An Inquiry as to the Higgs Boson's Mass

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The Higgs particle has a mass of about 125 GeV. If interaction with the higgs field assigns a particle its mass, how does the Higgs field assign itself mass?
 
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By interacting with the Higgs :D. In addition, the particle has a mass on its own.
Both contributions are relevant, and it is quite interesting (and a puzzle for the theory) that the difference of those is as small as 125GeV, as both parts are assumed to be many orders of magnitude larger.
 
The Higgs boson's mass arises in the standard model from the Higgs's interaction with itself.

Are you asking how it picks the value 125 GeV? This the standard model does not predict. The Higgs mass is a "free parameter"--you can pick any value from for it you want from a large range and still get a mathematically consistent theory. So you have to determine by experiment which mass Nature chose. That's why the LHC experiments had to initially search for the Higgs over a large range of masses before eventually zeroing in on the region around 125 GeV.
 

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