Model-independent analysis of new physics effects in \(B\rightarrow K^*_2(1430)\mu ^+ \mu ^-\) decay

Recently, the LHCb Collaboration provided updated measurements for the lepton flavour ratios \(R_K\) and \(R_{K^*}\). The currently observed values align with the predictions of the standard model. In light of these recent updates, our investigation delves into the repercussions of new physics characterized by universal couplings to electrons and muons. We specifically focus on their impact on various observables within the \(B\rightarrow K_2^*(1430)(\rightarrow K\pi )\mu ^+ \mu ^-\) decay. These observables include the differential branching ratio, forward-backward asymmetry (\(A_{FB}\)), longitudinal polarization asymmetry (\(F_L\)), and a set of optimized observables (\(P_i\)). Our findings indicate that the branching ratio of \(B\rightarrow K_2^*(\rightarrow K\pi )\mu ^+ \mu ^-\) decay can be suppressed up to \(25\%\) for various new physics solutions. Furthermore, all permissible new physics scenarios demonstrate finite enhancement in the muon forward-backward asymmetry \((A_{FB})\) as well as an increase in the value of the optimized angular observable \(P_2\). Moreover, in the presence of new physics zero crossing points for \(A_{FB}\) and \(P_2\) shift towards higher \(q^2\). The current data have a mild deviation from SM predictions in \(P_5'\) observable in the low-\(q^2\) bin. We also explored massive \(Z'\) models, which can generate universal 1D new physics scenarios, characterized by \(C_9^{NP}<0\), \(C_9^{NP}=-C_{10}^{NP}\), and \(C_9^{NP}=-C_9'\). Using additional constraints coming from \(B_s-\overline{B_s}\) mixing and neutrino trident process, we find that the conclusions of the model-independent analysis remain valid.