We offer a succinct review of the theoretical underpinnings of the tree and loop-level b decays in light of recent measurements of anomalies in heavy meson decays at LHCb and numerous other collider experiments hinting at a potential violation of lepton flavour universality (LFU) involving $b\to c l \nu_l$, and $b\to s l \nu_l$ along with the updated experimental background of various anomalies such as, anomalous magnetic moment of electron and muon by Fermilab $(a_{\mu}, a_e)$, mass of W boson by CDF, the CKM puzzle $(\mathcal{R}_{V_{us}})$. We undertake an investigation on LFU violating (LFUV) observables involving the $\mathcal{R}$-Ratios, the longitudinal polarization $(\mathcal{P}_L)$, the $\tau$-polarization $(\mathcal{P}_{\tau})$, and forward-backward asymmetry $(\mathcal{A}_{FB} )$ which are highly sensitive to the New Physics (NP) for the decay channel: $B_c \to \eta_c (J/\psi), D (D^*), l \nu_l$ in a model dependent framework. We also study the $q^2$ dependence of pseudoscalar and vector meson form factors for the above transitions. As flavor anomalies are the strongest hints for physics beyond standard model, it is therefore expected that if the ongoing evaluation of the data of LHC Run 2 confirms the measurements of Run 1, then the statistical significance of the effect in each decay channel separately is anticipated to reach 5 $\sigma$. Therefore the confirmation of these measurements would soon turn out to be remarkable evidence, unravelling the NP in the colliders fraternity.
Adrien Florio