In particle physics, a kaon (/ˈkeɪɒn/, also called K-meson and denoted K) is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness. The elementary charge, usually denoted e, is the Electric charge carried by a single Proton, or equivalently the negative of the electric charge carried The elementary charge, usually denoted e, is the Electric charge carried by a single Proton, or equivalently the negative of the electric charge carried In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them In Particle physics, a meson is a strongly interacting Boson &mdashthat is a Hadron with integer spin. Quantum numbers describe values of conserved numbers in the dynamics of the Quantum system. In the quark model they are understood to contain a single strange quark (or antiquark). In Physics, the quark model is a classification scheme for Hadrons in terms of their valence quarks, i The strange quark is a second- generation Quark with a charge of &minus(1/3 e and a strangeness of &minus1

Basic properties

The four kaons are :

1. The negatively charged K⁻ (containing a strange quark and an up antiquark) has mass 493. The strange quark is a second- generation Quark with a charge of &minus(1/3 e and a strangeness of &minus1 The up quark is a particle described by the Standard Model theory of Physics. 667±0. 013 MeV and mean lifetime (1. Given an assembly of elements the number of which decreases ultimately to zero the lifetime (also called the mean lifetime) is a certain number that characterizes the rate 2384±0. 0024)×10⁻⁸ seconds.
2. Its antiparticle, the positively charged K⁺ (containing an up quark and a strange antiquark) must (by CPT invariance) have mass and lifetime equal to that of K⁻. to most kinds of particles, there is an associated antiparticle with the same Mass and opposite Electric charge. CPT symmetry is a fundamental symmetry of Physical laws under transformations that involve the inversions of charge, parity and The mass difference is 0. 032±0. 090 MeV, consistent with zero. The difference in lifetime is (0. 11±0. 09)×10⁻⁸ seconds.
3. The K⁰ (containing a down quark and a strange antiquark) has mass 497. The down quark is a first-generation Quark with a charge of -(1/3 e. The strange quark is a second- generation Quark with a charge of &minus(1/3 e and a strangeness of &minus1 648±0. 022 MeV. It has mean squared charge radius of −0. 076±0. 018 fm².
4. Its antiparticle K⁰ (containing a strange quark and a down antiquark) has the same mass. The strange quark is a second- generation Quark with a charge of &minus(1/3 e and a strangeness of &minus1 The down quark is a first-generation Quark with a charge of -(1/3 e.

It is clear from the quark model assignments that the kaons form two doublets of isospin; that is, they belong to the fundamental representation of SU(2) called the 2. In Physics, the quark model is a classification scheme for Hadrons in terms of their valence quarks, i In Physics, and specifically Particle physics, isospin ( isotopic spin, isobaric spin) is a Quantum number related to the In Representation theory of Lie groups and Lie algebras a fundamental representation is an irreducible finite-dimensional representation of a semisimple Special Unit 2In Mathematics, the special unitary group of degree n, denoted SU( n) is the group of n × n One doublet of strangeness +1 contains the K⁺ and the K⁰. The antiparticles form the other doublet.

Particle	Symbol	Anti- particle	Quark Makeup	Spin and parity	Rest mass MeV/c2	S	C	B	Mean lifetime s	Decays to	Notes
Charged Kaon	K+	K−	us / su	Pseudoscalar	493. In Physics, a quark (kwɔrk kwɑːk or kwɑːrk is a type of Subatomic particle. In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. In Particle physics, flavour or flavor (see spelling differences) is a Quantum number of Elementary particles related to their In Particle physics, flavour or flavor (see spelling differences) is a Quantum number of Elementary particles related to their Given an assembly of elements the number of which decreases ultimately to zero the lifetime (also called the mean lifetime) is a certain number that characterizes the rate The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units 7	+1	0	0	1. 24×10-8	μ+ + νμ or π+ + π0
Neutral Kaon	K0	K0	ds / sd	Pseudoscalar	497. 7	+1	0	0	weak decay		Strong eigenstate - no definite lifetime
K-Short	KS	KS		Pseudoscalar	497. This is a list of known and predicted Mesons. Mesons are made of Quarks and as such are part of the Subatomic particle family called the Hadrons In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes 7	(*)	0	0	0. This is a list of known and predicted Mesons. Mesons are made of Quarks and as such are part of the Subatomic particle family called the Hadrons 89×10-10	π+ + π− or 2π0	Weak eigenstate - makeup is missing small CP-violating term
K-Long	KL	KL		Pseudoscalar	497. The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics 7	(*)	0	0	5. This is a list of known and predicted Mesons. Mesons are made of Quarks and as such are part of the Subatomic particle family called the Hadrons 2×10-8	π+ + e− + νe	Weak eigenstate - makeup is missing small CP-violating term

Although the K⁰ and its antiparticle K⁰ are usually produced via the strong force, they decay weakly. The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature Thus, once created the two are better thought of as composites of two weak eigenstates which have vastly different lifetimes:

1. The long-lived neutral kaon is called the KL ("K-long"), decays primarily into three pions, and has a mean lifetime of 5. In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes In Particle physics, pion (short for pi meson) is the collective name for three Subatomic particles, and. 18×10⁻⁸ seconds.
2. The short-lived neutral kaon is called the KS ("K-short"), decays primarily into two pions, and has a mean lifetime 8. 958×10⁻¹¹ seconds.

(See discussion of neutral kaon mixing below. In Particle physics, a kaon (/ˈkeɪɒn/ also called K-meson and denoted) is any one of a group of four Mesons distinguished by the fact that they )

An experimental observation made in 1964 that K-longs rarely decay into two pions was the discovery of CP violation (see below). In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics

Main decay modes for K⁺:

μ+ νμ	(leptonic, BR = (63. In Particle physics and Nuclear physics, the branching fraction for a decay is the fraction of particles which decay by an individual Decay mode with respect 43±0. 17)%);
π+ π0	(hadronic, BR = (21. 13±0. 14)%);
π+ π+ π−	(hadronic, BR = (5. 576±0. 031)%);
π+ π0 π0	(hadronic, BR = (1. 73±0. 04)%);
π0 e+ νe	(semileptonic, BR = (4. 87±0. 06)%)

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.  — I. I.  Bigi and A. I.  Sanda, CP violation, (ISBN 0-521-44349-0)

In 1947, G. D. Rochester and C. George Dixon Rochester, FRS ( February 4 1908 &ndash December 26 2001) was a British physicist known for having co-discovered C. Butler 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 cloud chamber, also known as the Wilson chamber, is used for detecting particles of Ionizing radiation. For the 1962 Bruce Conner film see Cosmic Ray (film Cosmic rays are energetic particles originating from space that impinge on 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 first breakthrough was obtained at Caltech, where a cloud chamber was taken up Mount Wilson, for greater cosmic ray exposure. The California Institute of Technology (commonly referred to as Caltech) is a private, Coeducational research university located in Pasadena Mount Wilson is one of the more prominent peaks in the San Gabriel Mountains, part of the Angeles National Forest in Los Angeles County California, USA 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 adopted: "L-meson" meant muon or pion. The muon (from the letter mu (μ--used to represent it is an Elementary particle with negative Electric charge and a spin of 1/2 In Particle physics, pion (short for pi meson) is the collective name for three Subatomic particles, and. "K-meson" meant a particle intermediate in mass between the pion and nucleon. In Physics a nucleon is a collective name for two Baryons the Neutron and the Proton. "Hyperon" meant any particle heavier than a nucleon. In Particle physics, a hyperon is any Baryon containing a Strange quark, but no Charm quarks or Bottom quarks Properties

The decays were extremely slow; typical lifetimes are of the order of 10⁻¹⁰ seconds. However, production in pion-proton reactions proceeds much faster, with a time scale of 10⁻²³ seconds. In Particle physics, pion (short for pi meson) is the collective name for three Subatomic particles, and. The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive 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. Abraham (Bram Pais (May 19 1918 Amsterdam, The Netherlands &mdash July 28 2000 Copenhagen, Denmark) was a Dutch -born American In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature 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 cyclotrons which were commissioned in Brookhaven National Laboratory in 1953 and in the Lawrence Berkeley Laboratory in 1955. In Quantum field theory, multiplicative quantum numbers are conserved Quantum numbers of a special kind A cyclotron is a type of Particle accelerator. Cyclotrons accelerate Charged particles using a high- Frequency, alternating Voltage (potential Brookhaven National Laboratory ( BNL) is a United States national laboratory located in Upton New York on Long Island, and was formally established The Ernest Orlando Lawrence Berkeley National Laboratory ( LBNL) is a U

Parity violation: the τ-θ puzzle

Two different decays were found for charged strange mesons:

Θ+	→	π+ + π0
τ+	→	π+ + π+ + π−

Since the two final states have different parity it was thought that the initial states should also have different parities, and hence be two distinct particles. In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. However, with increasingly precise measurements, there were found to be no difference between their masses and lifetimes, 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. In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature Since the mesons decay through weak interactions, parity need not be conserved, and the two decays may be caused by the same particle, now called the K⁺.

CP violation in neutral meson oscillations

Initially it was thought that although parity was violated, CP (charge parity) symmetry was conserved. In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics 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. In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics

Neutral kaon mixing

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 weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature The strange quark in the K⁰ turns into a down quark by successively emitting two W-bosons of opposite charge. The W and Z bosons are the Elementary particles that mediate the Weak force. The down antiquark in the K⁰ turns into a strange antiquark by absorbing 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. Murray Gell-Mann (born September 15, 1929) is an American Physicist who received the 1969 Nobel Prize in physics for his work Abraham (Bram Pais (May 19 1918 Amsterdam, The Netherlands &mdash July 28 2000 Copenhagen, Denmark) was a Dutch -born American They considered the CP-invariant time evolution of states with opposite strangeness. In matrix notation one can write

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). In Quantum physics, a quantum state is a mathematical object that fully describes a quantum system. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons The diagonal elements (M) of the Hamiltonian are due to strong interaction physics which conserves strangeness. In Quantum mechanics, the Hamiltonian H is the Observable corresponding to the Total energy of the system In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and 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 weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics

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. In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics 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 sum of the two states of opposite strangeness, and K₂, which is the difference. 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. 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. Leon Max Lederman (born July 15, 1922) is an American Experimental physicist and Nobel Prize in Physics laureate for The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes Given an assembly of elements the number of which decreases ultimately to zero the lifetime (also called the mean lifetime) is a certain number that characterizes the rate The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature

These two weak eigenstates are called the KL (K-long) and KS (K-short). CP symmetry, which was assumed at the time, implies that KS = K₁ and KL = K₂. In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics

Oscillation

An initially pure beam of K⁰ will turn into its antiparticle while propagating, which will turn back into the original particle, and so on. This is called particle oscillation. On observing the weak decay into leptons, it was found that a K⁰ always decayed into an electron, whereas the antiparticle K⁰ decayed into the positron. 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 this semileptonic decay showed the phenomenon of oscillation, and allowed the extraction of the mass splitting between the KS and KL. In Particle physics the semileptonic decay of a Hadron refers to a decay through the Weak interaction in which one Lepton (and the corresponding Since this is due to weak interactions it is very small, 10⁻¹⁵ times the mass of each state.

Regeneration

A beam of neutral kaons decays in flight so that the short-lived KS disappears, leaving a beam of pure long-lived KL. 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 with nucleons, whereas its antiparticle can create hyperons. In Scattering theory and in particular in Particle physics, elastic scattering is one of the specific forms of scattering In Physics a nucleon is a collective name for two Baryons the Neutron and the Proton. In Particle physics, a hyperon is any Baryon containing a Strange quark, but no Charm quarks or Bottom quarks Properties Due to the different interactions of the two components, quantum coherence between the two particles is lost. In Physics, coherence is a property of waves that enables stationary (i The emerging beam then contains different linear superpositions of the K⁰ and K⁰. Such a superposition is a mixture of KL and KS; the KS is regenerated by passing a neutral kaon beam through matter. Regeneration was observed by Oreste Piccioni and his collaborators at Lawrence Berkeley National Laboratory. The Ernest Orlando Lawrence Berkeley National Laboratory ( LBNL) is a U Soon thereafter, Robert Adair and his coworkers reported excess KS regeneration, thus opening a new chapter in this history.

CP violation

While trying to verify Adair's results, in 1964 James Cronin and Val Fitch of BNL found decays of KL into two pions (CP = +1). James Watson Cronin (born September 29, 1931) is an American nuclear physicist. Val Logsdon Fitch (born March 10, 1923, Merriman, Nebraska, USA) is an American nuclear physicist. Brookhaven National Laboratory ( BNL) is a United States national laboratory located in Upton New York on Long Island, and was formally established 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. In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics Alternative explanations such as non-linear quantum mechanics and a new unobserved particle 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. The Nobel Prize in Physics (Nobelpriset i fysik is awarded once a year by the Royal Swedish Academy of Sciences.

It turns out that although the KL and KS are weak eigenstates (because they have definite lifetimes for decay by way of the weak force), they are not quite CP eigenstates. The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes Given an assembly of elements the number of which decreases ultimately to zero the lifetime (also called the mean lifetime) is a certain number that characterizes the rate Instead, for small ε (and up to normalization),

KL = K₂ + εK₁

and similarly for KS. Thus occasionally the KL decays as a K₁ with CP = +1, and likewise the KS can decay with CP = −1. This is known as indirect CP violation, CP violation due to mixing of K⁰ 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. The W and Z bosons are the Elementary particles that mediate the Weak force. In the Standard Model of Particle physics, the Cabibbo-Kobayashi-Maskawa matrix ( CKM matrix, quark mixing matrix, sometimes also called

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

References and external links

• Particle data group on strange mesons
• The quark model, by J. In Particle physics, a hadron ( from the ἁδρός hadrós, " stout, thick " ( In Particle physics, a meson is a strongly interacting Boson &mdashthat is a Hadron with integer spin. In Particle physics, a hyperon is any Baryon containing a Strange quark, but no Charm quarks or Bottom quarks Properties In Particle physics, flavour or flavor (see spelling differences) is a Quantum number of Elementary particles related to their The strange quark is a second- generation Quark with a charge of &minus(1/3 e and a strangeness of &minus1 In Physics, the quark model is a classification scheme for Hadrons in terms of their valence quarks, i In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. In Physics, C-symmetry means the symmetry of physical laws under a charge -conjugation transformation. T Symmetry is the symmetry of physical laws under a Time reversal transformation &mdash T t \mapsto -t CPT symmetry is a fundamental symmetry of Physical laws under transformations that involve the inversions of charge, parity and In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvo whereby a Neutrino created with a specific Lepton J. J. Kokkedee
• Sozzi, M. S. (2008). Discrete symmetries and CP violation. Oxford University Press. ISBN 978-0-19-929666-8.  
• CP violation, by I. I. Bigi and A. I. Sanda (Cambridge University Press, 2000) ISBN 0-521-44349-0
• Griffiths, David (1987). Introduction to Elementary Particles. New York: John Wiley & Sons. ISBN 0-471-60386-4.