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We consider the current experimental constraints on the parameter space ofthe MSSM and NMSSM. Then in the allowed parameter space we examine the Higgspair production at the 14 TeV LHC via $b\bar{b}\to hh$ ($h$ is the 125 GeVSM-like Higg boson) with one-loop SUSY QCD correction and compare it with theproduction via $gg\to hh$. We obtain the following observations: (i) For theMSSM the production rate of $b\bar{b} \to hh$ can reach 50 fb and thus can becompetitive with $gg \to hh$, while for the NMSSM $b\bar{b} \to hh$ has a muchsmaller rate than $gg \to hh$ due to the suppression of the $hb\bar{b}$coupling; (ii) The SUSY-QCD correction to $b\bar{b} \to hh$ is sizable, whichcan reach $45\%$ for the MSSM and $15\%$ for the NMSSM within the $1\sigma$region of the Higgs data; (iii) In the heavy SUSY limit (all soft massparameters become heavy), the SUSY effects decouple rather slowly from theHiggs pair production (especially the $gg\to hh$ process), which, for $M_{\rmSUSY}=5$ TeV and $m_A<1$ TeV, can enhance the production rate by a factor of1.5 and 1.3 for the MSSM and NMSSM, respectively. So, the Higgs pair productionmay be helpful for unraveling the effects of heavy SUSY.

Higgs pair production with SUSY QCD correction: revisited under current experimental constraints