A magnon Bose-Einstein condensate (BEC) in superfluid 3He is a fine instrument for studying the surrounding macroscopic quantum system. At zero temperature, the BEC is subject to a few distinct forms of decay into other collective excitations, owing to momentum and energy conservation in a quantum vacuum. We study the vortex-Higgs mechanism: The vortices relax the requirement for momentum conservation, allowing the optical magnons of the BEC to transform into light Higgs quasiparticles. This facilitates a direct measurement of the dimensions of the B-phase double-core vortex, providing experimental access to elusive phenomena, such as the Kelvin wave cascade and core-bound Majorana fermions. Our paper expands the spectrum of possible interactions between magnetic quasiparticles in 3He−B and lays the groundwork for building magnon-based quantum devices.