Kaon

In particle physics, a kaon, also called a K meson and denoted, 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 and an up or down antiquark.
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. 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. 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:

, negatively charged has mass and mean lifetime.
positively charged must have mass and lifetime equal to that of. Experimentally, the mass difference is, consistent with zero; the difference in lifetimes is, also consistent with zero.
, neutrally charged has mass. It has mean squared charge radius of.
, neutrally charged 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 called the 2. One doublet of strangeness +1 contains the and the. The antiparticles form the other doublet.

Particle name	Particle symbol	Antiparticle symbol	Quark content	Rest mass	I^G	J^PC	S	C	B′	Mean lifetime	Commonly decays to
Kaon						0⁻	1	0	0		or or or
Kaon						0⁻	1	0	0
K-short		self				0⁻	List of mesons#Notes on neutral kaons\|	0	0		or
K-long		self				0⁻	List of mesons#Notes on neutral kaons\|	0	0		or or or

See Notes on neutral kaons in the article List of mesons, and neutral kaon mixing, below.
Strong eigenstate. No definite lifetime.
Weak eigenstate. Makeup is missing small CP–violating term.
The mass of the and are given as that of the. However, it is known that a relatively minute 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 superpositions of two weak eigenstates that have vastly different lifetimes:

The long-lived neutral kaon is called the , decays primarily into three pions, and has a mean lifetime of.
The short-lived neutral kaon is called the , decays primarily into two pions, and has a mean lifetime.

An experimental observation made in 1964 that K-longs rarely decay into two pions was the discovery of CP violation.
Main decay modes for :
Decay modes for the are charge conjugates of the ones above.

Parity violation

Two different decays were found for charged strange mesons into pions:
The intrinsic parity of the pion is P = −1, 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. 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 the weak interaction. 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.

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

While looking for the hypothetical nuclear meson, Louis Leprince-Ringuet found evidence for the existence of a positively charged heavier particle in 1944.
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 that 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.
In 1949, Rosemary Brown, 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.

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

This led to the so-called 'tau–theta' problem: what seemed to be the same particle decayed in two different modes, Theta to two pions, Tau to three pions. The solution to this puzzle turned out to be that weak interactions do not conserve parity.
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-Ringuet 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 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" that 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 that were never seen in the new synchrotrons that 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 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

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.
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. The diagonal elements 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 or the other, 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.
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 of the neutral kaons.
These two weak eigenstates are called the and . CP symmetry, which was assumed at the time, implies that = K₁ and = K₂.