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Higgs self-coupling in the MSSM and NMSSM after the LHC Run 1

Measuring the Higgs self-coupling is one of the crucial physics goals at the LHC Run-2 and other future colliders. In this work, we attempt to figure out the size of SUSY effects on the trilinear self-coupling of the 125 GeV Higgs boson in the MSSM and NMSSM after the LHC Run-1. Taking account of current experimental constraints, such as the Higgs data, flavor constraints, electroweak precision observables and dark matter detections, we obtain the observations: (1) In the MSSM, the ratio of $λ^{MSSM}_{3h}/λ^{SM}_{3h}$ has been tightly constrained by the LHC data, which can be only slightly smaller than 1 and minimally reach 97\%; (2) In the NMSSM with $λ<0.7$, a sizable reduction of $λ^{NMSSM}_{3h_2}/λ^{SM}_{3h_2}$ can occur and minimally reach 10\% when the lightest CP-even Higgs boson mass $m_{h_1}$ is close to the SM-like Higgs boson $m_{h_2}$ due to the large mixing angle between the singlet and doublet Higgs bosons; (3) In the NMSSM with $λ>0.7$, a large enhancement or reduction $-1.1<λ^{NMSSM}_{3h_1}/λ^{SM}_{3h_1}<2$ can occur, which is accompanied by a sizable change of $h_1τ^+τ^-$ coupling. The future colliders, such as the HL-LHC and ILC, will have the capacity to test these large deviations in the NMSSM.