The $CP$ violations and branching ratios for $B_c^+\to D_{(s)}^+\pi^+\pi^-(K^{+}K^{-})$ from interference of the vector mesons in Perturbative QCD

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Abstract Within the framework of the perturbative QCD approach utilizing $k_T$ factorization, we have investigated the CP violation and branching ratios in the decay processes of $B_{c}^{+}\to D_{(s)} ^{+}V(V\rightarrow\pi^{+}\pi^{-})$ and $B_{c}^{+}\to D_{(s)}^{+}V(V\rightarrow K^{+}K^{-})$, where V denotes the three vector mesons $\rho^0$, $\omega$, and $\phi$. During the $V\to \pi^+\pi^-$ and $V\to K^+K^-$ decay processes, we incorporated the $\rho^{0}-\omega-\phi$ mixing mechanism to describe the amplitudes of these quasi-two-body decays. Within the interference region of the three vector particles, we observed distinct changes in both CP violations and branching ratios. Furthermore, our study presents evidence for local CP violations and branching ratios that warrants further investigation through experiments. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.