Implications of light $Z'$ on semileptonic $B(B_{s}) \to T\{K_2^*(1430)$ $(f_2'(1525))\} \ell^+\ell^-$ decays at large recoil

Abstract

We probe the rare semileptonic decays $B_{(s)} \to K_2^*(1430)(f_2'(1525)) \ell^+\ell^-$ proceeding via $b\to s \ell \ell$ transition in the presence of a light $Z^{\prime}$ boson. We employ the presence of an additional vector type interaction and constrain the new physics coupling parameter using the existing experimental measurements on $R_K$ and $R_{K^*}$ observables. To understand the sensitivity of the new physics coupling, we investigate the impact of this coupling on various physical observables such as differential branching ratio, the forward-backward asymmetry, the lepton polarization asymmetry, the angular observable $P_5^{\prime}$, and the lepton universality parameters such as the ratio of the branching ratio $R_{f_2'(K_2^*)}$ and some important Q parameters of $B_{(s)} \to K_2^*(1430)(f_2'(1525)) \ell^+\ell^-$ processes at large recoil. We find some noticeable differences of the observables in the presence of light $Z^{\prime}$ contribution.