On testing violations of Bose and $CPT$ symmetries via Dalitz plots and Dalitz `prism'

Bose symmetry and $CPT$ symmetry are two very fundamental symmetries of Nature. However, the validity of these symmetries in diverse phenomena must be verified by experiments. We propose new techniques to probe these two fundamental symmetries in the realm of mesons by using the Dalitz plot of a few three-body meson decays. Since these symmetries are very fundamental in nature, their violations, if any, are expected to be extremely small. Hence observing their violations requires study of a huge data sample. In this context we introduce a new three-dimensional plot which we refer to as the Dalitz 'prism'. This provides an innovative means for acquiring the huge statistics required for such studies. Using the Dalitz plots and the Dalitz prisms we chart out the way to probe the violations of Bose and $CPT$ symmetries in a significant manner. Since mesons are unstable and composite particles, testing the validity of Bose symmetry and the $CPT$ symmetry in these cases are of paramount importance for fundamental physics.