Kaon

This is an article on Kaon in physics. For the ontology infrastructure of the same name, see KAON.

In particle physics, Kaons (also called K-mesons and denoted K) are a group of four mesons distinguished by the fact that they carry a quantum number called strangeness. In the quark model they are understood to contain a single strange quark (or antiquark).

Basic properties

The four kaons are

1. The K⁰ (containing a strange quark and a down antiquark) has mass 497.648 ± 0.022 MeV and mean lifetime (1.2384 ± 0.0024) × 10^-8 seconds. It has mean squared charge radius of -0.076 ± 0.018 fm².
2. Its antiparticle (containing a down quark and a strange antiquark) has the same mass and the lifetime difference is (7.8 ± 8.4) × 10^-18 and hence is consistent with zero. This provides a test of CPT invariance. The asymmetry in the mixing of the particle and antiparticle which parametrizes the extent of the breaking of T-symmetry is (6.66 ± 1.3 ± 1.0) × 10^-3.
3. The negatively charged K^- (containing a strange quark and an up antiquark) has mass 493.667 ± 0.013 MeV and mean lifetime (1.2384 ± 0.0024) × 10^-8 seconds.
4. Its antiparticle, the positively charged K⁺ (containing an up quark and a strange antiquark) has mass equal to that of K^-. The mass difference is 0.032 ± 0.090 MeV, and hence consistent with zero. The difference in lifetime is (0.11 ± 0.09) × 10^-8 seconds. These two numbers are tests of CPT invariance

It is clear from the quark model assignments that they form two doublets of isospin, ie, the fundamental representation of SU(2) called the 2. One doublet of strangeness -1 contains the K^- and the K⁰. The antiparticles form the other doublet.

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 0521443490)

In 1947, G. D. Rochester and C. 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 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 Cal Tech, 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 rare: 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. 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 cyclotrons which were commissioned in Brookhaven National Laboratory in 1953 and in the Lawrence Berkeley Laboratory in 1955.

Parity violation: the τ-θ puzzle

Two different decays were found for charged strange mesons

θ⁺  →  π⁺  +  π⁰  and  τ ⁺  →  π⁺  +  π⁺  +  π^-.

Since the two final states had different parity it was then thought that the initial states should also have different parities, and hence be two distinct particles. 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. Since the mesons decay through weak interactions, parity need not be conserved, and the two decays are of the same particle— now called the K⁺.

CP violation in neutral meson oscillations

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 adjoining figure).

These oscillations were first investigated by Murray Gell-Mann and Abraham Pais together. They considered the CP invariant time evolution of the 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 of the Hamiltonian are the strong interaction piece which conserves strangeness. The two diagonal elements have to be equal, since the particle and antiparticle must have equal masses in the absence of the weak interactions. The off-diagonal elements, which mixe the opposite strangeness particles, are due to the weak interactions. CP symmetry requires them to be real.

Mixing

The eigenstates are obtained by diagonalizing this matrix. This gives new eigenvectors, which we can call K_S which is the sum ofthe two states of opposite strangeness, and K_L, the difference. They have oppposite values of CP, with the sum having CP=1. Since the two pion final state also has CP=1, only the K_S can decay into this. The K_L must decay into three pions. It turns out that the mass of K_L is just a little larger than the sum of the masses of three pions, so this decay proceeds about 600 times slower. These two different modes of decay were observed by Leon Lederman and his coworkers in 1956, thus establishing the existence of two different neutral K mesons.

The lifetime of K_S is (0.8953 ± 0.0006) × 10^-10 seconds and that of the K_L is (5.18 ± 0.04) × 10^-8 seconds.

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 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. Analysis of the time dependence of this semileptonic decay showed the phenomenon of oscillation, and allowed the extraction of the mass splitting between the K_S and K_L. Since this is due to weak interactions it is very small — 10^-15 times the mass of each state.

Regeneration

A beam of neutral K mesons decays in flight so that the K_S disappears very soon leaving a beam of pure K_L. If this is shot into a nucleus, then the K₀ and its antiparticle interact differently with the matter. The K₀ undergoes quasi-elastic scattering with nucleons, whereas its antiparticle can create hyperons. 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 K₀ and its antiparticle. This can be resolved into a K_L and a K_S state — thus the latter is regenerated by passing a neutral K beam through matter. Regeneration was observed by Piccioni and his collaborators in LBL. Soon thereafter, Adair and his coworkers reported excess K_S 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 K_L into two pions. As explained in an earlier section, this required the initial and final states to have different values of CP, and hence immediately suggested CP violation. Escape routes such as non-linear quantum mechanics and a new unobserved particle were soon ruled out, leaving CP violation as the only possibility.

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

References and external links

• Particle data group on strange mesons (http://pdg.lbl.gov/2004/listings/mxxxcomb.html#mesonsstrange)
• The quark model, by J.J.J. Kokkedee (http://www.amazon.com/exec/obidos/tg/detail/-/B0006BYWZW/qid=1118211699/sr=8-4/ref=sr_8_xs_ap_i4_xgl14/102-3287261-6119321?v=glance&s=books&n=507846) [ASIN B0006BYWZW]
• CP violation, by I.I. Bigi and A.I. Sanda (http://www.amazon.com/exec/obidos/tg/detail/-/0521443490/qid=1118640297/sr=1-1/ref=sr_1_1/102-7631552-5785747?v=glance&s=books) (Cambridge University Press, 2000) [ISBN 0521443490]

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