In supersymmetric theories, spin-0 particles, known as scalars or spin-0 bosons, indeed have superpartners. Supersymmetry is a theoretical framework that proposes a symmetry between fermions (particles with half-integer spin) and bosons (particles with integer spin). According to supersymmetry, for each known elementary particle in the Standard Model of particle physics, there exists a supersymmetric partner particle with spin differing by a half-unit.
For spin-0 particles in the Standard Model, such as the Higgs boson, the proposed superpartners are scalar particles known as "scalar partners" or "scalarinos" in supersymmetric theories. These scalar partners have not been observed experimentally, and if they exist, they would have different masses and quantum numbers compared to their Standard Model counterparts.
Supersymmetry is an appealing extension to the Standard Model because it provides solutions to certain theoretical issues and offers a potential explanation for the hierarchy problem (the large disparity between the weak scale and the Planck scale). However, it is important to note that, to date, no direct experimental evidence supporting supersymmetry has been found at the Large Hadron Collider (LHC) or other particle physics experiments. This has led some physicists to explore alternative theories and frameworks beyond supersymmetry.
The absence of experimental confirmation for supersymmetry has put certain aspects of the theory under scrutiny, and its exact form, if it exists, remains an open question in particle physics. Ongoing research continues to investigate the potential existence of superpartners, including scalar partners, and to explore alternative ideas and frameworks for addressing the outstanding questions in fundamental physics.