Study of the $b\to d\mathrm{\ell }\mathrm{\ell }$ transitions in the Standard Model and test of New Physics sensitivities

After incorporating all the available experimental data and the most up-to-date Lattice and light cone sum rule (LCSR) inputs on the form factors, we analyze the exclusive $b\to u\mathrm{\ell }{\nu }_{\mathrm{\ell }}$ and $b\to d\mathrm{\ell }\mathrm{\ell }$ decays simultaneously. We have extracted the shape of all the associated form factors using which we provide predictions in the standard model for the branching ratios, direct CP asymmetries and isospin asymmetry for $B\to \pi \mathrm{\ell }\mathrm{\ell }$ and various angular observables for $B\to \rho \mathrm{\ell }\mathrm{\ell }$ transitions. Also, we have tested the sensitivities of these observables towards physics beyond the standard model (BSM).For the $B\to \rho \mathrm{\ell }\mathrm{\ell }$ decays, we have defined tagged and untagged observables and predicted them in the SM and BSM. In the context of BSM, we have found some compelling information. The respective predictions in a few benchmark scenarios are given, which can be tested in the experiments at the LHCb and the Belle.