Analysis of anomalies using weak effective Hamiltonian with complex couplings and their impact on various physical observables

Recently, the experimental measurements of the branching ratios and different polarization asymmetries for processes occurring through flavor-changing-charged current transitions by BABAR, Belle, and LHCb have revealed some significant differences from the corresponding Standard Model (SM) predictions. This has triggered an interest to search for physics beyond the SM in the context of various new physics (NP) models and using the model-independent weak effective Hamiltonian (WEH). Assuming left-handed neutrinos, we add the dimension-six vector, (pseudo-)scalar, and tensor operators with complex Wilson coefficients (WCs) to the SM WEH. Using 60%, 30%, and 10% constraints resulting from the branching ratio of , we reassess the parametric space of these new physics WCs accommodating the current anomalies based on the most recent HFLAV data of and and Belle data of and . We find that the allowed parametric region of left-handed scalar couplings strongly depends on the constraints of the branching ratio, and the maximum pull from the SM predictions results from the <60% branching ratio limit. Also, the parametric region changes significantly if we extend the analysis by adding LHCb data of and . Furthermore, due to the large uncertainties in the measurements of and , we derive the sum rules which complement them with and . Using the best-fit points of the new complex WCs along with the latest measurements of , we predict the numerical values of the observable , , and from the sum rules. The simultaneous dependence of abovementioned physical observables on the NP WCs is established by plotting their correlation with and , which are useful to discriminate between various NP scenarios. We find that the most significant impact of NP results from the WC . Finally, we study the impact of these NP couplings on various angular and triple product asymmetries that could be measured in some ongoing and future experiments. The precise measurements of these observables are important to check the SM and extract the possible NP.