Is the mass of a particle an exact number by experience? Or is it a consequence of some theory in physics?
The masses of particles and resonances are meticulously measured over the last hundred years and the values of the mass and quantum numbers determined experimentally are recorded in the Particle Data Group summaries.
The mainstream theoretical model , modeling the interactions of these particles, is the standard model, which uses quantum field theory for its calculations. Theory is continually developing , no one has claimed that there exists a Theory of Everything at present, so the existence of the particles cannot be a consequence of a theory. Particles exist, theories model their interactions.