Isospin Invariance and Generalized Bose Statistics applied to Low Energy K⁺⁻K⁰ and π⁺⁻π⁰ Space Symmetries

The use of isospin invariance and Generalized Bose statistics shows that the Bose-Einstein correlation (BEC) of identical bosons seen in the $K^+K^+$ and $\pi^+ \pi^+$ systems can be extended to apply to $K^+ K^o$ and $\pi^+ \pi^o$ pairs when they are produced from an initial state with isospin zero; e.g. by the fragmentation of gluons or of a strange quark pair accompanied by gluons. This might be useful in constructing more realistic model dependent Monte Carlo programs for the investigation of the isospin structure of the particles produced in a given kinematic region like the central region in high energy hadronic collisions or quark-gluon plasma. Some of the consequences of this extension are here applied to the hadronic $Z^o$ decays. In particular the study addresses the question how much of the observed low $K^o_S K^o_S$ mass enhancement is to be attributed to a BEC effect and how much to the $f_0(980)\to K^o_S K^o_S$ decay. Finally we point out the restrictions imposed by the extension on the choice of reference samples for the BEC studies.