Understanding the Relationship Between Mass and the Higgs Field

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Perhaps a Higgnorant question? Anyway. Am I correct in thinking that the mass of a Higgs-field-interacting particle is the energy stored in the Higgs field by that interaction?
 
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No. Without going into details, it does not even have the same units. Energy stored in a field would have an energy density (energy per volume), while the Higgs mass has an energy, without a volume.
 
The question of how much energy does the Higgs receives from self interaction is a interesting one, but indeed it is not directly related to the measured mass.