Kaon

Template:Short description {{#invoke:other uses|otheruses}} Template:Distinguish Template:Infobox Particle[[File:Kaon-Decay.svg|thumb|300px| The decay of a kaon (Template:SubatomicParticle) into three pions (2 Template:SubatomicParticle, 1 Template:SubatomicParticle) is a process that involves both weak and strong interactions.

Weak interactions : The strange antiquark (Template:SubatomicParticle) of the kaon transmutes into an up antiquark (Template:SubatomicParticle) by the emission of a [[W and Z bosons|Template:SubatomicParticle boson]]; the Template:SubatomicParticle boson subsequently decays into a down antiquark 

(Template:SubatomicParticle) and an up quark (Template:SubatomicParticle).

Strong interactions: An up quark (Template:SubatomicParticle) emits a gluon (Template:SubatomicParticle) which decays into a down quark (Template:SubatomicParticle) and a down antiquark (Template:SubatomicParticle).]] In particle physics, a kaon, also called a K meson and denoted Template:SubatomicParticle,Template:Efn is any of a group of four mesons distinguished by a quantum number called strangeness. In the quark model they are understood to be bound states of a strange quark (or antiquark) and an up or down antiquark (or quark).

Kaons have proved to be a copious source of information on the nature of fundamental interactions since their discovery by George Rochester and Clifford Butler at the Department of Physics and Astronomy, University of Manchester in cosmic rays in 1947. They were essential in establishing the foundations of the Standard Model of particle physics, such as the quark model of hadrons and the theory of quark mixing (the latter was acknowledged by a Nobel Prize in Physics in 2008). Kaons have played a distinguished role in our understanding of fundamental conservation 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 the NA48 experiment at CERN and the KTeV experiment at Fermilab.

Basic properties

The four kaons are:

1. Template:SubatomicParticle, negatively charged (containing a strange quark and an up antiquark) has mass Template:Val and mean lifetime Template:Val.
2. Template:SubatomicParticle (antiparticle of above) positively charged (containing an up quark and a strange antiquark) must (by CPT invariance) have mass and lifetime equal to that of Template:SubatomicParticle. Experimentally, the mass difference is Template:Val, consistent with zero; the difference in lifetimes is Template:Val, also consistent with zero.
3. Template:SubatomicParticle, neutrally charged (containing a down quark and a strange antiquark) has mass Template:Val. It has mean squared charge radius of Template:Val.
4. Template:SubatomicParticle, neutrally charged (antiparticle of above) (containing a strange quark and a down antiquark) has the same mass.

As the quark model shows, assignments that the kaons form two doublets of isospin; that is, they belong to the fundamental representation of SU(2) called the 2. One doublet of strangeness +1 contains the Template:SubatomicParticle and the Template:SubatomicParticle. The antiparticles form the other doublet (of strangeness −1).

Properties of kaons

Particle name	Particle Template:Brsymbol	Antiparticle Template:Brsymbol	Quark Template:Brcontent	Rest mass (MeV/c2)	IG	JPC	S	C	B′	Mean lifetime Template:BrTemplate:Bracket	Commonly decays to Template:Br(> 5% of decays)
citation	CitationClass=web }}</ref>	Template:SubatomicParticle	Template:SubatomicParticle	Template:SubatomicParticleTemplate:SubatomicParticle	Template:Val	Template:Sfrac	0−	1	0	0	Template:Val	Template:Math or Template:Math or Template:Math or Template:Math
citation	CitationClass=web }}</ref>	Template:SubatomicParticle	Template:SubatomicParticle	Template:SubatomicParticleTemplate:SubatomicParticle	Template:Val	Template:Sfrac	0−	1	0	0	{{#if:[§]|[§]|[1]}}	{{#if:[§]|[§]|[2]}}
citation	CitationClass=web }}</ref>	Template:SubatomicParticle	Self	<math>\mathrm{\tfrac{d\bar{s} - s\bar{d}}{\sqrt{2}}}\,</math>{{#if:[†]|[†]|[3]}}<ref name="cambridge">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref><ref name="southampton">{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>	Template:Val{{#if:[‡]|[‡]|[4]}}	Template:Sfrac	0−	[*]	0	0	Template:Val	Template:Math or Template:Math
citation	CitationClass=web }}</ref>	Template:SubatomicParticle	Self	<math>\mathrm{\tfrac{d\bar{s} + s\bar{d}}{\sqrt{2}}}\,</math>{{#if:[†]|[†]|[5]}}<ref name="cambridge"></ref><ref name="southampton"></ref>	Template:Val{{#if:[‡]|[‡]|[6]}}	Template:Sfrac	0−	[*]	0	0	Template:Val	Template:Math or Template:Math or Template:Math or Template:Math

File:Quark structure kaon plus.svg

Quark structure of the kaon (K⁺).

^[*] See Notes on neutral kaons in the article List of mesons, and neutral kaon mixing, below.Template:Br ^[§]^{{#if:| }} Strong eigenstate. No definite lifetime (see neutral kaon mixing).Template:Br ^[†]^{{#if:| }} Weak eigenstate. Makeup is missing small CP–violating term (see neutral kaon mixing).Template:Br ^[‡]^{{#if:| }} The mass of the Template:SubatomicParticle and Template:SubatomicParticle are given as that of the Template:SubatomicParticle. However, it is known that a relatively minute difference between the masses of the Template:SubatomicParticle and Template:SubatomicParticle on the order of Template:Val exists.<ref name=PDGK-long/>

Although the Template:SubatomicParticle and its antiparticle Template:SubatomicParticle are usually produced via the strong force, they decay weakly. Thus, once created the two are better thought of as superpositions of two weak eigenstates which have vastly different lifetimes:

• The long-lived neutral kaon is called the Template:SubatomicParticle ("K-long"), decays primarily into three pions, and has a mean lifetime of Template:Val.
• The short-lived neutral kaon is called the Template:SubatomicParticle ("K-short"), decays primarily into two pions, and has a mean lifetime Template:Val.
  File:Quark structure antikaon.svg

  Quark structure of the antikaon (K⁻).

(See discussion of neutral kaon mixing below.)

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

Main decay modes for Template:SubatomicParticle:

File:Quark structure neutral kaon.svg

Quark structure of the neutral kaon (K⁰).

Results	Mode	Branching ratio
Template:Math	leptonic	Template:Val
Template:Math	hadronic	Template:Val
Template:Math	hadronic	Template:Val
Template:Math	hadronic	Template:Val
Template:Math	semileptonic	Template:Val
Template:Math	semileptonic	Template:Val

Decay modes for the Template:SubatomicParticle are charge conjugates of the ones above.

Parity violation

Two different decays were found for charged strange mesons into pions:

Template:SubatomicParticle	→	Template:SubatomicParticle + Template:SubatomicParticle
Template:SubatomicParticle	→	Template:SubatomicParticle + Template:SubatomicParticle + Template:SubatomicParticle

The intrinsic parity 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 the τ–θ puzzle. It was resolved only by the discovery of parity violation in weak interactions (most importantly, by the Wu experiment). Since the mesons decay through weak interactions, parity is not conserved, and the two decays are actually decays of the same particle,<ref name="Lee 1956">Template:Cite journal</ref> now called the Template:SubatomicParticle.

History

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)<ref>Template:Cite book</ref>

While looking for the hypothetical nuclear meson, Louis Leprince-Ringuet found evidence for the existence of a positively charged heavier particle in 1944.<ref name=":0">Template:Cite journal</ref><ref name=":1">Template:Cite conference</ref>

In 1947, G.D. Rochester and C.C. Butler of the University of Manchester published two cloud chamber photographs of cosmic 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.

File:The "k track plate" showing three-pion decay mode of a kaon, 15 Jan 1949.png

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 of Cecil Powell of the University of Bristol, spotted her 'k' track, made by a particle of very similar mass that decayed to three pions.<ref name=":2">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name=Brown-Camerini-etal-1949/>Template:Rp

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)<ref name=":2" />

This led to the so-called 'tau–theta' problem:<ref name="Sheehy2024">Template:Cite journal</ref> what seemed to be the same particle (now called Template:SubatomicParticle) decayed in two different modes, Theta to two pions (parity +1), Tau to three pions (parity −1).<ref name="Brown-Camerini-etal-1949">Template:Cite journal Note same issue: Template:Cite journal</ref> The solution to this puzzle turned out to be that weak interactions do not conserve parity.<ref name="Lee 1956" />

The first breakthrough was obtained at Caltech, where a cloud chamber was taken up Mount 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 a muon or charged pion; "K meson" meant a particle intermediate in mass between the pion and nucleon.

Leprince-Rinquet coined the still-used term "hyperon" to mean any particle heavier than a nucleon.<ref name=":0"/><ref name=":1"/> The Leprince-Ringuet particle turned out to be the K⁺ meson.<ref name=":0"/><ref name=":1"/>

The decays were extremely slow; typical lifetimes are of the order of Template:Val. However, production in pion–proton reactions proceeds much faster, with a time scale of Template:Val. The problem of this mismatch was solved by Abraham Pais who postulated the new quantum number called "strangeness" which is conserved in strong interactions but violated by the weak interactions. Strange particles appear copiously due to "associated production" of a strange and an antistrange particle together. It was soon shown that this could not be a multiplicative quantum number, because that would allow reactions which were never seen in the new synchrotrons which were commissioned in Brookhaven National Laboratory in 1953 and in the Lawrence Berkeley Laboratory in 1955.

CP violation in neutral meson oscillations

Initially it was thought that although parity was violated, CP (charge parity) symmetry was conserved. In order to understand the discovery of CP 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

File:Kaon-box-diagram-with-bar.svg

Two different neutral K mesons, carrying different strangeness, can turn from one into another through the weak interactions, since these interactions do not conserve strangeness. The strange quark in the anti-Template:SubatomicParticle turns into a down quark by successively absorbing two W-bosons of opposite charge. The down antiquark in the anti-Template:SubatomicParticle 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 called neutral 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 by Murray Gell-Mann and Abraham Pais together. They considered the CP-invariant time evolution of states with opposite strangeness. In matrix notation one can write

<math> \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} ,</math>

where ψ is a quantum state of the system specified by the amplitudes of being in each of the two basis states (which are a and b at time t = 0). The diagonal elements (M) of the Hamiltonian are due to strong 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 to weak interactions; CP symmetry requires them to be real.

The consequence of the matrix H 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 by CP 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 call K₁ which is the difference of the two states of opposite strangeness, and K₂, which is the sum. The two are eigenstates of CP with opposite eigenvalues; K₁ has CP = +1, and K₂ has CP = −1 Since the two-pion final state also has CP = +1, only the K₁ can decay this way. The K₂ must decay into three pions. <ref>* Template:Cite book</ref>

Since the mass of K₂ 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 of K₁ into two pions. These two different modes of decay were observed by Leon Lederman and his coworkers in 1956, establishing the existence of the two weak eigenstates (states with definite lifetimes under decays via the weak force) of the neutral kaons.

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

Oscillation

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} An initially pure beam of Template:SubatomicParticle will turn into its antiparticle, Template:SubatomicParticle, while propagating, which will turn back into the original particle, Template:SubatomicParticle, and so on. This is called particle oscillation. On observing the weak decay into leptons, it was found that a Template:SubatomicParticle always decayed into a positron, whereas the antiparticle Template:SubatomicParticle decayed into the electron. The earlier analysis yielded a relation between the rate of electron and positron production from sources of pure Template:SubatomicParticle and its antiparticle Template:SubatomicParticle. Analysis of the time dependence of this semileptonic decay showed the phenomenon of oscillation, and allowed the extraction of the mass splitting between the Template:SubatomicParticle and Template:SubatomicParticle. Since this is due to weak interactions it is very small, 10⁻¹⁵ times the mass of each state, namely Template:Nowrap.<ref> Template:Cite journal </ref>

Regeneration

A beam of neutral kaons decays in flight so that the short-lived Template:SubatomicParticle disappears, leaving a beam of pure long-lived Template:SubatomicParticle. If this beam is shot into matter, then the Template:SubatomicParticle and its antiparticle Template:SubatomicParticle interact differently with the nuclei. The Template:SubatomicParticle undergoes quasi-elastic scattering with nucleons, whereas its antiparticle can create hyperons. 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 Template:SubatomicParticle and Template:SubatomicParticle. Such a superposition is a mixture of Template:SubatomicParticle and Template:SubatomicParticle; the Template:SubatomicParticle is regenerated by passing a neutral kaon beam through matter.<ref>Template:Cite journal</ref> Regeneration was observed by Oreste Piccioni and his collaborators at Lawrence Berkeley National Laboratory.<ref>Template:Cite journal</ref> Soon thereafter, Robert Adair and his coworkers reported excess Template:SubatomicParticle regeneration, thus opening a new chapter in this history.

CP violation

While trying to verify Adair's results, J. Christenson, James Cronin, Val Fitch and Rene Turlay of Princeton University found decays of Template:SubatomicParticle into two pions (CP = +1) in an experiment performed in 1964 at the Alternating Gradient Synchrotron at the Brookhaven laboratory.<ref>Template:Cite journal</ref> As explained in an earlier section, this required the assumed initial and final states to have different values of CP, and hence immediately suggested CP 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 the Nobel Prize in Physics for this discovery in 1980.

It turns out that although the Template:SubatomicParticle and Template:SubatomicParticle are weak eigenstates (because they have definite lifetimes for decay by way of the weak force), they are not quite CP eigenstates. Instead, for small ε (and up to normalization),

Template:SubatomicParticle = K₂ + εK₁

and similarly for Template:SubatomicParticle. Thus occasionally the Template:SubatomicParticle decays as a K₁ with CP = +1, and likewise the Template:SubatomicParticle can decay with CP = −1. This is known as indirect CP violation, CP violation due to mixing of Template:SubatomicParticle and its antiparticle. There is also a direct 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 the W boson and thus have CP violation predicted by the CKM matrix. Direct CP violation was discovered in the kaon decays in the early 2000s by the NA48 and KTeV experiments at CERN and Fermilab.<ref> Template:Cite book</ref>

See also

• Hadrons, mesons, hyperons and flavour
• Strange quark and the quark model
• Parity (physics), charge conjugation, time reversal symmetry, CPT invariance and CP violation
• Neutrino oscillation
• Neutral particle oscillation

Bibliography

• Template:Cite journal
• Template:Cite journal
• The quark model, by J.J.J. Kokkedee Template:Full citation needed
• Template:Cite book
• Template:Cite book
• Template:Cite book

External links

• The neutral K-meson – The Feynman Lectures on Physics
• Template:Commons category-inline