You could characterize it gravity-wise, but we can already characterize it gravity-wise (sort of). We really only care about a field to the extent it can interact with other fields, and as of now gravity isn't really a quantum field, but a distinct thing. I think most people hope to eventually get relativity under the quantum umbrella, but we're nowhere near that yet. If relativity is just a description of the stage the other fields dance on, then we're just kinda screwed. We could determine the mass of the particle (assuming we could ever be confident in separate particles at all), but no other properties.