Abstract
When a neutral meson $(P^0 \text{ or } \bar P^0)$ decays to two vector particles, a large number of observables can be constructed from differential decay rate based on the polarization of final state. But, theoretically, all of them are not independent to each other and hence, some relations among observables emerge. These relations have been well studied in the scenario with no $T$ and $CPT$ violation in neutral meson mixing and no direct $CP$ violation as well. In this paper, we have studied the relations among observables in the presence of $T$, $CP$ and $CPT$ violating effects in mixing only. We find that except four of them, all the other old relations get violated and new relations appear if $T$ and $CPT$ violations in mixing are present. Invalidity of these relation will signify the presence of direct violation of $T$, $CP$ and $CPT$ (i.e. violation in the decay itself).
Highlights
CPT invariance is believed to be a sacred principle of any locally Lorentz invariant quantum field theory
When a neutral meson (P0 or P 0) decays to two vector particles, a large number of observables can be constructed from the differential decay rate based on the polarization of the final state
We have studied the behavior of observables for neutral meson decaying to two vectors in the presence of T, CP, and CPT violation in mixing
Summary
CPT invariance is believed to be a sacred principle of any locally Lorentz invariant quantum field theory. One can argue that these quantities are usually dominated by strong or electromagnetic interactions and there exits a possibility for tiny CPT violating effects, mediated by weak interactions, to be undetectable in those direct experiments In this regard, the mixing of the neutral pseudoscalar meson (K0, D0, B0d; B0s) with its own antiparticle is a promising area [4] to search for CPT violating effects as this phenomenon is a second order electroweak process. The effects of CPT violation on the modes where neutral pseudoscalar meson decays to two vectors (P0 or P 0 → V1V2) are not very well studied.
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