Time-dependent study of KS → π+π− decays for flavour physics measurements

Abstract

Nowadays High Energy Physics experiments can accumulate unprecedented statistics of heavy flavour decays that allows to apply new methods, based on the study of very rare phenomena, which used to be just desperate. In this paper we propose a new method to measure composition of K⁰-$\overline{K}$⁰, produced in a decay of heavy hadrons. This composition contains important information, in particular about weak and strong phases between amplitudes of the produced K⁰ and $\overline{K}$⁰. We consider possibility to measure these parameters with time-dependent K⁰ → π⁺π⁻ analysis. Due to C P -violation in kaon mixing time-dependent decay rates of K⁰ and $\overline{K}$⁰ differ, and the initial amplitudes revealed in the CP-violating decay pattern. We perform phenomenological study of K⁰ decay evolution initially produced as a combination $a\left(|K^0\left(t\right)\right.⟩+b\left(|{\overline{K}}^0\left(t\right)\right.⟩$, where a and b, complex amplitudes, could also be dependent on decay time of heavy mother particle. In particular we consider cases of charmed hadrons decays: D⁺ → K⁰π⁺, $D_s^{+}$ → K⁰K⁺, Λ → pK⁰ and with some assumptions D⁰ → K⁰π⁰. This can be used to test the sum rule for charmed mesons and to obtain input for the full constraint of the two body amplitudes of D-mesons.