We have recently discovered a pressure-induced quantum phase transition (QPT) at 4.3 kbar in the gapped quantum magnet piperazinium hexachlorodicuprate (PHCC) by means of muon-spin rotation and inelastic neutron scattering (INS) measurements. The Heisenberg nature of the spins and the 3-dimensional spin network of PHCC allows, for the first time, the study of SO(3) symmetry breaking right at the upper critical dimension. This transition is of particular interest due to the presence of a Higgs (amplitude) mode. Previous INS experiments deep in the ordered phase have allowed us to identify the ordering wave vector. Here, we propose to measure the temperature dependence of the dynamic structure factor around the ordering vector at the QCP to study the universal scaling behavior and to reveal the special role of the upper critical dimension.