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Measuring the trilinear neutral Higgs boson couplings in the minimal supersymmetric standard model at $e^+ e^-$ colliders in the light of the discovery of a Higgs boson

We consider the measurement of the trilinear couplings of the neutral Higgs bosons in the Minimal Supersymmetric Standard Model~(MSSM) at a high energy $e^+ e^-$ linear collider in the light of the discovery of a Higgs boson at the CERN Large Hadron Collider~(LHC). We identify the state observed at the LHC with the lightest Higgs boson~($h^0$) of the MSSM, and impose the constraints following from this identification, as well as other experimental constraints on the MSSM parameter space. In order to measure trilinear neutral Higgs couplings, we consider different processes where the heavier Higgs boson ($H^0$) of the MSSM is produced in electron-positron collisions, which subsequently decays into a pair of lighter Higgs bosons. We identify the regions of the MSSM parameter space where it may be possible to measure the trilinear couplings of the Higgs boson at a future electron-positron collider. A measurement of the trilinear Higgs couplings is a crucial step in the construction of the Higgs potential, and hence in establishing the phenomena of spontaneous symmetry breaking in gauge theories.