Explaining the $B_{d(s)}\to K^{(\ast )}{\bar{K}}^{(\ast )}$ puzzle via chiral-flip in $R$-parity violating MSSM with seesaw mechanism

We study the non-leptonic puzzle of $B_{d(s)}\to K^{(\ast )}{\bar{K}}^{(\ast )}$ decay in the $R$-parity violating minimal supersymmetric standard model (RPV-MSSM) extended with the inverse seesaw mechanism. In this model, the chiral flip of sneutrinos can contribute to the observables $L_{K\bar{K}}$ and $L_{K^{\ast }{\bar{K}}^{\ast }}$, that is benefit for explaining the relevant puzzle. We also find that this unique effect can engage in the $B_s$-${\bar{B}}_s$ mixing. We utilize the scenario of complex ${\lambda }^{\mathrm{\prime }}$ couplings to fulfill the recent stringent constraint of $B_s$-${\bar{B}}_s$ mixing, and examine other related bounds of $B,K$-meson decays, lepton decays, neutrino data, $Z$ decays, oblique parameters, CP violations (CPV), etc. Besides, inspired by the new measurement of $\mathcal{B}(B^{+}\to K^{+}\nu \bar{\nu })$ by Belle II, which shows about $2.7\sigma$ higher than the Standard Model (SM) prediction, we also investigate the New Physics (NP) enhancement to this observable.