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

We consider the current experimental constraints on the parameter space of the MSSM and NMSSM. Then in the allowed parameter space we examine the Higgs pair production at the 14 TeV LHC via $bbar{b}to hh$ ($h$ is the 125 GeV SM-like Higg boson) with one-loop SUSY QCD correction and compare it with the production via $ggto hh$. We obtain the following observations: (i) For the MSSM the production rate of $bbar{b} to hh$ can reach 50 fb and thus can be competitive with $gg to hh$, while for the NMSSM $bbar{b} to hh$ has a much smaller rate than $gg to hh$ due to the suppression of the $hbbar{b}$ coupling; (ii) The SUSY-QCD correction to $bbar{b} to hh$ is sizable, which can reach $45%$ for the MSSM and $15%$ for the NMSSM within the $1sigma$ region of the Higgs data; (iii) In the heavy SUSY limit (all soft mass parameters become heavy), the SUSY effects decouple rather slowly from the Higgs pair production (especially the $ggto hh$ process), which, for $M_{rm SUSY}=5$ TeV and $m_A<1$ TeV, can enhance the production rate by a factor of 1.5 and 1.3 for the MSSM and NMSSM, respectively. So, the Higgs pair production may be helpful for unraveling the effects of heavy SUSY.