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.
Quark correlation functions in deep-inelastic semi-inclusive processes