Self-interacting $O(N)$ scalar dark matter multiplet in a Higgs-portal model with a light scalar mediator

We investigate self-interacting dark matter in an $O(N)$-symmetric real scalar multiplet model with Higgs-portal interactions involving the Standard Model Higgs and a real singlet scalar. After spontaneous breaking of the singlet ${\mathbb{Z}}_2$ symmetry, the singlet scalar mixes with the SM Higgs boson. We focus on the regime where the resulting light scalar serves as a mediator, leading to sizable and velocity-dependent self-interactions. We impose constraints from Higgs measurements, rare $B$-meson decays, the dark matter relic abundance, spin-independent direct-detection searches, and scalar coupling perturbativity. We find viable parameter regions in which destructive interference between scalar-mediated scattering amplitudes suppresses the direct-detection cross section while allowing self-interactions relevant to dwarf-galaxy scales. Among these viable parameter regions, a subset also satisfies electroweak vacuum stability up to the Planck scale. Finally, we show that future long-lived-particle searches can probe part of the viable parameter space, providing complementary tests of Higgs-portal self-interacting dark matter with a light scalar mediator.