View source for Pion

{{Short description|Subatomic particle; lightest meson}}
{{Other uses}}
{{Infobox Particle
| name        = Pion
| image       = Image:Quark structure pion.svg
| caption     = The quark structure of the positively charged pion.
| num_types   = 3
| composition =
 {{plainlist|
* {{math|{{SubatomicParticle|Pion+}}}} : {{SubatomicParticle|Up quark}}{{SubatomicParticle|Down antiquark}}
* {{math|{{SubatomicParticle|Pion0}}}} : <math>\rm \tfrac{u\overline{u} - d\overline{d}}{\sqrt{2}}</math>
* {{math|{{SubatomicParticle|Pion-}}}} : {{SubatomicParticle|Down quark}}{{SubatomicParticle|Up antiquark}}
 }}
| statistics  = [[Boson]]ic
| group       = [[Meson]]s
| interaction = [[Strong interaction|Strong]], [[Weak interaction|weak]], [[Electromagnetic interaction|electromagnetic]], and [[gravity]]
| antiparticle=
 {{plainlist|
* {{math|{{SubatomicParticle|Pion+}}}} :  {{math|{{SubatomicParticle|Pion-}}}}
* {{math|{{SubatomicParticle|Pion0}}}} :  self
 }}
| theorized   = [[Hideki Yukawa]] (1935)
| discovered  =
 {{plainlist|
* {{math|{{SubatomicParticle|Pion+-}}}} : [[César Lattes]], [[Giuseppe Occhialini]], [[Cecil Powell]] (1947)
* {{math|{{SubatomicParticle|Pion0}}}} : 1950
 }} 
| symbol      = {{math|{{SubatomicParticle|Pion+}}}}, {{math|{{SubatomicParticle|Pion0}}}}, and {{math|{{SubatomicParticle|Pion-}}}}
| mass        =
 {{plainlist|
* {{math|{{SubatomicParticle|Pion+-}}}} : {{val|139.57039|(18)|ul=MeV/c2}}{{px2}}<ref name=pdg>{{cite journal | title=Review of Particle Physics | last1=Zyla | first1=P.A. | last2=Barnett | first2=R.M. | display-authors=1 | collaboration = Particle Data Group | journal=Progress of Theoretical and Experimental Physics | volume = 2020 | page = 083C01 | year = 2020 | issue=8 | doi=10.1093/ptep/ptaa104| doi-access=free | hdl=11585/772320 | hdl-access=free }}</ref>
* {{math|{{SubatomicParticle|Pion0}}}} : {{val|134.9768|(5)|u=MeV/c2}}{{px2}}<ref name=pdg/>
 }}
| mean_lifetime =
 {{plainlist|
* {{math|{{SubatomicParticle|Pion+-}}}} : {{val|2.6|e=-8|ul=s}}
* {{math|{{SubatomicParticle|Pion0}}}} : {{val|8.5|e=-17|u=s}}
 }}
| decay_particle = 
| electric_charge =
 {{plainlist|
* {{math|{{SubatomicParticle|Pion+-}}}} : {{+-}}1 [[Elementary charge|''e'']] 
* {{math|{{SubatomicParticle|Pion0}}}} : 0&nbsp;''e''
 }}
| charge_radius = {{math|{{SubatomicParticle|Pion+-}}}} : {{+-}}{{val|0.659|(4)|u=[[Femtometre|fm]]}}{{px2}}<ref name=pdg/>
| color_charge=  0
| spin        =  0&nbsp;[[reduced Planck constant|''ħ'']]
| strangeness = 
| charm = 
| bottomness = 
| topness = 
| isospin =
 {{plainlist|
* {{math|{{SubatomicParticle|Pion+-}}}} : ±1
* {{math|{{SubatomicParticle|Pion0}}}} : 0
 }}
| hypercharge = 0
| parity = −1
| c_parity = +1
}}

In [[particle physics]], a '''pion''' ({{IPAc-en|'|p|ai|.|Q|n}}, {{respell|PIE|on}}) or '''pi meson''', denoted with the [[Greek alphabet|Greek]] letter [[pi (letter)|pi]] ({{math|{{SubatomicParticle|Pion}}}}), is any of three [[subatomic particle]]s: {{math|{{SubatomicParticle|Pion0}}}}, {{math|{{SubatomicParticle|Pion+}}}}, and {{math|{{SubatomicParticle|Pion-}}}}. Each pion consists of a [[quark]] and an [[antiquark]] and is therefore a [[meson]]. Pions are the lightest mesons and, more generally, the lightest [[hadron]]s. They are unstable, with the charged pions {{math|{{SubatomicParticle|Pion+}}}} and {{math|{{SubatomicParticle|Pion-}}}} decaying after a [[mean lifetime]] of 26.033&nbsp;[[nanosecond]]s ({{val|2.6033|e=-8}}&nbsp;seconds), and the neutral pion {{math|{{SubatomicParticle|Pion0}}}} decaying after a much shorter lifetime of 85&nbsp;[[attosecond]]s ({{val|8.5|e=-17}}&nbsp;seconds).<ref name=pdg/> Charged pions most often [[particle decay|decay]] into [[muon]]s and [[muon neutrino]]s, while neutral pions generally decay into [[gamma ray]]s.

The exchange of [[virtual particle|virtual]] pions, along with [[vector meson|vector]], [[rho meson|rho]] and [[omega meson]]s, provides an explanation for the [[nuclear force|residual strong force]] between [[nucleon]]s. Pions are not produced in [[radioactive decay]], but commonly are in high-energy collisions between [[hadron]]s. Pions also result from some matter–antimatter [[Annihilation#Proton–antiproton annihilation|annihilation]] events. All types of pions are also produced in natural processes when high-energy [[cosmic-ray]] protons and other hadronic cosmic-ray components interact with [[matter]] in Earth's [[atmosphere]]. In 2013, the detection of characteristic gamma rays originating from the decay of neutral pions in two [[supernova remnants]] has shown that pions are produced copiously after supernovas, most probably in conjunction with production of high-energy protons that are detected on Earth as cosmic rays.<ref name=ackermann-2013>
{{cite journal
 | last1=Ackermann | first1 = M. 
 | display-authors=etal
 | year=2013
 | title=Detection of the characteristic pion-decay signature in supernova remnants
 | journal=[[Science (journal)|Science]]
 | volume=339 | issue=6424 | pages=807–811
 | arxiv = 1302.3307
 | bibcode = 2013Sci...339..807A
 | doi =10.1126/science.1231160
 | pmid=23413352| s2cid=29815601
}}</ref>

The pion also plays a crucial role in cosmology, by imposing an upper limit on the energies of cosmic rays surviving collisions with the [[cosmic microwave background]], through the [[Greisen–Zatsepin–Kuzmin limit]].<ref>{{cite journal |last=Greisen |first=K. |year=1966 |title=End to the Cosmic-Ray Spectrum? |journal=Physical Review Letters |volume=16 |issue=17 |pages=748–750 |doi=10.1103/PhysRevLett.16.748|bibcode=1966PhRvL..16..748G }}</ref>

== History ==
[[File:Nuclear Force anim smaller.gif|thumb|upright=1.6|An animation of the [[nuclear force]] (or residual strong force) interaction. The small colored double disks are gluons. For the choice of anticolors, see {{section link|Color charge|Red, green, and blue}}.]]
[[File:Pn Scatter Quarks.svg|thumb|upright=1.4|[[Feynman diagram]] for the same process as in the animation, with the individual [[quark]] constituents shown, to illustrate how the ''fundamental'' [[strong interaction]] gives rise to the nuclear force. Straight lines are quarks, while multi-colored loops are [[gluon]]s (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion "in-flight", are not shown.<br/>The {{math|{{SubatomicParticle|Pion0}}}} meson contains an [[antiparticle|anti]]-quark, shown as travelling in the opposite direction, as per the [[Feynman–Stueckelberg interpretation]].]]
Theoretical work by [[Hideki Yukawa]] in 1935 had predicted the existence of [[meson]]s as the carrier particles of the [[strong nuclear force]]. From the range of the strong nuclear force (inferred from the radius of the [[atomic nucleus]]), Yukawa predicted the existence of a particle having a mass of about {{val|100|u=MeV/c2}}. Initially after its discovery in 1936, the [[muon]] (initially called the "mu meson") was thought to be this particle, since it has a mass of {{val|106|u=MeV/c2}}. However, later experiments showed that the muon did not participate in the strong nuclear interaction. In modern terminology, this makes the muon a [[lepton]], and not a meson. However, some communities of astrophysicists continue to call the muon a "mu-meson".{{According to whom|date=January 2023}} The pions, which turned out to be examples of Yukawa's proposed mesons, were discovered later: the charged pions in 1947, and the neutral pion in 1950.

In 1947, the first true mesons, the charged pions, were found by the collaboration led by [[Cecil Powell]] at the [[University of Bristol]], in England. The discovery article had four authors: [[César Lattes]], [[Giuseppe Occhialini]], [[Hugh Muirhead]] and Powell.<ref>{{Cite journal |last1=LATTES |first1=C. M. G. |last2=MUIRHEAD |first2=H. |last3=OCCHIALINI |first3=G. P. S. |last4=POWELL |first4=C. F. |year=1947 |title=Processes Involving Charged Mesons |journal=[[Nature (journal)|Nature]] |publisher=Springer Science and Business Media LLC |volume=159 |issue=4047 |pages=694–697 |doi=10.1038/159694a0 |bibcode=1947Natur.159..694L |issn=0028-0836}}</ref> Since the advent of [[particle accelerator]]s had not yet come, high-energy subatomic particles were only obtainable from atmospheric [[cosmic ray]]s. [[Photographic emulsion]]s based on the [[gelatin-silver process]] were placed for long periods of time in sites located at high-altitude mountains, first at [[Pic du Midi de Bigorre]] in the [[Pyrenees]], and later at [[Chacaltaya]] in the [[Andes Mountains]], where the plates were struck by cosmic rays.
After development, the [[photographic plate]]s were inspected under a [[microscope]] by a team of about a dozen women.<ref>{{Cite journal |last1=Vieira |first1=Cássio Leite |last2=Videira |first2=Antonio Augusto Passos |date=March 2014 |title=Carried by History: Cesar Lattes, Nuclear Emulsions, and the Discovery of the Pi-meson |url=http://link.springer.com/10.1007/s00016-014-0128-6 |journal=Physics in Perspective |language=en |volume=16 |issue=1 |pages=2–36 |bibcode=2014PhP....16....3V |doi=10.1007/s00016-014-0128-6 |issn=1422-6944 |s2cid=122718292|url-access=subscription }}</ref> [[Marietta Kurz]] was the first person to detect the unusual "double meson" tracks, characteristic for a pion decaying into a [[muon]], but they were too close to the edge of the photographic emulsion and deemed incomplete. A few days later, Irene Roberts observed the tracks left by pion decay that appeared in the discovery paper. Both women are credited in the figure captions in the article.

In 1948, [[César Lattes|Lattes]], [[Eugene Gardner]], and their team first artificially produced pions at the [[University of California at Berkeley|University of California]]'s [[cyclotron]] in [[Berkeley, California]], by bombarding [[carbon]] atoms with high-speed [[alpha particle]]s. Further advanced theoretical work was carried out by [[Riazuddin (physicist)|Riazuddin]], who in 1959 used the [[dispersion relation]] for [[Compton scattering]] of [[virtual photon]]s on pions to analyze their charge radius.<ref>{{Cite journal |last=Riazuddin |date=1959-05-15  |title=Charge radius of the pion |url=https://link.aps.org/doi/10.1103/PhysRev.114.1184 |journal=[[Physical Review]] |language=en |volume=114 |issue=4 |pages=1184–1186 |bibcode=1959PhRv..114.1184R |doi=10.1103/PhysRev.114.1184 |issn=0031-899X|url-access=subscription }}</ref>

Since the neutral pion is not [[electric charge|electrically charged]], it is more difficult to detect and observe than the charged pions are. Neutral pions do not leave tracks in photographic emulsions or Wilson [[cloud chamber]]s. The existence of the neutral pion was inferred from observing its decay products from [[cosmic ray]]s, a so-called "soft component" of slow electrons with photons. The {{math|{{SubatomicParticle|Pion0}}}} was identified definitively at the University of California's cyclotron in 1949 by observing its decay into two photons.<ref>{{Cite journal |last1=Bjorklund |first1=R. |last2=Crandall |first2=W.E. |last3=Moyer |first3=B.J. |last4=York |first4=H.F. |date=1950-01-15  |title=High energy photons from proton–nucleon collisions |url=https://escholarship.org/content/qt9qd089vt/qt9qd089vt.pdf?t=p0uv3w |journal=[[Physical Review]] |language=en |volume=77 |issue=2 |pages=213–218 |bibcode=1950PhRv...77..213B |doi=10.1103/PhysRev.77.213 |issn=0031-899X |hdl=2027/mdp.39015086480236}}</ref> Later in the same year, they were also observed in cosmic-ray balloon experiments at Bristol University.

{{blockquote|... Yukawa choose the letter {{math|π}} because of its resemblance to the [[Kanji]] character for [[Wikt:介#Japanese|介]] [''kai''], which means "to mediate", based on the idea that the meson works as a strong force mediator particle between hadrons.<ref>{{cite AV media |last=Zee |first=Anthony |author-link=Anthony Zee |date=7 December 2013 |title=Quantum Field Theory, Anthony Zee {{!}} Lecture&nbsp;2 of 4 (lectures given in 2004) |publisher=aoflex |medium=video |via=YouTube |url=https://www.youtube.com/watch?v=aypGTsLN0ck |time-caption=Quote at |time=57{{sup|m}}04{{sup|s}} of 1{{sup|h}}26{{sup|m}}39{{sup|s}}}}</ref>}}

== Possible applications ==
The use of pions in medical radiation therapy, such as for cancer, was explored at a number of research institutions, including the [[Los Alamos National Laboratory]]'s [[Los Alamos Neutron Science Center|Meson Physics Facility]], which treated 228&nbsp;patients between 1974 and 1981 in [[New Mexico]],<ref>{{cite journal |last1=von&nbsp;Essen |first1=C. F. |last2=Bagshaw |first2=M. A. |last3=Bush |first3=S. E. |last4=Smith |first4=A. R. |last5=Kligerman |first5=M. M. |year=1987 |title=Long-term results of pion therapy at Los Alamos |journal=International Journal of Radiation Oncology, Biology, Physics |volume=13 |issue=9 |pages=1389–1398 |pmid=3114189 |doi=10.1016/0360-3016(87)90235-5}}</ref> and the [[TRIUMF]] laboratory in [[Vancouver, British Columbia]].

== Theoretical overview ==
In the standard understanding of the [[strong force]] interaction as defined by [[quantum chromodynamics]], pions are loosely portrayed as [[Goldstone boson]]s of spontaneously [[Chiral symmetry breaking|broken chiral symmetry]]. That explains why the masses of the three kinds of pions are considerably less than that of the other mesons, such as the scalar or vector mesons. If their current [[quark]]s were massless particles, it could make the chiral symmetry exact and thus the Goldstone theorem would dictate that all pions have a zero mass.

In fact, it was shown by Gell-Mann, Oakes and Renner (GMOR)<ref name="GMOR">{{cite journal |last1=Gell-Mann |first1=M. |last2=Renner |first2=B. |title=Behavior of current divergences under SU{{sub|3}}×SU{{sub|3}} |journal=Physical Review |volume=175 |issue=5 |pages=2195–2199 |year=1968 |bibcode=1968PhRv..175.2195G |doi=10.1103/PhysRev.175.2195 |url=https://authors.library.caltech.edu/3634/1/GELpr68.pdf}}</ref> that the square of the pion mass is proportional to the sum of the quark masses times the [[Vacuum expectation value|quark condensate]]: 
<math display=block>M^2_\pi = (m_\text{u}+m_\text{d})B+\mathcal{O}(m^2),</math> 
with {{mvar|B}} the quark condensate: 
<math display=block>B = \left\vert \frac{\rm \langle 0 \vert \bar{u}u \vert 0 \rangle}{f^2_\pi} \right\vert_{m_\text{q} \to 0}</math> 
This is often known as the '''GMOR relation''' and it explicitly shows that <math>M_\pi=0</math> in the massless quark limit. The same result also follows from [[Light-front quantization applications#Light-front holography|light-front holography]].<ref name="Light-Front Holographic QCD and Emerging Confinement">{{cite journal |first1=S.J. |last1=Brodsky |first2=G. F. |last2=de Teramond |first3=H.G. |last3=Dosch |first4=J. |last4=Erlich |year=2015 |title=Light-front holographic QCD and emerging confinement |journal=Physics Reports |volume=584 |pages=1–105  |doi=10.1016/j.physrep.2015.05.001 |arxiv=1407.8131 |bibcode=2015PhR...584....1B }}</ref>

Empirically, since the light quarks actually have minuscule nonzero masses, the pions also have nonzero [[rest mass]]es. However, those masses are ''almost an order of magnitude smaller'' than that of the nucleons, roughly<ref name=GMOR/> <math>\ m_\pi \approx \tfrac{ \sqrt{ v\ m_\text{q}\ } }{\ f_\pi } \approx \sqrt{ m_\text{q}\ }\ </math> 45&nbsp;MeV, where {{math|''m''{{sub|q}}}} are the relevant current quark masses, around {{val|5|-|10|u=MeV/c2}}.

The pion is one of the particles that mediate the residual strong interaction between a pair of [[nucleons]]. This interaction is attractive: it pulls the nucleons together. Written in a non-relativistic form, it is called the [[Yukawa potential]]. The pion, being spinless, has [[kinematics]] described by the [[Klein–Gordon equation]]. In the terms of [[quantum field theory]], the [[effective field theory]] [[Lagrangian (field theory)|Lagrangian]] describing the pion-nucleon interaction is called the [[Yukawa interaction]].

The nearly identical masses of {{math|{{SubatomicParticle|Pion+-}}}} and {{math|{{SubatomicParticle|Pion0}}}} indicate that there must be a symmetry at play: this symmetry is called the [[SU(2)]] [[flavour symmetry]] or [[isospin]]. The reason that there are three pions, {{math|{{SubatomicParticle|Pion+}}}}, {{math|{{SubatomicParticle|Pion-}}}} and {{math|{{SubatomicParticle|Pion0}}}}, is that these are understood to belong to the triplet representation or the [[Adjoint representation of a Lie group|adjoint representation]] '''3''' of SU(2). By contrast, the up and down quarks transform according to the [[fundamental representation]] '''2''' of SU(2), whereas the anti-quarks transform according to the conjugate representation '''2*'''.

With the addition of the [[strange quark]], the pions participate in a larger, SU(3), flavour symmetry,  in the adjoint representation, '''8''', of SU(3). The other members of this [[Eightfold way (physics)#Meson octet|octet]] are the four [[kaon]]s and the [[eta meson]].

Pions are [[pseudoscalar (physics)|pseudoscalar]]s under a [[parity (physics)|parity]] transformation. Pion currents thus couple to the axial vector current and  so  participate in the [[chiral anomaly]].

== 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''}}}}.

{{anchor|Dalitz_decay_anchor}}The second largest {{math|{{SubatomicParticle|Pion0}}}} decay mode ({{nowrap|BR{{sub|γe{{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>

== See also ==
* [[Pionium]]
* [[Quark model]]
* [[Static forces and virtual-particle exchange]]
* [[Sanford–Wang parameterisation]]

== References ==
{{reflist|25em}}

== Further reading ==
* {{cite book
 |first1=G.E. |last1=Brown |author1-link=Gerald Edward Brown
 |first2=A.D. |last2=Jackson
 |year=1976
 |title=The Nucleon-Nucleon Interaction
 |publisher=North-Holland Publishing
 |place=Amsterdam, NL
 |isbn=0-7204-0335-9
}}

== External links ==
* {{Commons category-inline}}
* [http://pdg.lbl.gov/2004/tables/mxxx.pdf Mesons] at the Particle Data Group

{{Particles}}
{{Authority control}}

[[Category:Mesons]]