Final-state rescattering mechanism of double-charm baryon decays: $\mathcal{B}_{cc}\to\mathcal{B}_{c}P$

In this study, we examine the non-leptonic weak decays of doubly charmed baryons, denoted as ${\cal B}_{cc}\to{\cal B}_{c}P$, where ${\cal B}_{cc}$ represents the doubly charmed baryons, specifically $(\Xi_{cc}^{++},\Xi_{cc}^{+},\Omega_{cc}^{+})$. The notation ${\cal B}_{c}$ denotes the singly charmed baryons, specifically $({\cal B}_{\bar{3}},{\cal B}_{6})$, while $P$ signifies the light pseudoscalar. These terms are pertinent to the non-leptonic decay modes under discussion. While the short-distance contributions can be precisely estimated through theoretical calculations, addressing the long-distance contributions for final-state-interaction effects presents a significant challenge. In order to address this issue, we utilize the rescattering mechanism of final state interaction effects to compute the long-distance contributions. We initially derive the entire hadronic loop contributions for these two-body nonleptonic decays of doubly charmed baryons. In subsequent analyses, we are able to calculate relative strong phases. As a result, we can provide predictions for their decay asymmetry parameters and CP violations. Furthermore, we employ experimental data from the LHCb collaboration, specifically the ratio $Br(\Xi_{cc}^{++}\to\Xi_{c}^{\prime+}\pi^{+})/Br(\Xi_{cc}^{++}\to\Xi_{c}^{+}\pi^{+})=(1.41\pm0.17\pm0.10)$, to ascertain the model parameters $\eta=0.9\pm0.2$. Consequently, we present the predictions of branching ratios and decay asymmetry parameters for 67 distinct decay processes and $CP$ violations for the singly Cabibbo suppressed channels. This not only strengthens the validity of our theoretical predictions, but also provides a more comprehensive theoretical framework for the future identification of other doubly charmed baryons.