Kaon

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 (Butler and Rochester)
Types	4
Mass	K± :493.677±0.016MeV/c2 K0 :497.611±0.013 MeV/c2
Mean lifetime	K± :(1.2380±0.0020)×10−8s K S:(8.954±0.004)×10−11s K L:(5.116±0.021)×10−8s
Electric charge	K± :±1e K0 :0e
Spin	0ħ
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 bothweakandstrong 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 mesonand denoted
K
,is any of a group of fourmesonsdistinguished by aquantum numbercalledstrangeness.In thequark modelthey are understood to bebound statesof astrange quark(or antiquark) and anupordownantiquark (or quark).

Kaons have proved to be a copious source of information on the nature offundamental interactionssince their discovery incosmic raysin 1947. They were essential in establishing the foundations of theStandard Modelof particle physics, such as thequark modelofhadronsand the theory ofquark mixing(the latter was acknowledged by aNobel Prize in Physicsin 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 experimentatCERNand the KTeV experiment atFermilab.

Basic properties

The four kaons are:

1. 
   K⁻
   ,negatively charged (containing astrange quarkand anup antiquark) has mass493.677±0.013 MeVandmean lifetime(1.2380±0.0020)×10⁻⁸s.
2. 
   K⁺
   (antiparticleof above) positively charged (containing anup quarkand 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)×10⁻⁸s,also consistent with zero.
3. 
   K⁰
   ,neutrally charged (containing adown quarkand astrange antiquark) has mass497.648±0.022 MeV.It has mean squaredcharge radiusof−0.076±0.01fm².
4. 
   K⁰
   ,neutrally charged (antiparticle of above) (containing astrange quarkand adown antiquark) has the same mass.

As thequark modelshows, assignments that the kaons form twodoubletsofisospin;that is, they belong to thefundamental representationofSU(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)	IG	JPC	S	C	B'	Mean lifetime(s)	Commonly decays to (>5% of decays)
Kaon	K+	K−	u s	493.677±0.016	1⁄2	0−	1	0	0	(1.2380±0.0020)×10−8	μ+ + ν μor π+ + π0 or π+ + π+ + π− or π0 + e+ + ν e
Kaon	K0	K0	d s	497.611±0.013	1⁄2	0−	1	0	0	[§]	[§]
K-Short	K0 S	Self	$\mathrm {\tfrac {d{\bar {s}}-s{\bar {d}}}{\sqrt {2}}} \,$[†]	497.611±0.013[‡]	1⁄2	0−	[*]	0	0	(8.954±0.004)×10−11	π+ + π− or π0 + π0
K-Long	K0 L	Self	$\mathrm {\tfrac {d{\bar {s}}+s{\bar {d}}}{\sqrt {2}}} \,$[†]	497.611±0.013[‡]	1⁄2	0−	[*]	0	0	(5.116±0.021)×10−8	π± + e∓ + ν eor π± + μ∓ + ν μor π0 + π0 + π0 or π+ + π0 + π−

Quark structure of the kaon (K⁺).

^[*]SeeNotes on neutral kaonsin the articleList of mesons,andneutral kaon mixing,below.
^[§]^Strongeigenstate.No definite lifetime (seeneutral kaon mixing).
^[†]^Weakeigenstate.Makeup is missing smallCP–violatingterm (seeneutral kaon mixing).
^[‡]^The mass of the
K⁰
_Land
K⁰
_Sare given as that of the
K⁰
.However, it is known that a relatively minute difference between the masses of the
K⁰
_Land
K⁰
_Son the order of3.5×10⁻⁶eV/c²exists.

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 weakeigenstateswhich have vastly different lifetimes:

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

  

  Quark structure of the antikaon (K⁻).

(See discussion ofneutral kaon mixingbelow.)

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

Two different decays were found for charged strange mesons intopions:

Θ+	→	π+ + π0
τ+	→	π+ + π+ + π−

The intrinsicparityof 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 violationinweak 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,now called the
K⁺
.

History

See also:Strangeness

The discovery of hadrons with the internal quantum number "strangeness" marks the beginning of a most exciting epoch in particle physics that even now, fifty years later, has not yet found its conclusion... by and large experiments have driven the development, and that major discoveries came unexpectedly or even against expectations expressed by theorists. — Bigi & Sanda (2016)

While looking for the hypotheticalnuclear meson,Louis Leprince-Ringuetfound evidence for the existence of a positively charged heavier particle in 1944.

In 1947,G.D. RochesterandC.C. Butlerof theUniversity of Manchesterpublished twocloud chamberphotographs ofcosmic ray-induced events, one showing what appeared to be a neutral particle decaying into two charged pions, and one which appeared to be a charged particle decaying into a charged pion and something neutral. The estimated mass of the new particles was very rough, about half a proton's mass. More examples of these "V-particles" were slow in coming.

The "k track plate" showing the three-pion decay mode of a kaon. The kaon enters from the left, and decays at the point labelled A

In 1949,Rosemary Brown(later Rosemary Fowler), a research student ofCecil Powellof theUniversity of Bristol,spotted her 'k' track, made by a particle of very similar mass that decayed to three pions.

I knew at once that it was new and would be very important. We were seeing things that hadn't been seen before - that's what research in particle physics was. It was very exciting. — Fowler (2024)

This led to the so-called 'tau–theta' problem:what seemed to be the same particle (now called
K⁺
) decayed in two different modes, Theta to two pions (parity +1), Tau to three pions (parity −1).The solution to this puzzle turned out to be that weak interactionsdo not conserve parity.

The first breakthrough was obtained atCaltech,where a cloud chamber was taken upMount Wilson,for greater cosmic ray exposure. In 1950, 30 charged and 4 neutral "V-particles" were reported. Inspired by this, numerous mountaintop observations were made over the next several years, and by 1953, the following terminology was being used: "L meson" for either amuonor chargedpion;"K meson" meant a particle intermediate in mass between the pion andnucleon.

Leprince-Rinquet coined the still-used term "hyperon"to mean any particle heavier than a nucleon.The Leprince-Ringuet particle turned out to be the K⁺meson.

The decays were extremely slow; typical lifetimes are of the order of10⁻¹⁰s.However, production inpion–protonreactions proceeds much faster, with a time scale of10⁻²³s.The problem of this mismatch was solved byAbraham Paiswho postulated the new quantum number called "strangeness"which is conserved instrong interactionsbut violated by theweak interactions.Strange particlesappear copiously due to "associated production" of a strange and an antistrange particle together. It was soon shown that this could not be amultiplicative quantum number,because that would allow reactions which were never seen in the newsynchrotronswhich were commissioned inBrookhaven National Laboratoryin 1953 and in theLawrence Berkeley Laboratoryin 1955.

CP violation in neutral meson oscillations

Initially it was thought that althoughparitywas violated,CP (charge parity) symmetrywas 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

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-bosonsof 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-MannandAbraham Paistogether. They considered the CP-invariant time evolution of states with opposite strangeness. In matrix notation one can write

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

whereψis aquantum stateof the system specified by the amplitudes of being in each of the twobasis states(which areaandbat timet= 0). The diagonal elements (M) of theHamiltonianare due tostrong interactionphysics 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 symmetryrequires them to be real.

The consequence of the matrixHbeing 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

The eigenstates are obtained by diagonalizing this matrix. This gives new eigenvectors, which we can callK₁which is the difference of the two states of opposite strangeness, andK₂,which is the sum. The two are eigenstates ofCPwith opposite eigenvalues;K₁hasCP= +1, andK₂hasCP= −1 Since the two-pion final state also hasCP= +1, only theK₁can decay this way. TheK₂must decay into three pions.

Since the mass ofK₂is 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 ofK₁into two pions. These two different modes of decay were observed byLeon Ledermanand his coworkers in 1956, establishing the existence of the twoweakeigenstates(states with definitelifetimesunder 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=K₁and
K
_L=K₂.

Oscillation

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 decayshowed the phenomenon of oscillation, and allowed the extraction of the mass splitting between the
K
_Sand
K
_L.Since this is due to weak interactions it is very small, 10⁻¹⁵times the mass of each state, namely∆M_K= M(K_L) − M(K_S) = 3.484(6)×10⁻¹²MeV.

Regeneration

A beam of neutral kaons decays in flight so that the short-lived
K
_Sdisappears, 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 scatteringwithnucleons,whereas its antiparticle can createhyperons.Quantum coherencebetween 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
_Land
K
_S;the
K
_Sis regenerated by passing a neutral kaon beam through matter.Regeneration was observed byOreste Piccioniand his collaborators atLawrence Berkeley National Laboratory.Soon thereafter, Robert Adair and his coworkers reported excess
K
_Sregeneration, thus opening a new chapter in this history.

CP violation

While trying to verify Adair's results, J. Christenson,James Cronin,Val FitchandRene TurlayofPrinceton Universityfound decays of
K
_Linto two pions (CP= +1) in anexperiment performed in 1964at theAlternating Gradient Synchrotronat theBrookhaven laboratory.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 Physicsfor this discovery in 1980.

It turns out that although the
K
_Land
K
_Sareweakeigenstates(because they have definitelifetimesfor decay by way of the weak force), they are not quiteCPeigenstates. Instead, for small ε (and up to normalization),

K
_L=K₂+ εK₁

and similarly for
K
_S.Thus occasionally the
K
_Ldecays as aK₁withCP= +1, and likewise the
K
_Scan decay withCP= −1. This is known asindirect CP violation,CP violation due to mixing of
K⁰
and its antiparticle. There is also adirect CP violationeffect, 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 bosonand thus have CP violation predicted by theCKM matrix.Direct CP violation was discovered in the kaon decays in the early 2000s by theNA48andKTeVexperiments at CERN and Fermilab.

See also

• Hadrons,mesons,hyperonsandflavour
• Strange quarkand thequark model
• Parity (physics),charge conjugation,time reversal symmetry,CPT invarianceandCP violation
• Neutrino oscillation
• Neutral particle oscillation

Bibliography

• 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.S2CID227119789.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
• Sozzi, M.S. (2008).Discrete symmetries and CP violation.Oxford University Press.ISBN978-0-19-929666-8.
• Bigi, I. I.; Sanda, A.I. (2000).CP violation.Cambridge University Press.ISBN0-521-44349-0.
• Griffiths, D. J. (1987).Introduction to Elementary Particle.John Wiley & Sons.ISBN0-471-60386-4.

External links

• The neutral K-meson – The Feynman Lectures on Physics
• Media related toKaonat Wikimedia Commons