In recent times, several discrepancies at the level of $(2-3)sigma$ have been observed in the decay processes mediated by flavour changing neutral current (FCNC) transitions $b to s ell^+ ell^-$, which may be considered as the smoking-gun signal of New Physics (NP). These intriguing hints of NP have attracted a lot of attention and many attempts are made to look for the possible NP signature in other related processes, which are mediated through the same quark-level transitions. In this work, we perform a comprehensive analysis of the FCNC decays of $B$ meson to axial vector mesons $ K_1(1270)$ and $ K_1(1400)$, which are admixture of the $1^3P_1$ and $1^1P_1$ states $K_{1A}$ and $K_{1B}$, in a model independent framework. Using the $ B to K_1$ form factors evaluated in the light cone sum rule approach, we investigate the rare exclusive semileptonic decays $ B to K_1(1270) mu^+ mu^-$ and $ B to K_1(1400) mu^+ mu^-$. Considering all the possible relevant operators for $b to s ell^+ ell^-$ transitions, we study their effects on various observables such as branching fractions, lepton flavor universality violating ratio ($R_{K_1})$, forward-backward asymmetries, and lepton polarization asymmetries of these processes. These results will not only enhance the theoretical understanding of the mixing angle but also serve as a good tool for probing New Physics.
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