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Inspired by the recent experimental results which show deviations from thestandard model (SM) predictions of $b\rightarrow s \ell^+\ell^-$ transitions,we study the $R$-parity violating minimal supersymmetric standard model(RPV-MSSM) extended by the inverse seesaw mechanism. The trilinear $R$-parityviolating terms, together with the chiral mixing of sneutrinos, induce the loopcontributions to the $b\rightarrow s \ell^+\ell^-$ anomaly. We study theparameter space of the single-parameter scenario $C^{\rm NP}_{9,\mu}=-C^{\rmNP}_{10,\mu}=C_{\rm V}$ and the double-parameter scenario $(C_{\rm V},C_{\rmU})$, respectively, constrained by other experimental data such as$B_s-\bar{B}_s$ mixing, $B\rightarrow X_s \gamma$ decay, the lepton flavourviolating decays, etc. Both the single-parameter and the double-parameterscenario can resolve the long existing muon anomalous magnetic moment problemas well, and allow the anomalous $t\rightarrow cg$ process to reach thesensitivity at the Future Circular hadron-hadron Collider (FCC-hh).

Studying the $b\rightarrow s \ell^+\ell^-$ anomalies and $(g-2)_{\mu}$ in $R$-parity violating MSSM framework with the inverse seesaw mechanism