In some sense that's the cosmological constant problem and it applies to all particles, not just the Higgs. If a field with zero excitations were to weigh some

In some sense that's the cosmological constant problem and it applies to all particles, not just the Higgs. If a field with zero excitations were to weigh something (more specifically, have a positive energy density) on the scale of its single-excitation mass, it would be larger than the observed energy density of the universe by dozens of orders of magnitude, even if you're just talking about the extremely light neutrinos. But in fact, zero excitations looks to weigh zero...or 10^-60 - 10^-120 https://en.wikipedia.org/wiki/Cosmological_constant_problem https://en.wikipedia.org/wiki/Cosmological_constant_problem