Complete one-loop effects of SUSY QCD in $b\bar{b}h$ production at the LHC under current experimental constraints

Inspired by the recent LHC Higgs data and null search results of supersymmetry (SUSY), we scan the parameter space of the Minimal Supersymmetric Standard Model (MSSM) with relatively heavy sparticles (1-3 TeV). Then in the parameter space allowed by current collider experiments and dark matter detections, we calculate the complete one-loop SUSY QCD corrections to $pp\to b\bar{b}h$ at the LHC with $\sqrt{s}=14$ TeV and obtain the following observations: (i) For the large values of $\tan\beta$ and low values of $m_{A}$, the SUSY QCD effects can be quite large, which, however, have been excluded by the latest results of LHC search for $H/A \to \tau^{+}\tau^{-}$; (ii) For modest values of $\tan\beta$ and $m_{A}$ which so far survived all experimental constraints, the SUSY QCD corrections can maximally reach about -9%.