Kaon
Encyclopedia
In particle physics
, a kaon (icon, also called a K-meson and denoted The positively charged kaon used to be called τ+ and θ+, as it was supposed to be two different particles until the 1960s. See the parity violation section above.) is any one of a group of four meson
s distinguished by the fact that they carry a quantum number
called strangeness. In the quark model
they are understood to contain a strange quark
(or antiquark), paired with 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 in 1947. They were essential in establishing the foundations of the Standard Model
of particle physics, such as the quark model
of hadron
s and the theory of quark mixing (the latter was acknowledged by a Nobel Prize in Physics
in 2008). Kaons played a distinguished role in our understanding of fundamental conservation law
s: the discovery of CP violation
(a phenomenon generating the observed matter-antimatter asymmetry of the universe), which was acknowledged by a Nobel prize in 1980, was made in the kaon system.
The four kaons are :
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. One doublet of strangeness +1 contains the and the . The antiparticles form the other doublet (of strangeness −1).
[a] Strong eigenstate. No definite lifetime (see kaon notes below)
[b] Weak eigenstate. Makeup is missing small CP–violating
term (see notes on neutral kaons below).
[c] The mass of the and are given as that of the . However, it is known that a difference between the masses of the and on the order of exists.
Although the and its antiparticle are usually produced via the strong force, they decay weakly. Thus, once created the two are better thought of as composites of two weak eigenstates which have vastly different lifetimes:
(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 :
Decay modes for the are charge conjugates of the ones above.
In 1947, G. D. Rochester
and Clifford Charles 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.
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 adopted: "L-meson" meant muon
or pion
. "K-meson" meant a particle intermediate in mass between the pion and nucleon
. "Hyperon
" meant any particle heavier than a nucleon.
The decays were extremely slow; typical lifetimes are of the order of . However, production in pion
-proton
reactions proceeds much faster, with a time scale of . The problem of this mismatch was solved by Abraham Pais
who postulated the new quantum number called "strangeness" which is conserved in strong interaction
s but violated by the weak interaction
s. 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 synchrotron
s which were commissioned in Brookhaven National Laboratory
in 1953 and in the Lawrence Berkeley Laboratory in 1955.
The intrinsic parity of a meson is P=−1, and parity is a multiplicative quantum number. Therefore, the two final states have different parity
(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 interaction
s. Since the mesons decay through weak interactions, parity is not conserved, and the two decays are actualy decays of the same particle, now called the .
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.
, 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
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.
eigenstates (states with definite lifetimes under decays via the weak force) of the neutral kaons.
These two weak eigenstates are called the (K-long) and (K-short). CP symmetry, which was assumed at the time, implies that = K1 and = K2.
showed the phenomenon of oscillation, and allowed the extraction of the mass splitting between the and . Since this is due to weak interactions it is very small, 10−15 times the mass of each state.
with nucleon
s, whereas its antiparticle can create hyperon
s. Due to the different interactions of the two components, quantum coherence between the two particles is lost. The emerging beam then contains different linear superpositions of the and . Such a superposition is a mixture of and ; the is regenerated by passing a neutral kaon beam through matter. Regeneration was observed by Oreste Piccioni
and his collaborators at Lawrence Berkeley National Laboratory
. Soon thereafter, Robert Adair and his coworkers reported excess regeneration, thus opening a new chapter in this history.
and Val Fitch of BNL
found decays of into two pions (CP = +1). 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 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.
It turns out that although the and 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),
and similarly for . Thus occasionally the decays as a K1 with CP = +1, and likewise the can decay with CP = −1. This is known as indirect CP violation, CP violation due to mixing of 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.
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, a kaon (icon, also called a K-meson and denoted The positively charged kaon used to be called τ+ and θ+, as it was supposed to be two different particles until the 1960s. See the parity violation section above.) is any one of a group of four meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s distinguished by the fact that they carry a quantum number
Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
called strangeness. In the quark model
Quark model
In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons....
they are understood to contain a strange quark
Strange quark
The strange quark or s quark is the third-lightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...
(or antiquark), paired with an up
Up quark
The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...
or down
Down quark
The down quark or d quark is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...
antiquark (or quark).
Kaons have proved to be a copious source of information on the nature of fundamental interactions since their discovery in 1947. They were essential in establishing the foundations of the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
of particle physics, such as the quark model
Quark model
In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons....
of hadron
Hadron
In particle physics, a hadron is a composite particle made of quarks held together by the strong force...
s and the theory of quark mixing (the latter was acknowledged by a Nobel Prize in Physics
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
in 2008). Kaons played a distinguished role in our understanding of fundamental conservation law
Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
s: the discovery of CP violation
CP violation
In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
(a phenomenon generating the observed matter-antimatter asymmetry of the universe), which was acknowledged by a Nobel prize in 1980, was made in the kaon system.
Basic properties
- The negatively charged (containing a strange quarkStrange quarkThe strange quark or s quark is the third-lightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...
and an up antiquarkUp quarkThe up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...
) has mass and mean lifetime . - Its antiparticleAntiparticleCorresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...
, the positively charged (containing an up quark and a strange antiquark) must (by CPT invariance) have mass and lifetime equal to that of . The mass difference is , consistent with zero. The difference in lifetime is . - The (containing a down quarkDown quarkThe down quark or d quark is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...
and a strange antiquarkStrange quarkThe strange quark or s quark is the third-lightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...
) has mass . It has mean squared charge radius of . - Its antiparticle (containing a strange quarkStrange quarkThe strange quark or s quark is the third-lightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...
and a down antiquarkDown quarkThe down quark or d quark is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...
) has the same mass.
It is clear from the quark model
Quark model
In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons....
assignments that the kaons form two doublets of isospin
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...
; that is, they belong to the fundamental representation
Fundamental representation
In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group...
of SU(2) called the 2. One doublet of strangeness +1 contains the and the . The antiparticles form the other doublet (of strangeness −1).
| Particle name | Particle symbol |
Antiparticle symbol |
Quark content |
Rest mass (MeV/c Speed of light The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time... 2) |
I Isospin In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number... G |
JP Parity (physics) In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:... C C parity In physics, C parity or charge parity is a multiplicative quantum number of some particles that describes its behavior under a symmetry operation of charge conjugation .... |
S Strangeness In particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time... |
C | B' Bottomness In physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a... |
Mean lifetime (s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... ) |
Commonly decays to (>5% of decays) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Kaon | 0− | 1 | 0 | 0 | |
||||||
| Kaon | 0− | 1 | 0 | 0 | |||||||
| K-Short | Self |  |
0− | (*) | 0 | 0 | |
||||
| K-Long | Self |  |
0− | (*) | 0 | 0 | |
||||
[a] Strong eigenstate. No definite lifetime (see kaon notes below)
[b] Weak eigenstate. Makeup is missing small CP–violating
CP violation
In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
term (see notes on neutral kaons below).
[c] The mass of the and are given as that of the . However, it is known that a difference between the masses of the and on the order of exists.
Although the and its antiparticle are usually produced via the strong force, they decay weakly. Thus, once created the two are better thought of as composites of two weak eigenstates which have vastly different lifetimes:
- The long-lived neutral kaon is called the ("K-long"), decays primarily into three pionPionIn particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
s, and has a mean lifetime of . - The short-lived neutral kaon is called the ("K-short"), decays primarily into two pions, and has a mean lifetime .
(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
CP violation
In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
(see below).
Main decay modes for :
| Results | Mode | branching ratio Branching ratio 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 to the total number of particles which decay. It is equal to the ratio of the partial decay constant to the overall decay constant... |
|---|---|---|
| leptonic | ||
| hadronic | ||
| hadronic | ||
| hadronic | ||
| semileptonic |
Decay modes for the are charge conjugates of the ones above.
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
George Rochester
George Dixon Rochester, FRS was a British physicist known for having co-discovered, with Sir Clifford Charles Butler, a subatomic particle called the kaon....
and Clifford Charles Butler
Clifford Charles Butler
Sir Clifford Charles Butler FRS was an English physicist, best known for the discovery of the hyperon and meson types of particles...
of the University of Manchester
University of Manchester
The University of Manchester is a public research university located in Manchester, United Kingdom. It is a "red brick" university and a member of the Russell Group of research-intensive British universities and the N8 Group...
published two cloud chamber
Cloud chamber
The cloud chamber, also known as the Wilson chamber, is a particle detector used for detecting ionizing radiation. In its most basic form, a cloud chamber is a sealed environment containing a supersaturated vapor of water or alcohol. When a charged particle interacts with the mixture, it ionizes it...
photographs of cosmic ray
Cosmic ray
Cosmic rays are energetic charged subatomic particles, originating from outer space. They may produce secondary particles that penetrate the Earth's atmosphere and surface. The term ray is historical as cosmic rays were thought to be electromagnetic radiation...
-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 first breakthrough was obtained at Caltech
California Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
, where a cloud chamber was taken up Mount Wilson
Mount Wilson (California)
Mount Wilson is one of the better known peaks in the San Gabriel Mountains, part of the Angeles National Forest in Los Angeles County, California. It is the location of the Mount Wilson Observatory and has become the astronomical center of Southern California with and telescopes, and and tall...
, 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 adopted: "L-meson" meant muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
or pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
. "K-meson" meant a particle intermediate in mass between the pion and nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
. "Hyperon
Hyperon
In particle physics, a hyperon is any baryon containing one or more strange quarks, but no charm quarks or bottom quarks.-Properties and behavior of hyperons:...
" meant any particle heavier than a nucleon.
The decays were extremely slow; typical lifetimes are of the order of . However, production in pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
-proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
reactions proceeds much faster, with a time scale of . The problem of this mismatch was solved by Abraham Pais
Abraham Pais
Abraham Pais was a Dutch-born American physicist and science historian. Pais earned his Ph.D. from University of Utrecht just prior to a Nazi ban on Jewish participation in Dutch universities during World War II...
who postulated the new quantum number called "strangeness" which is conserved in strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
s but violated by the weak interaction
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
s. 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
Multiplicative quantum number
In quantum field theory, multiplicative quantum numbers are conserved quantum numbers of a special kind. A given quantum number q is said to be additive if in a particle reaction the sum of the q-values of the interacting particles is the same before and after the reaction. Most conserved quantum...
, because that would allow reactions which were never seen in the new synchrotron
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...
s which were commissioned in Brookhaven National Laboratory
Brookhaven National Laboratory
Brookhaven National Laboratory , is a United States national laboratory located in Upton, New York on Long Island, and was formally established in 1947 at the site of Camp Upton, a former U.S. Army base...
in 1953 and in the Lawrence Berkeley Laboratory in 1955.
Parity violation
Two different decays were found for charged strange mesons:| → | + | |
| → | + + |
The intrinsic parity of a meson is P=−1, and parity is a multiplicative quantum number. Therefore, the two final states have different parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
(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 interaction
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
s. Since the mesons decay through weak interactions, parity is not conserved, and the two decays are actualy decays of the same particle, now called the .
CP violation in neutral meson oscillations
Initially it was thought that although parityParity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
was violated, CP (charge parity) symmetry was conserved. In order to understand the discovery of CP violation
CP violation
In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
, 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
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 oscillationsNeutral particle oscillations
In particle physics, neutral particle oscillation is the transmutation of a neutral particle with nonzero internal quantum numbers into its antiparticle...
, 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
Murray Gell-Mann
Murray Gell-Mann is an American physicist and linguist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles...
and Abraham Pais
Abraham Pais
Abraham Pais was a Dutch-born American physicist and science historian. Pais earned his Ph.D. from University of Utrecht just prior to a Nazi ban on Jewish participation in Dutch universities during World War II...
together. 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). The diagonal elements (M) of the Hamiltonian
Hamiltonian (quantum mechanics)
In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
are due to strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
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 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 weakWeak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
eigenstates (states with definite lifetimes under decays via the weak force) of the neutral kaons.
These two weak eigenstates are called the (K-long) and (K-short). CP symmetry, which was assumed at the time, implies that = K1 and = K2.
Oscillation
An initially pure beam of 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 always decayed into an electron, whereas the antiparticle decayed into the positron. The earlier analysis yielded a relation between the rate of electron and positron production from sources of pure and its antiparticle . Analysis of the time dependence of this semileptonic decaySemileptonic decay
In particle physics the semileptonic decay of a hadron refers to a decay through the weak interaction in which one lepton is produced in addition to one or more hadrons.An example of a semileptonic decay is...
showed the phenomenon of oscillation, and allowed the extraction of the mass splitting between the and . 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 disappears, leaving a beam of pure long-lived . If this beam is shot into matter, then the and its antiparticle interact differently with the nuclei. The undergoes quasi-elastic scatteringElastic scattering
In scattering theory and in particular in particle physics, elastic scattering is one of the specific forms of scattering. In this process, the kinetic energy of the incident particles is conserved, only their direction of propagation is modified .-Electron elastic scattering:When an alpha particle...
with nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
s, whereas its antiparticle can create hyperon
Hyperon
In particle physics, a hyperon is any baryon containing one or more strange quarks, but no charm quarks or bottom quarks.-Properties and behavior of hyperons:...
s. Due to the different interactions of the two components, quantum coherence between the two particles is lost. The emerging beam then contains different linear superpositions of the and . Such a superposition is a mixture of and ; the is regenerated by passing a neutral kaon beam through matter. Regeneration was observed by Oreste Piccioni
Oreste Piccioni
Oreste Piccioni was an Italian-American physicist who made important contributions to elementary particle physics during the early years of its history....
and his collaborators at Lawrence Berkeley National Laboratory
Lawrence Berkeley National Laboratory
The Lawrence Berkeley National Laboratory , is a U.S. Department of Energy national laboratory conducting unclassified scientific research. It is located on the grounds of the University of California, Berkeley, in the Berkeley Hills above the central campus...
. Soon thereafter, Robert Adair and his coworkers reported excess regeneration, thus opening a new chapter in this history.
CP violation
While trying to verify Adair's results, in 1964 James CroninJames Cronin
James Watson Cronin is an American nuclear physicist.Cronin was born in Chicago, Illinois and attended Southern Methodist University in Dallas, Texas. Cronin and co-researcher Val Logsdon Fitch were awarded the 1980 Nobel Prize in Physics for a 1964 experiment that proved that certain subatomic...
and Val Fitch of BNL
Brookhaven National Laboratory
Brookhaven National Laboratory , is a United States national laboratory located in Upton, New York on Long Island, and was formally established in 1947 at the site of Camp Upton, a former U.S. Army base...
found decays of into two pions (CP = +1). 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
CP violation
In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
. 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
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
for this discovery in 1980.
It turns out that although the and are weak
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
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),
- = K2 + εK1
and similarly for . Thus occasionally the decays as a K1 with CP = +1, and likewise the can decay with CP = −1. This is known as indirect CP violation, CP violation due to mixing of 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.
See also
- HadronHadronIn particle physics, a hadron is a composite particle made of quarks held together by the strong force...
s, mesonMesonIn particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s, hyperonHyperonIn particle physics, a hyperon is any baryon containing one or more strange quarks, but no charm quarks or bottom quarks.-Properties and behavior of hyperons:...
s and flavourFlavour (particle physics)In particle physics, flavour or flavor is a quantum number of elementary particles. In quantum chromodynamics, flavour is a global symmetry... - Strange quarkStrange quarkThe strange quark or s quark is the third-lightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...
and the quark modelQuark modelIn physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons.... - Parity (physics)Parity (physics)In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
, charge conjugation, time reversal symmetryT-symmetryT Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...
, CPT invariance and CP violationCP violationIn particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped... - Neutrino oscillationNeutrino oscillationNeutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvowhereby a neutrino created with a specific lepton flavor can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates...