SUSY effects in $R_b$: revisited under current experimental constraints

In this note we revisit the SUSY effects in $R_b$ under current experimental constraints including the LHC Higgs data, the $B$-physics measurements, the dark matter relic density and direct detection limits, as well as the precision electroweak data. We first perform a scan to figure out the currently allowed parameter space and then display the SUSY effects in $R_b$. We find that although the SUSY parameter space has been severely restrained by current experimental data, both the general MSSM and the natural-SUSY scenario can still alter $R_b$ with a magnitude sizable enough to be observed at future $Z$-factories (ILC, CEPC, FCC-ee, Super $Z$-factory) which produce $10^9-10^{12}$ $Z$-bosons. To be specific, assuming a precise measurement $\delta R_b = 2.0 \times 10^{-5}$ at FCC-ee, we can probe a right-handed stop up to 530 GeV through chargino-stop loops, probe a sbottom to 850 GeV through neutralino-sbottom loops and a charged Higgs to 770 GeV through the Higgs-top quark loops for a large $\text{tan}\beta$. The full one-loop SUSY correction to $R_b$ can reach $1 \times 10^{-4}$ in natural SUSY and $2 \times 10^{-4}$ in the general MSSM.