The Higgs pair production in gluon fusion is a sensitive probe ofbeyond-Standard Model (BSM) phenomena and its detection is a major goal for theLHC and higher energy hadron collider experiments. In this work we reanalyzethe possible modifications of the Higgs pair production cross section withinlow energy supersymmetry models. We show that the supersymmetric contributionsto the Higgs pair production cross section are strongly correlated with theones of the single Higgs production in the gluon fusion channel. Motivated bythe analysis of ATLAS and CMS Higgs production data, which allows moderatedeviations of the Higgs coupling to gluons with respect to its Standard Model(SM) value, we show that the Higgs pair production may be significantlyincreased with respect to the SM predictions. In addition, the scalarsuperpartner's contribution may lead to significant modification of thedi-Higgs invariant mass distribution with respect to the SM predictions. Thesecontributions, however, become small for values of the lightest scalartop-quark (stop) mass significantly above the weak scale and for small valuesof the stop mixing parameter. They are therefore constrained by theexperimental lower stop mass bound and the vacuum stability constraints. Wealso analyze the combined effects on the di-Higgs production rate of amodification of the Higgs trilinear and top-quark Yukawa couplings in thepresence of light stops. In particular, we show that due to the destructiveinterference of the triangle and box amplitude contributions to the di-Higgsproduction cross section, even a small modification of the top-quark Yukawacoupling can lead to a significant increase of the di-Higgs production rate.
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