Explaining the $B \to K\mu^+\mu^-$ Anomaly in the Left-Right Inverse Seesaw Model

We investigate the long-standing anomaly in the rare decay B into Kll within the Left-Right Inverse Seesaw (LRIS) model. Global analyses of the B into s mu mu data consistently indicate a significant negative shift in the vector Wilson coefficient, $\Delta C{9} \approx -1$, while the axial coefficient $\Delta C{10}$ remains consistent with zero. We show that a charged-scalar/heavy-neutrino box diagram in the LRIS model naturally generates this pattern through a \emph{non-decoupling} mechanism: the right-handed coupling produces a contribution to $\Delta C{9}$ that is unsuppressed in the heavy-neutrino limit, while the simultaneous presence of a comparable left-handed Dirac Yukawa coupling ensures the automatic cancellation $\Delta C{10} \approx 0$. The otherwise large contribution to $B_s$--$\bar{B}_s$ mixing is suppressed by several orders of magnitude through a GIM-like phase structure in the right-handed quark mixing matrix. A numerical scan over the model parameter space identifies a viable region, consistent with all current flavor and collider constraints. The $b \to s\gamma$ constraint is satisfied with two orders of magnitude to spare throughout the viable band. These results motivate correlated searches for the charged scalar and the heavy right-handed neutrinos at the LHC and future high-luminosity experiments.