Abstract
The phenomenological structure of inclusive cross-sections of the production of two neutral K mesons in hadron–hadron, hadron–nucleus and nucleus–nucleus collisions is theoretically investigated taking into account the strangeness conservation in strong and electromagnetic interactions. Relations describing the dependence of the correlations of two short-lived and two long-lived neutral kaons $K_S^0K_S^0,K_L^0K_L^0$ and the correlations of “mixed” pairs $K_S^0K_L^0$ at small relative momenta upon the space-time parameters of the generation region of K0 and K̅0 mesons have been obtained. These relations involve the contributions of Bose-statistics and S -wave strong final-state interaction of two K0 (K̅0) mesons as well as of the K0 and K̅0 mesons, and also the additional contribution of transitions K+K– → K0 K̅0, and they depend upon the relative fractions of generated pairs K0K0, K̅0 K̅0 and K0 K̅0. It is shown that under the strangeness conservation the correlation functions of the pairs $K_S^0K_S^0$ and $K_L^0K_L^0$, produced in the same inclusive process, coincide, and the difference between the correlation functions of the pairs $K_S^0K_S^0$ and $K_S^0K_L^0$ is conditioned exclusively by the production of the pairs of non-identical neutral kaons K0 K̅0. For comparison, analogous correlations for the pairs of neutral heavy mesons D0, B0 and $B_s^0$, generated in multiple inclusive processes with charm (beauty) conservation, are also theoretically analyzed. These correlations are described by quite similar expressions: in particular, just as for K0 mesons, the correlation functions for the pairs of states with the same CP parity (RS S = RLL) and with different CP parity (RS L) do not coincide, and the difference between them is conditioned exclusively by the production of pairs D0 D̅0, B0B̅0 and $B_s^0\bar B_s^0$. However, contrary to the case of K0 mesons, here the distinction of CP-even and CP-odd states encounters difficulties – due to the insignificant differences of their lifetimes and the relatively small probability of purely CP-even and CP-odd decay channels. Nevertheless, one may hope that it will become possible at future colliders.
Highlights
In the work [1] the properties of the density matrix of two neutral K mesons, following from the strangeness conservation in strong and electromagnetic interactions, have been investigated
The strangeness conservation leads to the fact that all the double inclusive cross-sections of production of pairs KS0 KS0, KL0KL0 and KS0 KL0 prove to be symmetric with respect to the permutation of momenta p1 and p2, and, besides, prove to be invariant with respect to the replacement of the short-lived state KS0 by the long-lived state KL0, and vice versa [1]: fS S (p1, p2) = fLL(p1, p2), fS L(p1, p2) = fLS (p1, p2)
+ λK 0K 0 1 + FK 0 (2k) + 2 bint(k) + λK0K 0 1 − FK0K 0 (2k). It follows from Eqs. (2) and (4) that the correlation functions of pairs of neutral K mesons with close momenta, which are created in inclusive processes, satisfy the relation: RS S (k) − RS L(k) = 2λK0K 0 FK0K 0 (2k) + Bint(k)
Summary
In the work [1] the properties of the density matrix of two neutral K mesons, following from the strangeness conservation in strong and electromagnetic interactions, have been investigated. Taking into account the strangeness conservation, the pairs of neutral kaons K0K0, K 0K 0 and K0K 0 are produced incoherently This means that in the K0-K 0 representation the nondiagonal elements of the density matrix between the states K0K0 and K 0K 0, K0K0 and K0K 0, K 0K 0 and K0K 0 are equal to zero. For the pairs of non-identical kaon states KS0 KL0, the correlation functions at small relative momenta have the form: RS L(k) = RLS (k) = λK0K0 [1 + FK0 (2k) + 2 bint(k)] +. (2) and (4) that the correlation functions of pairs of neutral K mesons with close momenta, which are created in inclusive processes, satisfy the relation: RS S (k) − RS L(k) = 2λK0K 0 FK0K 0 (2k) + Bint(k).
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