Pion

For other uses, seePion (disambiguation).

Pion

The quark structure of the positively charged pion.
Composition	π+ : u d π0 :$(u{\overline {u}}-d{\overline {d}})/{\sqrt {2}}$ π− : d u
Statistics	Bosonic
Family	Mesons
Interactions	Strong,weak,electromagnetic,andgravity
Symbol	π+ , π0 ,and π−
Antiparticle	π+ : π− π0 :self
Theorized	Hideki Yukawa(1935)
Discovered	π± :César Lattes,Giuseppe Occhialini,Cecil Powell(1947) π0 :1950
Types	3
Mass	π± :139.57039(18)MeV/c2 π0 :134.9768(5) MeV/c2
Mean lifetime	π± :2.6×10−8s π0 :8.5×10−17s
Electric charge	π± :±1e π0 :0e
Charge radius	π± :±0.659(4)fm
Color charge	0
Spin	0ħ
Isospin	π± :±1 π0 :0
Hypercharge	0
Parity	−1
C parity	+1

Inparticle physics,apion(/ˈpaɪ.ɒn/,PIE-on) orpi meson,denoted with theGreekletterpi(
π
), is any of threesubatomic particles:
π⁰
,
π⁺
,and
π⁻
.Each pion consists of aquarkand anantiquarkand is therefore ameson.Pions are the lightest mesons and, more generally, the lightesthadrons.They are unstable, with the charged pions
π⁺
and
π⁻
decaying after amean lifetimeof 26.033nanoseconds(2.6033×10⁻⁸seconds), and the neutral pion
π⁰
decaying after a much shorter lifetime of 85attoseconds(8.5×10⁻¹⁷seconds).Charged pions most oftendecayintomuonsandmuon neutrinos,while neutral pions generally decay intogamma rays.

The exchange ofvirtualpions, along withvector,rhoandomega mesons,provides an explanation for theresidual strong forcebetweennucleons.Pions are not produced inradioactive decay,but commonly are in high-energy collisions betweenhadrons.Pions also result from some matter–antimatterannihilationevents. All types of pions are also produced in natural processes when high-energycosmic-rayprotons 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 twosupernova remnantshas 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.

The pion also plays a crucial role in cosmology, by imposing an upper limit on the energies of cosmic rays surviving collisions with thecosmic microwave background,through theGreisen–Zatsepin–Kuzmin limit.

History

An animation of thenuclear force(or residual strong force) interaction. The small colored double disks are gluons. For the choice of anticolors, seeColor charge § Red, green, and blue.

Feynman diagramfor the same process as in the animation, with the individualquarkconstituents shown, to illustrate how thefundamentalstrong interactiongives rise to the nuclear force. Straight lines are quarks, while multi-colored loops aregluons(the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion "in-flight", are not shown.
The
π⁰
pion contains ananti-quark, shown to travel in the opposite direction, as per theFeynman–Stueckelberg interpretation.

Theoretical work byHideki Yukawain 1935 had predicted the existence ofmesonsas the carrier particles of thestrong nuclear force.From the range of the strong nuclear force (inferred from the radius of theatomic nucleus), Yukawa predicted the existence of a particle having a mass of about100 MeV/c².Initially after its discovery in 1936, themuon(initially called the "mu meson" ) was thought to be this particle, since it has a mass of106 MeV/c².However, later experiments showed that the muon did not participate in the strong nuclear interaction. In modern terminology, this makes the muon alepton,and not a meson. However, some communities of astrophysicists continue to call the muon a "mu-meson".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 byCecil Powellat theUniversity of Bristol,in England. The discovery article had four authors:César Lattes,Giuseppe Occhialini,Hugh Muirheadand Powell.Since the advent ofparticle acceleratorshad not yet come, high-energy subatomic particles were only obtainable from atmosphericcosmic rays.Photographic emulsionsbased on thegelatin-silver processwere placed for long periods of time in sites located at high-altitude mountains, first atPic du Midi de Bigorrein thePyrenees,and later atChacaltayain theAndes Mountains,where the plates were struck by cosmic rays. After development, thephotographic plateswere inspected under amicroscopeby a team of about a dozen women.Marietta Kurzwas the first person to detect the unusual "double meson" tracks, characteristic for a pion decaying into amuon,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,Lattes,Eugene Gardner,and their team first artificially produced pions at theUniversity of California'scyclotroninBerkeley, California,by bombardingcarbonatoms with high-speedalpha particles.Further advanced theoretical work was carried out byRiazuddin,who in 1959 used thedispersion relationforCompton scatteringofvirtual photonson pions to analyze their charge radius.

Since the neutral pion is notelectrically charged,it is more difficult to detect and observe than the charged pions are. Neutral pions do not leave tracks in photographic emulsions or Wilsoncloud chambers.The existence of the neutral pion was inferred from observing its decay products fromcosmic rays,a so-called "soft component" of slow electrons with photons. The
π⁰
was identified definitively at the University of California's cyclotron in 1949 by observing its decay into two photons.Later in the same year, they were also observed in cosmic-ray balloon experiments at Bristol University.

... Yukawa choose the letterπbecause of its resemblance to theKanjicharacter forGiới[kai], which means "to mediate". Due to the concept that the meson works as a strong force mediator particle between hadrons.

Possible applications

The use of pions in medical radiation therapy, such as for cancer, was explored at a number of research institutions, including theLos Alamos National Laboratory's Meson Physics Facility, which treated 228 patients between 1974 and 1981 inNew Mexico,and theTRIUMFlaboratory inVancouver, British Columbia.

Theoretical overview

In the standard understanding of thestrong forceinteraction as defined byquantum chromodynamics,pions are loosely portrayed asGoldstone bosonsof spontaneouslybroken 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 currentquarkswere 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)that the square of the pion mass is proportional to the sum of the quark masses times thequark condensate:${\textstyle M_{\pi }^{2}=(m_{u}+m_{d})B+{\mathcal {O}}(m^{2})}$,with${\textstyle B=\vert \langle 0\vert {\bar {u}}u\vert 0\rangle /f_{\pi }^{2}\vert _{m_{q}\to 0}}$the quark condensate. This is often known as theGMOR relationand it explicitly shows that${\textstyle M_{\pi }=0}$in the massless quark limit. The same result also follows fromLight-front holography.

Empirically, since the light quarks actually have minuscule nonzero masses, the pions also have nonzerorest masses.However, those masses arealmost an order of magnitude smallerthan that of the nucleons, roughlym_π≈⁠√v m_q/f_π⁠≈√m_q45 MeV, wherem_qare the relevant current-quark masses in MeV, around 5−10 MeV.

The pion is one of the particles that mediate the residual strong interaction between a pair ofnucleons.This interaction is attractive: it pulls the nucleons together. Written in a non-relativistic form, it is called theYukawa potential.The pion, being spinless, haskinematicsdescribed by theKlein–Gordon equation.In the terms ofquantum field theory,theeffective field theoryLagrangiandescribing the pion-nucleon interaction is called theYukawa interaction.

The nearly identical masses of
π^±
and
π⁰
indicate that there must be a symmetry at play: this symmetry is called theSU(2)flavour symmetryorisospin.The reason that there are three pions,
π⁺
,
π⁻
and
π⁰
,is that these are understood to belong to the triplet representation or theadjoint representation3of SU(2). By contrast, the up and down quarks transform according to thefundamental representation2of SU(2), whereas the anti-quarks transform according to the conjugate representation2*.

With the addition of thestrange quark,the pions participate in a larger, SU(3), flavour symmetry, in the adjoint representation,8,of SU(3). The other members of thisoctetare the fourkaonsand theeta meson.

Pions arepseudoscalarsunder aparitytransformation. Pion currents thus couple to the axial vector current and so participate in thechiral anomaly.

Basic properties

Pions, which aremesonswith zerospin,are composed of first-generationquarks.In thequark model,anup quarkand an anti-down quarkmake up a
π⁺
,whereas adown quarkand an anti-up quarkmake up the
π⁻
,and these are theantiparticlesof one another. The neutral pion
π⁰
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 identicalquantum numbers,and hence they are only found insuperpositions.The lowest-energy superposition of these is the
π⁰
,which is its own antiparticle. Together, the pions form a triplet ofisospin.Each pion has overallisospin(I= 1)and third-componentisospin equal to its charge(I_z= +1, 0, or −1).

Charged pion decays

Feynman diagramof the dominant leptonic pion decay.

Kaondecay in anuclear emulsion.The positively-charged kaon enters at the top of the image and decays into a
π⁻
meson (a) and two
π⁺
mesons (bandc). The
π⁻
meson interacts with anucleusin the emulsion atB.

The
π^±
mesons have amassof139.6MeV/c²and amean lifetimeof2.6033×10⁻⁸s.They decay due to theweak interaction.The primary decay mode of a pion, with abranching fractionof 0.999877, is aleptonicdecay into amuonand amuon neutrino:

π+	→	μ+	+	ν μ
π−	→	μ−	+	ν μ

The second most common decay mode of a pion, with a branching fraction of 0.000123, is also a leptonic decay into anelectronand the correspondingelectron antineutrino.This "electronic mode" was discovered atCERNin 1958:

π+	→	e+	+	ν e
π−	→	e−	+	ν e

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,

$$R_{\pi }=\left({\frac {m_{e}}{m_{\mu }}}\right)^{2}\left({\frac {m_{\pi }^{2}-m_{e}^{2}}{m_{\pi }^{2}-m_{\mu }^{2}}}\right)^{2}=1.283\times 10^{-4}$$

and is aspineffect known ashelicitysuppression.

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 leftchiralitycomponent 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.

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 oflepton universality.Experimentally, this ratio is1.233(2)×10⁻⁴.

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 "pionbeta 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).

π−	→	π0	+	e−	+	ν e
π+	→	π0	+	e+	+	ν e

The rate at which pions decay is a prominent quantity in many sub-fields of particle physics, such aschiral perturbation theory.This rate is parametrized by thepion decay constant(f_π),related to thewave functionoverlap of the quark and antiquark, which is about130 MeV.

Neutral pion decays

The
π⁰
meson has a mass of135.0 MeV/c²and a mean lifetime of8.5×10⁻¹⁷s.It decays via theelectromagnetic force,which explains why its mean lifetime is much smaller than that of the charged pion (which can only decay via theweak force).

Anomaly-induced neutral pion decay.

The dominant
π⁰
decay mode, with abranching ratioofBR_γγ= 0.98823,is into twophotons:

π0

→

2 γ

The decay
π⁰
→ 3
γ
(as well as decays into any odd number of photons) is forbidden by theC-symmetryof the electromagnetic interaction: The intrinsic C-parity of the
π⁰
is +1, while the C-parity of a system ofnphotons is (−1)ⁿ.

The second largest
π⁰
decay mode (BR_γee= 0.01174) is the Dalitz decay (named afterRichard Dalitz), which is a two-photon decay with an internal photon conversion resulting a photon and anelectron-positronpair in the final state:

π0

→

γ

+

e−

+

e+

The third largest established decay mode (BR_2e2e=3.34×10⁻⁵) is the double-Dalitz decay, with both photons undergoing internal conversion which leads to further suppression of the rate:

π0

→

e−

+

e+

+

e−

+

e+

The fourth largest established decay mode is theloop-inducedand therefore suppressed (and additionallyhelicity-suppressed) leptonic decay mode (BR_ee=6.46×10⁻⁸):

π0

→

e−

+

e+

The neutral pion has also been observed to decay intopositroniumwith a branching fraction on the order of 10⁻⁹.No other decay modes have been established experimentally. The branching fractions above are thePDGcentral values, and their uncertainties are omitted, but available in the cited publication.

Pions

Particle name	Particle symbol	Antiparticle symbol	Quark content	Rest mass(MeV/c2)	IG	JPC	S	C	B'	Mean lifetime(s)	Commonly decays to (>5% of decays)
Pion	π+	π−	u d	139.57039±0.00018	1−	0−	0	0	0	2.6033 ± 0.0005 × 10−8	μ+ + ν μ
Pion	π0	Self	${\tfrac {\mathrm {u{\bar {u}}} -\mathrm {d{\bar {d}}} }{\sqrt {2}}}$[a]	134.9768±0.0005	1−	0−+	0	0	0	8.5 ± 0.2 × 10−17	γ + γ

^[a]^Make-up inexact due to non-zero quark masses.

See also

• Pionium
• Quark model
• Static forces and virtual-particle exchange
• Sanford-Wang parameterisation

Further reading

• Gerald Edward Brownand A. D. Jackson,The Nucleon-Nucleon Interaction(1976), North-Holland Publishing, AmsterdamISBN0-7204-0335-9

External links

• Media related toPionsat Wikimedia Commons
• Mesonsat the Particle Data Group