Remarks on Cp Asymmetries in D

We consider the interference of resonant amplitudes leading to the final state KSπ π inD/D0 decays. Each of these amplitudes consists of both Cabibbo allowed and doubly Cabibbo suppressed transitions. The role of strong phase arising out of Breit-Wigner resonant propagators is emphasised. Invoking the ∆S = ∆Q rule, KS in the final state is identified as the mass eigenstate of superposed weak eigenstates K and K̄. A nonzero CP asymmetry appears to be possible in three body decays. electronic address: [email protected] 1 As immense activities are on at charm/B factories searching for CP violating effects, the study of weak dynamics of charm sector acquires renewed interest. The CP asymmetry occurs if there exist nonvanishing weak and strong phases provided by a pair of amplitudes which are distinct by both phases with respect to one another, through interference [1]. For instance, in the two body D decays into Kπ, the strong phase arises due to strong interaction effects such as rescattering and final state interaction. But, such a strong phase is small, for example it is about 13 in the model of Buccella et al [2], thus resulting in a CP asymmetry of O(10) [3,4]. Alternatively, one can look at three body modes. The three body final state is reached by more than one way, namely, nonresonant and resonant modes. There are many resonant modes: That is, D → M1R → M1[M2M3]R, where R stands for resonance and M ’s for mesons. Given two resonant modes that lead to the same final state, there arise distinct strong phase between them due to the Breit-Wigner (BW) resonant propagator and the angular momentum quantum numbers of the resonance and of its decay products [5]. Thus, a strong phase is nontrivial. Besides, the correlation between the net strangeness (produced) and the net charge (involved), namely, the ∆S = ∆Q rule. Unlike in strange decays where violation strangenesscharge symmetry means the mixing of KS and KL [6], in charm decays into strange final state, this rule qualifies KS is the mixed state of the weak eigen states K 0 and K̄. This rule implies the coherent superposition of CA and DCS transitions. In this letter, we look at the significance of strong phase that arises due to BW propagators of intermediate resonances which lead to a common final state in D three body decays, as an extension of the Atwood and Soni’s proposal for B decays [5] to charm sector and the importance of invoking the ∆S = ∆Q rule thereof. For D → KSπ π, we consider the resonant modes of K(890), ρ(770) and f0(990): In the strange decays, this is change in strangeness.