So if mass and charge are both just attributes of particles, what is the "charge equivalent" of the Higgs boson? And if there isn't one, then why is it assumed

So if mass and charge are both just attributes of particles, what is the "charge equivalent" of the Higgs boson? And if there isn't one, then why is it assumed the HB exists? Why cant particles have a innate "mass charge" in the same way they have an "electric charge"?