$B \to X_{\mathrm{s}} l^{+} l^{-}$ in the $μ$ from $ν$ Supersymmetric Standard Model

We investigate the impact of new physics on the rare inclusive decay $B \to X_{\mathrm{s}} l^{+} l^{-}$ within the framework of the $\mu$ from $\nu$ Supersymmetric Standard Model ($\mu\nu$SSM). The dominant contributions to the relevant Wilson coefficients and their corresponding particles are identified and analyzed. By performing a systematic scan over the relevant parameter space, we elucidate the underlying physical mechanisms governing these dominant contributions and demonstrate their consistency with the experimentally allowed regions. Experimental constraints from the decays $\bar{B} \to X_{\mathrm{s}}\gamma$, $B_{\mathrm{s}}^{0} \to \mu^{+} \mu^{-}$, and the $125\,\text{GeV}$ SM-like Higgs boson are also incorporated. We perform a systematic interference decomposition of the Wilson-coefficient contributions to the forward-backward asymmetry, identifying the $C_7C_{10}$ and $C_9C_{10}$ interference terms as the dominant contributions governing its behavior in both the low- and high-$q^2$ regions.