link=yes|Gamma}} }}}} (as well as decays into any odd number of photons) is forbidden by the [[C-symmetry]] of the electromagnetic interaction: The intrinsic C-parity of the {{math|{{SubatomicParticle|Pion0}}}} is +1, while the C-parity of a system of {{mvar|n}} photons is {{math|(&minus;1){{sup|''n''}}}}.

The second largest {{math|{{SubatomicParticle|Pion0}}}} decay mode ({{nobr|BR{{sub|''γ''e{{overbar|e}}}} {{=}} 0.01174}}) is the Dalitz decay (named after [[Richard Dalitz]]), which is a two-photon decay with an internal photon conversion resulting in a photon and an [[electron]]-[[positron]] pair in the final state:
<math display=block>\pi^0 \longrightarrow \gamma + \rm e^- + e^+</math>

The third largest established decay mode ({{nobr|BR{{sub|2e2{{overbar|e}}}} {{=}} 3.34{{x10^|-5}}}}) is the double-Dalitz decay, with both photons undergoing internal conversion which leads to further suppression of the rate:
<math display=block>\pi^0 \longrightarrow \rm 2 \ e^- + 2\ e^+</math>

The fourth largest established decay mode is the [[Feynman diagram|loop-induced]] and therefore suppressed (and additionally [[Helicity (particle physics)|helicity]]-suppressed) leptonic decay mode ({{nowrap|1=BR{{sub|e{{overbar|e}}}} = 6.46{{x10^|-8}}}}):
<math display=block>\pi^0 \longrightarrow \rm e^- + e^+</math>

The neutral pion has also been observed to decay into [[positronium]] with a branching fraction on the order of {{10^|-9}}. No other decay modes have been established experimentally. The branching fractions above are the [[Particle Data Group|PDG]] central values, and their uncertainties are omitted, but available in the cited publication.<ref name=pdg/>

{| class="wikitable sortable" style="text-align: center;"
|+ Pions
|-
! class=unsortable | Particle <br/>name
! Particle <br/>symbol
! Antiparticle <br/>symbol
! class=unsortable | Quark <br/>content<ref name=PDGQuarkmodel>{{cite web |first1=C. |last1=Amsler |display-authors=etal |collaboration=[[Particle Data Group]] |year=2008 |url=http://pdg.lbl.gov/2008/reviews/quarkmodrpp.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://pdg.lbl.gov/2008/reviews/quarkmodrpp.pdf |archive-date=2022-10-09 |url-status=live |title=Quark Model |publisher=[[Lawrence Berkeley Laboratory]]}}</ref>
! [[Rest mass]] {{bracket|[[electron volt|MeV]]/[[speed of light|''c'']]<sup>2</sup>}}
! width="50" | [[Isospin|''I'']]<sup>[[G parity|G]]</sup>
! width="50" | [[Total angular momentum|''J'']]<sup>[[Parity (physics)|P]][[C parity|C]]</sup>
! width="50" | [[strangeness|''S'']]
! width="50" | [[charm (quantum number)|''C'']]
! width="50" | [[bottomness|''B''′]]
! [[Mean lifetime]] {{bracket|[[second|s]]}}
! class=unsortable|Commonly decays to <br/>(>&nbsp;5% of decays)
|-
| Pion<ref name=pdg/>
| {{math|{{SubatomicParticle|Pion+}}}}
| {{math|{{SubatomicParticle|Pion-}}}}
| {{SubatomicParticle|link=yes|Up quark}}{{SubatomicParticle|link=yes|Down antiquark}}
| {{nobr|{{gaps|139.570|39}} ± {{gaps|0.000|18}}}}
| 1<sup>&minus;</sup>
| 0<sup>&minus;</sup>
| 0
| 0
| 0
| {{val|2.6033|0.0005|e=-8}}
| {{SubatomicParticle|link=yes|antimuon}} + {{SubatomicParticle|link=yes|muon neutrino}}
|-
| Pion<ref name=pdg/>
| {{math|{{SubatomicParticle|Pion0}}}}
| Self
| <math>\tfrac{\mathrm{u\bar{u}} - \mathrm{d\bar{d}}}{\sqrt 2}</math><sup>{{ref|quarkcontent|[a]}}</sup>
| {{val|134.9768|0.0005}}
| 1<sup>&minus;</sup>
| 0<sup>&minus;+</sup>
| 0
| 0
| 0
| {{val|8.5|0.2|e=-17}}
| {{math|{{SubatomicParticle|link=yes|Photon}} + {{SubatomicParticle|link=yes|Photon}}}}
|}
<sup>[a]</sup> {{note|quarkcontent}} The quark composition of the {{math|{{SubatomicParticle|Pion0}}}} is not exactly divided between up and down quarks, due to complications from non-zero quark masses.<ref>{{cite book |last=Griffiths |first=D.J. |author-link=David J. Griffiths |year=1987 |title=Introduction to Elementary Particles |publisher=[[John Wiley & Sons]] |isbn=0-471-60386-4 }}</ref>