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Related to Kaons: Pions
(K-mesons), a group of unstable elementary particles that includes two charged particles (K+ and K-) and two neutral particles (K° and K̄°), with zero spin and a mass about 970 times greater than that of the electron. Kaons take part in strong interactions—that is, they are hadrons. They have no baryon charge and have a nonzero quantum strangeness number (S), which characterizes their behavior in processes that result from strong interaction: for K+ and K°, S = +1, and for K- and K̄° (which are the antiparticles of K+ and K°), S = — 1.
|Table 1. Main characteristics and methods of decay of kaons|
|Massm (MeV)||Strangeness S||Lifetime τ (sec)||Methods of decay||Probability of decay (percent)|
|K+||494||+1||1.2 X 10-8||μ±+ ν||64|
|π± + π- + π+||5.57|
|π± + π° + π°||1.70|
|μ± + π° + v||3.18|
|θ± + π° + ν||4.85|
|θ± + ν||1.2 × 1.2 × 10-5|
|Approximately 50% according to K°s, scheme and approximately 50% according to K°L scheme (see Table 2)|
Together with hyperons, kaons form the group of strange particles (particles for which S ≠ 0).
The kaons K+ and 0 take part identically in strong interactions; they have approximately identical masses and differ only in electric charge. They can be combined into one group, an isotopic doublet, and are considered as different charge states of a single particle with isotopic spin I = ½. The kaons K- and K̄° constitute an analogous group. Because of the difference in strangeness, the neutral kaons K° and K̄° are different particles that participate differently in strong interactions.
According to the current classification of elementary particles, the kaons (K+, K°, K-, and K̄°), together with the pi-mesons (π+, π0, π-) and the ŋo-meson, constitute one group (an octet) of particles that participate in strong interactions in an approximately identical manner.
The discovery of kaons was associated with the work of a large number of scientists in various countries. Several particles whose masses, measured with the best accuracy attainable at the time, were approximately identical but whose methods of decay were different were discovered in cosmic rays in the period 1947–51. These were the 0-mesons, which decay into two pi-mesons, and r-mesons, which decay into three pi-mesons. Significant progress in the study of these particles began in 1954, when they were produced by means of charged-particle accelerators. Careful measurements of mass and lifetime showed that in all these cases different methods of decay of the same particles, called kaons, were observed.
The discovery of kaons played an important role in the physics of elementary particles; it helped to establish a new characteristic of strongly interacting particles (hadrons)—strangeness—and to devise their current classification. The study of the decay of kaons provided the first information on the nonconservation of spatial and charge parity in weak interactions and on the violation of combined parity.
Strong interactions. Kaons have nonzero strangeness S, and since S is conserved in strong interactions, this influences processes of strong interactions involving kaons in a characteristic way. Thus, K+ and K°, which have S = +1, are produced by collisions of “nonstrange” particles—pi-mesons and nucléons (protons and neutrons)—only together with hyperons or K- or K°, which have negative strangeness.
Since all hyperons have negative strangeness, they are produced more easily in processes caused by K- and K̄° than in processes caused by K+ and K°. For example, the reaction K̄° + p → ʌ + π+ is possible, whereas the reaction K° + p→ ʌ + π+ is prohibited by the law of conservation of strangeness in strong interactions (here p is a proton and ʌ is a hyperón). The production of hyperons in beams of K+ and K° is less probable, since it requires the appearance of several additional K+ or K° together with the hyperon. Therefore, slow K+ and K° interact more weakly with matter than do K- and K̄°.
Weak interactions. The decay of kaons is due to weak interaction and takes place with a change of 1 in strangeness (strangeness is not conserved in weak interactions). Decay may occur by various methods (Table 1) and conforms to empirical rules that define the change in the strangeness and isotopic spin of hadrons and in other factors. In the decay of kaons spatial parity and charge parity are not conserved. This is manifested in the possibility of decay into both 2π-mesons and 3π-mesons.
The processes of strong and weak interaction of kaons are shown in Figure 1.
Speciflc_properties of neutral kaons. It was noted above that K° - and K̄°-mesons, which differ from each other in the value
|Table 2. Main methods of decay of decay of Kos and KoL|
|Mass m||Lifetime τ (sec)||Methods of decay||Probability of decay (percent)|
|In Tables 1 and 2 π± and πo are charged and neutral pi-mesons, μ‡ are muons, e‡ is an electron or positron, υ is a neutrino (or antineutrino), and γ is a gamma quantum|
|K°s||≈mko||0.86 × 10-10||π+ + π-||68.7|
|πo + πo||31.3|
|KoL||≈mko||5.4 × 10-6||πo + πo + πo||21.5|
|π+ + π- + πo||12.6|
|π± + μ∓ + v||26.8|
|π± + e∓ + v||38.8|
|π+ + π-||0.16|
|mkL − mks ≈ 3 × 10-6 eV||πo + πo||0.12|
|γ + γ||5 × 10-4|
of the quantum strangeness number, take part in processes of strong interaction as two different particles. However, since strangeness is not conserved in processes of weak interaction (and in particular in the decay of kaons), the mutual transformations K° ⇄ K̄° prove to be possible. The existence of such transitions between a particle and an antiparticle, which have different values for one of the quantum numbers characterizing elementary particles, accounts for the specific, unique properties of neutral kaons. For any other particles the existence of such transitions is prohibited by the strict laws of conservation of electric or baryon charge (and obviously also for the lepton charge for neutrino-antineutrino transitions).
Because of the transitions K° ⇄ K̄°, not K° and K̄° but the two quantum-mechanical superpositions of these states will be the states that have a certain energy and lifetime. These superpositions correspond to particles with different masses and lifetimes, the long-lived K°L-meson and the short-lived K°s-meson. The difference in the masses of K°L and Kos is due to the weak interaction that effects the transitions K° ⇄ K̄° KoL and Kos is extremely small. The lifetime and methods of decay of K0L and K0s are shown in Table 2.
Thus, although the states K° and K̄°, which have specific values for strangeness (which is conserved in strong interaction), are manifested in processes induced by strong interaction, in processes of weak interaction (decays) they are manifested as the particles of state K0t and K0s. The states Kos and KoL are close to the superpositions of the states that are called Ko1 and Ko2:
That is, K°s and K0 “consist” of approximately 50 percent K° and 50 percent K0. Similarly, the kaons K° and K̄° may be said to “consist” of approximately 50 percent K°s and 50 per-cent K0L The fact that the states K° and K° represent a super-position of the two states K°s and K0L with different masses and lifetimes leads to the appearance of peculiar oscillations (“pulsations”): K0, arising as a result of a strong interaction, is partially converted at a certain distance from the point of production into K̄0 because of weak interaction and therefore proves capable of inducing the nuclear reactions characteristic of K̄0 and prohibited for K0—for example, the reaction K̄0 + p→> ° + π+ (the Pais-Piccioni effect). Another peculiar phenomenon is the so-called regeneration of short-lived K Vmesons when long-lived K0L-mesons pass through matter: at sufficiently great distances from the site of formation of a K° or K̄° beam, the beam consists almost exclusively of long-lived K%, since the short-lived K°L decay earlier. Therefore, at such distances only the decay characteristic of K0L is observed (Table 2). The re-appearance of K°s in the beam would seem impossible. How-ever, if a beam of K0L is passed through a layer of matter, because of the difference in the way in which the K° and K̄° that constitute K0L, interact with matter, the relative composition of the beam is altered, and an addition of K0s with decay characteristic of K̄°s appears in the K°L beam.
Combinations of K01 and K02 have a definite symmetry with respect to the combined inversion operation (CP): upon transition from particle to antiparticle (the charge conjugation operation C) with simultaneous spatial reflection (the operation P), the wave function corresponding to the state K01 remains unchanged, but the wave function of K02 changes its sign. Therefore, the state K01 can decay into 2π (a system that has the same properties with respect to the operation CP as does K01), but K02 cannot. Since the probability of decay into 2π greatly exceeds the probability of other methods (channels) of decay, the great difference in the lifetimes of the long-lived and short-lived kaons was considered to be an indication of the existence in nature of symmetry with respect to the combined inversion operation, and the states K0s and K0L were identified with K01 and K02. However, in 1964 it was determined that the long-lived kaon decays into 2π with a probability of approximately 0.2 percent. This attests to the violation of CP-symmetry and to the difference between the states K0s and K0L on the one hand and K01 and K02 on the other. The nature of the forces that disrupt CP-symmetry has not yet been elucidated. Available experimental data do not contradict the possibility of existence in nature of a special “superweak” interaction that violates CP-symmetry and is manifested in the decay of neutral kaons.
REFERENCESMarkov, M. A. Giperony i K-mezony. Moscow, 1958.
Dalitz, R. Strannye chastitsy i sil’nye vzaimodeistviia. Moscow, 1964. (Translated from English.)
Okun’, L. B. Slaboe vzaimodeistvie elementarnykh chastits. Moscow, 1963.
Lee, T., and C. S. Wu. Slabye vzaimodeistviia. Moscow, 1968. (Translated from English.)
Gasiorowicz, S. Fizika elementarnykh chastits. Moscow, 1969. (Translated from English.)
Adair, R. K., and E. K. Fowler. Strannye chastitsy. Moscow, 1966. (Translated from English.)
S. S. GERSHTEIN