Implications of new physics in B → K 1 μ + μ − decay processes

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