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Kaon

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From Wikipedia, the free encyclopedia

Quantum particle

For other uses, seeKaon (disambiguation).

Not to be confused withKōan.

Kaon
Composition	K⁺ : u s K⁰ : d s K⁻ : s u
Statistics	Bosonic
Family	Mesons
Interactions	Strong,weak,electromagnetic,gravitational
Symbol	K⁺ , K⁰ , K⁻
Antiparticle	K⁺ : K⁻ K⁰ : K⁰ K⁻ : K⁺
Discovered	1947 (Clifford Butler andGeorge Rochester atDepartment of Physics and Astronomy, University of Manchester)
Types	4
Mass	K^± :493.677±0.016 MeV/c² K⁰ :497.611±0.013 MeV/c²
Mean lifetime	K^± :(1.2380±0.0020)×10⁻⁸ s K _S:(8.954±0.004)×10⁻¹¹ s K _L:(5.116±0.021)×10⁻⁸ s
Electric charge	K^± : ±1 e K⁰ : 0 e
Spin	0 ħ
Strangeness	K⁺ , K⁰ : +1 K⁻ , K⁰ : −1
Isospin	K⁺ , K⁰ : +⁠1/2⁠ K⁰ , K⁻ : −⁠1/2⁠
Parity	−1

The decay of a kaon (
K⁺
) into threepions (2
π⁺
, 1
π⁻
) is a process that involves bothweak andstrong interactions.Weak interactions : Thestrange antiquark (
s
) of the kaon transmutes into anup antiquark (
u
) by the emission of a
W⁺
boson; the
W⁺
boson subsequently decays into adown antiquark (
d
) and anup quark (
u
).Strong interactions: An up quark (
u
) emits agluon (
g
) which decays into a down quark (
d
) and a down antiquark (
d
).

Inparticle physics, akaon, also called aK meson and denoted
K
,^[a] is any of a group of fourmesons distinguished by aquantum number calledstrangeness. In thequark model they are understood to bebound states of astrange quark (or antiquark) and anup ordown antiquark (or quark).

Kaons have proved to be a copious source of information on the nature offundamental interactions since their discovery byGeorge Rochester andClifford Butler at theDepartment of Physics and Astronomy, University of Manchester incosmic rays in 1947. They were essential in establishing the foundations of theStandard Model of particle physics, such as thequark model ofhadrons and the theory ofquark mixing (the latter was acknowledged by aNobel Prize in Physics in 2008). Kaons have played a distinguished role in our understanding of fundamentalconservation laws:CP violation, a phenomenon generating the observed matter–antimatter asymmetry of the universe, was discovered in the kaon system in 1964 (which was acknowledged by a Nobel Prize in 1980). Moreover, direct CP violation was discovered in the kaon decays in the early 2000s by theNA48 experiment atCERN and the KTeV experiment atFermilab.

Basic properties

[edit]

The four kaons are:

K⁻
, negatively charged (containing astrange quark and anup antiquark) has mass493.677±0.013 MeV andmean lifetime(1.2380±0.0020)×10⁻⁸ s.
K⁺
(antiparticle of above) positively charged (containing anup quark and astrange antiquark) must (byCPT invariance) have mass and lifetime equal to that of
K⁻
. Experimentally, the mass difference is0.032±0.090 MeV, consistent with zero; the difference in lifetimes is(0.11±0.09)×10⁻⁸ s, also consistent with zero.
K⁰
, neutrally charged (containing adown quark and astrange antiquark) has mass497.648±0.022 MeV. It has mean squaredcharge radius of−0.076±0.01 fm².
K⁰
, neutrally charged (antiparticle of above) (containing astrange quark and adown antiquark) has the same mass.

As thequark model shows, assignments that the kaons form twodoublets ofisospin; that is, they belong to thefundamental representation ofSU(2) called the2. One doublet of strangeness +1 contains the
K⁺
and the
K⁰
. The antiparticles form the other doublet (of strangeness −1).

Properties of kaons
Particle name	Particle symbol	Antiparticle symbol	Quark content	Rest mass (MeV/c²)	I^G	J^PC	S	Mean lifetime (s)	Commonly decays to (>5% of decays)
Kaon^[1]	K⁺	K⁻	u s	493.677±0.016	1⁄2	0⁻	1	(1.2380±0.0020)×10⁻⁸	μ⁺ + ν _μ or π⁺ + π⁰ or π⁺ + π⁺ + π⁻ or π⁰ + e⁺ + ν _e
Kaon^[2]	K⁰	K⁰	d s	497.611±0.013	1⁄2	0⁻	1	^{^[§]}	^{^[§]}
K-Short^[3]	K⁰ _S	Self	$\mathrm {\tfrac {d{\bar {s}}-s{\bar {d}}}{\sqrt {2}}} \,$ ^{^[†]}^[4]^[5]	497.611±0.013^{^[‡]}	1⁄2	0⁻	^[*]	(8.954±0.004)×10⁻¹¹	π⁺ + π⁻ or π⁰ + π⁰
K-Long^[6]	K⁰ _L	Self	$\mathrm {\tfrac {d{\bar {s}}+s{\bar {d}}}{\sqrt {2}}} \,$ ^{^[†]}^[4]^[5]	497.611±0.013^{^[‡]}	1⁄2	0⁻	^[*]	(5.116±0.021)×10⁻⁸	π^± + e^∓ + ν _e or π^± + μ^∓ + ν _μ or π⁰ + π⁰ + π⁰ or π⁺ + π⁰ + π⁻

^[*] SeeNotes on neutral kaons in the articleList of mesons, andneutral kaon mixing, below.
^[§]^Strong eigenstate. No definite lifetime (seeneutral kaon mixing).
^[†]^Weak eigenstate. Makeup is missing smallCP–violating term (seeneutral kaon mixing).
^[‡]^ The mass of the
K⁰
_L and
K⁰
_S are given as that of the
K⁰
. However, it is known that a relatively minute difference between the masses of the
K⁰
_L and
K⁰
_S on the order of3.5×10⁻⁶ eV/c² exists.^[6]

Although the
K⁰
and its antiparticle
K⁰
are usually produced via thestrong force, they decayweakly. Thus, once created the two are better thought of as superpositions of two weakeigenstates which have vastly different lifetimes:

Thelong-lived neutral kaon is called the
K
_L ("K-long"), decays primarily into threepions, and has a mean lifetime of5.18×10⁻⁸ s.
Theshort-lived neutral kaon is called the
K
_S ("K-short"), decays primarily into two pions, and has a mean lifetime8.958×10⁻¹¹ s.
Quark structure of the antikaon (K⁻).

(See discussion ofneutral kaon mixing below.)

An experimental observation made in 1964 that K-longs rarely decay into two pions was the discovery ofCP violation (see below).

Main decay modes for
K⁺
:

Quark structure of the neutral kaon (K⁰).

Results	Mode	Branching ratio
μ⁺ ν _μ	leptonic	63.55±0.11%
π⁺ π⁰	hadronic	20.66±0.08%
π⁺ π⁺ π⁻	hadronic	5.59±0.04%
π⁺ π⁰ π⁰	hadronic	1.761±0.022%
π⁰ e⁺ ν _e	semileptonic	5.07±0.04%
π⁰ μ⁺ ν _μ	semileptonic	3.353±0.034%

Decay modes for the
K⁻
are charge conjugates of the ones above.

Parity violation

[edit]

Two different decays were found for charged strange mesons intopions:

Θ⁺	→	π⁺ + π⁰
τ⁺	→	π⁺ + π⁺ + π⁻

The intrinsicparity of the pion is P = −1 (since the pion is a bound state of a quark and an antiquark, which have opposite parities, with zero angular momentum), and parity is a multiplicative quantum number. Therefore, assuming the parent particle has zero spin, the two-pion and the three-pion final states have different parities (P = +1 and P = −1, respectively). It was thought that the initial states should also have different parities, and hence be two distinct particles. However, with increasingly precise measurements, no difference was found between the masses and lifetimes of each, respectively, indicating that they are the same particle. This was known as theτ–θ puzzle. It was resolved only by the discovery ofparity violation inweak interactions (most importantly, by theWu experiment). Since the mesons decay through weak interactions, parity is not conserved, and the two decays are actually decays of the same particle,^[7] now called the
K⁺
.

History

[edit]

CP violation in neutral meson oscillations

[edit]

Initially it was thought that althoughparity was violated,CP (charge parity) symmetry was conserved. In order to understand the discovery ofCP violation, it is necessary to understand the mixing of neutral kaons; this phenomenon does not require CP violation, but it is the context in which CP violation was first observed.

Neutral kaon mixing

[edit]

Two different neutral K mesons, carrying different strangeness, can turn from one into another through theweak interactions, since these interactions do not conserve strangeness. The strange quark in the anti-
K⁰
turns into a down quark by successively absorbing twoW-bosons of opposite charge. The down antiquark in the anti-
K⁰
turns into a strange antiquark by emitting them.

Since neutral kaons carry strangeness, they cannot be their own antiparticles. There must be then two different neutral kaons, differing by two units of strangeness. The question was then how to establish the presence of these two mesons. The solution used a phenomenon calledneutral particle oscillations, by which these two kinds of mesons can turn from one into another through the weak interactions, which cause them to decay into pions (see the adjacent figure).

These oscillations were first investigated byMurray Gell-Mann andAbraham Pais together. They considered the CP-invariant time evolution of states with opposite strangeness. In matrix notation one can write

\psi (t)=U(t)\psi (0)={\rm {e}}^{iHt}{\begin{pmatrix}a\\b\end{pmatrix}},\qquad H={\begin{pmatrix}M&\Delta \\\Delta &M\end{pmatrix}},

whereψ is aquantum state of the system specified by the amplitudes of being in each of the twobasis states (which area andb at timet = 0). The diagonal elements (M) of theHamiltonian are due tostrong interaction physics which conserves strangeness. The two diagonal elements must be equal, since the particle and antiparticle have equal masses in the absence of the weak interactions. The off-diagonal elements, which mix opposite strangeness particles, are due toweak interactions;CP symmetry requires them to be real.

The consequence of the matrixH being real is that the probabilities of the two states will forever oscillate back and forth. However, if any part of the matrix were imaginary, as is forbidden byCP symmetry, then part of the combination will diminish over time. The diminishing part can be either one component (a) or the other (b), or a mixture of the two.

Mixing

[edit]

The eigenstates are obtained by diagonalizing this matrix. This gives new eigenvectors, which we can callK₁ which is the difference of the two states of opposite strangeness, andK₂, which is the sum. The two are eigenstates ofCP with opposite eigenvalues;K₁ hasCP = +1, andK₂ hasCP = −1 Since the two-pion final state also hasCP = +1, only theK₁ can decay this way. TheK₂ must decay into three pions.^[14]

Since the mass ofK₂ is just a little larger than the sum of the masses of three pions, this decay proceeds very slowly, about 600 times slower than the decay ofK₁ into two pions. These two different modes of decay were observed byLeon Lederman and his coworkers in 1956, establishing the existence of the twoweak eigenstates (states with definitelifetimes under decays via theweak force) of the neutral kaons.

These two weak eigenstates are called the
K
_L (K-long, τ) and
K
_S (K-short, θ).CP symmetry, which was assumed at the time, implies that
K
_S = K₁ and
K
_L = K₂.

Oscillation

[edit]

Main article:Neutral particle oscillation

An initially pure beam of
K⁰
will turn into its antiparticle,
K⁰
, while propagating, which will turn back into the original particle,
K⁰
, and so on. This is called particle oscillation. On observing the weak decayinto leptons, it was found that a
K⁰
always decayed into a positron, whereas the antiparticle
K⁰
decayed into the electron. The earlier analysis yielded a relation between the rate of electron and positron production from sources of pure
K⁰
and its antiparticle
K⁰
. Analysis of the time dependence of thissemileptonic decay showed the phenomenon of oscillation, and allowed the extraction of the mass splitting between the
K
_S and
K
_L. Since this is due to weak interactions it is very small, 10⁻¹⁵ times the mass of each state, namely ∆M_K = M(K_L) − M(K_S) = 3.484(6)×10⁻¹² MeV.^[15]

Regeneration

[edit]

A beam of neutral kaons decays in flight so that the short-lived
K
_S disappears, leaving a beam of pure long-lived
K
_L. If this beam is shot into matter, then the
K⁰
and its antiparticle
K⁰
interact differently with the nuclei. The
K⁰
undergoes quasi-elastic scattering withnucleons, whereas its antiparticle can createhyperons.Quantum coherence between the two particles is lost due to the different interactions that the two components separately engage in. The emerging beam then contains different linear superpositions of the
K⁰
and
K⁰
. Such a superposition is a mixture of
K
_L and
K
_S; the
K
_S is regenerated by passing a neutral kaon beam through matter.^[16] Regeneration was observed byOreste Piccioni and his collaborators atLawrence Berkeley National Laboratory.^[17] Soon thereafter, Robert Adair and his coworkers reported excess
K
_S regeneration, thus opening a new chapter in this history.

CP violation

[edit]

While trying to verify Adair's results, J. Christenson,James Cronin,Val Fitch andRene Turlay ofPrinceton University found decays of
K
_L into two pions (CP = +1)in anexperiment performed in 1964 at theAlternating Gradient Synchrotron at theBrookhaven laboratory.^[18] As explained inan earlier section, this required the assumed initial and final states to have different values ofCP, and hence immediately suggestedCP violation. Alternative explanations such as nonlinear quantum mechanics and a new unobserved particle (hyperphoton) were soon ruled out, leaving CP violation as the only possibility. Cronin and Fitch received theNobel Prize in Physics for this discovery in 1980.

It turns out that although the
K
_L and
K
_S areweak eigenstates (because they have definitelifetimes for decay by way of the weak force), they are not quiteCP eigenstates. Instead, for small ε (and up to normalization),

K
_L =K₂ + εK₁

and similarly for
K
_S. Thus occasionally the
K
_L decays as aK₁ withCP = +1, and likewise the
K
_S can decay withCP = −1. This is known asindirect CP violation, CP violation due to mixing of
K⁰
and its antiparticle. There is also adirect CP violation effect, in which the CP violation occurs during the decay itself. Both are present, because both mixing and decay arise from the same interaction with theW boson and thus have CP violation predicted by theCKM matrix. Direct CP violation was discovered in the kaon decays in the early 2000s by theNA48 andKTeV experiments at CERN and Fermilab.^[19]

Footnotes

[edit]

^Until the 1960s the positively charged kaon was formerly called τ⁺ or θ⁺, as it was believed to be two different particles. See the§ Parity violation.

References

[edit]

^Zyla, P.A.; et al. (2020)."Particle listings –
K^±
"(PDF).
^Zyla, P.A.; et al. (2020)."Particle listings –
K⁰
"(PDF).
^Zyla, P.A.; et al. (2020)."Particle listings –
K⁰
_S"(PDF).
^^a ^bM.A. Thomson."The CKM Matrix and CP Violation"(PDF).Cambridge HEP group. Retrieved2024-06-02.
^^a ^b"Parity, Charge Conjugation and CP"(PDF).University of Southampton. Retrieved2024-06-02.
^^a ^bZyla, P.A.; et al. (2020)."Particle listings –
K⁰
_L"(PDF).
^^a ^bLee, T. D.;Yang, C. N. (1 October 1956)."Question of Parity Conservation in Weak Interactions".Physical Review.104 (1): 254.Bibcode:1956PhRv..104..254L.doi:10.1103/PhysRev.104.254.One way out of the difficulty is to assume that parity is not strictly conserved, so that
Θ⁺
and
τ⁺
are two different decay modes of the same particle, which necessarily has a single mass value and a single lifetime.
^Bigi, I.I.; Sanda, A.I. (2016-10-06).CP Violation. Cambridge Monographs on Particle Physics, Nuclear Physics, and Cosmology. Vol. 28 (5th ed.). Cambridge University Press.ISBN 978-0-521-44349-4.
^^a ^b ^cDegrange, Bernard; Fontaine, Gérard; Fleury, Patrick (2013)."Tracking Louis Leprince-Ringuet's contributions to cosmic-ray physics".Physics Today.66 (6): 8.Bibcode:2013PhT....66f...8D.doi:10.1063/PT.3.1989.ISSN 0031-9228.
^^a ^b ^cRavel, Olivier (2012)."Early cosmic ray research in France". In Ormes, Jonathan F. (ed.).Centenary Symposium 2012: Discovery of cosmic rays. AIP Conference Proceedings. Vol. 1516. Denver, Colorado:American Institute of Physics. pp. 67–71.Bibcode:2013AIPC.1516...67R.doi:10.1063/1.4792542.ISBN 978-0-7354-1137-1.
^^a ^b"Physicist pioneer, 98, honoured 75 years after discovery".BBC News. 2024-07-23. Retrieved2024-07-23.
^^a ^bBrown, R.; Camerini, U.; Fowler, P.H.; Muirhead, H.; Powell, C.F.; Ritson, D.M. (1949). "Part 2: Observations with electron-sensitive plates exposed to cosmic radiation".Nature.163 (4133):82–87.Bibcode:1949Natur.163...82B.doi:10.1038/163082a0.S2CID 12974912. Note same issue:Brown; et al. (1949). "Part 1".Nature.163 (4133):47–51.doi:10.1038/163047a0.S2CID 4097342.
^Sheehy, Suzie (2024-01-15)."How a forgotten physicist's discovery broke the symmetry of the Universe".Nature.625 (7995):448–449.Bibcode:2024Natur.625..448S.doi:10.1038/d41586-024-00109-5.PMID 38225463. Retrieved23 July 2024.
^*Griffiths, D. J. (1987).Introduction to Elementary Particle.John Wiley & Sons.ISBN 0-471-60386-4.
^Aoki, S.; Aoki, Y.; Bečirević, D.; Blum, T.; Colangelo, G.; Collins, S.; et al. (2020). "FLAG Review 2019".The European Physical Journal C.80 (2): 113.arXiv:1902.08191.Bibcode:2020EPJC...80..113A.doi:10.1140/epjc/s10052-019-7354-7.S2CID 119401756.
^Pais, A.; Piccioni, O. (1 December 1955). "Note on the Decay and Absorption of the θ⁰".Physical Review.100 (5):1487–1489.doi:10.1103/PhysRev.100.1487.
^Good, R. H.; Matsen, R. P.; Muller, F.; Piccioni, O.; Powell, W. M.; White, H. S.; Fowler, W. B.; Birge, R. W. (15 November 1961). "Regeneration of Neutral K Mesons and Their Mass Difference".Physical Review.124 (4):1223–1239.Bibcode:1961PhRv..124.1223G.doi:10.1103/PhysRev.124.1223.
^Christenson, J. H.; Cronin, J. W.; Fitch, V. L.; Turlay, R. (27 July 1964)."Evidence for the 2π Decay of the K₂⁰ Meson".Physical Review Letters.13 (4):138–140.Bibcode:1964PhRvL..13..138C.doi:10.1103/physrevlett.13.138.
^ANZIVINO, GIUSEPPINA (2001). "Measurement of Direct Cp Violation by Na48".Multiparticle Dynamics. pp. 7–14.arXiv:hep-ph/0111393.doi:10.1142/9789812778048_0002.ISBN 978-981-02-4844-4.S2CID 15184466.

Bibliography

[edit]

Amsler, C.; Doser, M.; Antonelli, M.; Asner, D.; Babu, K.; Baer, H.; et al. (Particle Data Group) (2008)."Review of Particle Physics"(PDF).Physics Letters B.667 (1):1–1340.Bibcode:2008PhLB..667....1A.doi:10.1016/j.physletb.2008.07.018.hdl:1854/LU-685594.S2CID 227119789. Archived fromthe original(PDF) on 2020-09-07. Retrieved2019-12-13.
Eidelman, S.; Hayes, K.G.; Olive, K.A.; Aguilar-Benitez, M.; Amsler, C.; Asner, D.; et al. (Particle Data Group) (2004). "Review of Particle Physics".Physics Letters B.592 (1): 1.arXiv:astro-ph/0406663.Bibcode:2004PhLB..592....1P.doi:10.1016/j.physletb.2004.06.001.
The quark model, by J.J.J. Kokkedee^{[full citation needed]}
Sozzi, M.S. (2008).Discrete symmetries and CP violation.Oxford University Press.ISBN 978-0-19-929666-8.
Bigi, I. I.; Sanda, A.I. (2000).CP violation.Cambridge University Press.ISBN 0-521-44349-0.
Griffiths, D. J. (1987).Introduction to Elementary Particle.John Wiley & Sons.ISBN 0-471-60386-4.

External links

[edit]

Look upkaon in Wiktionary, the free dictionary.

The neutral K-meson – The Feynman Lectures on Physics
Media related toKaon at Wikimedia Commons

Particles in physics

Elementary

Fermions

Quarks	Up (quark antiquark) Down (quark antiquark) Charm (quark antiquark) Strange (quark antiquark) Top (quark antiquark) Bottom (quark antiquark)
Leptons	Electron Positron Muon Antimuon Tau Antitau Neutrino Electron neutrino Electron antineutrino Muon neutrino Muon antineutrino Tau neutrino Tau antineutrino

Bosons

Gauge	Photon Gluon W and Z bosons
Scalar	Higgs boson

Ghost fields

Faddeev–Popov ghosts

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Superpartners

Gauginos	Gluino Gravitino Photino
Others	Axino Chargino Higgsino Neutralino Sfermion (Stop squark)

Others

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Hadrons

Baryons	Nucleon Proton Antiproton Neutron Antineutron Delta baryon Lambda baryon Sigma baryon Xi baryon Omega baryon
Mesons	Pion Rho meson Eta and eta prime mesons Bottom eta meson Phi meson J/psi meson Omega meson Upsilon meson Kaon B meson D meson Quarkonium
Exotic hadrons	Tetraquark (Double-charm tetraquark) Pentaquark