What geometry can represent what physicists mean by the Higgs boson? A geometric understanding is required by good philosophy of physics. This good philosophy points to Einstein-Davis and Kaluza-Klein theory, that the most substantial part of classical physics must be accounted for by the intrinsic possibilities of curved spacetime.
The Higgs boson is said to provide mass to charged particles. But, in geometry, mass translates to a path in a higher dimension that is partially aligned with time for the (conserved) spacetime dilation that is the particle.
But this path seems to be over an extremely small closed course (quantization). So it would be an absurdity for large scale time in the main to be aligned with this closed course.
I would be inclined to think that charges should be massless and the path orthogonal to time in order to allow scope for long stretches of time - unless time is also partially aligned with an extremely divergent higher dimension. And some small scale quantization affiliated with this divergent higher dimension seems to be what physicists mean by the Higgs particle. It is quite true that, so far as spacetime applies, a charge results from a (quantized) change of size in a closed dimension. Then I would be inclined to think that to keep macroscopic time on track implies a compensating change in the matching divergent dimension. Even with this understanding, the question is whether this can ever separate from the charge.
But time finds a way! Contrary to the above inclination is the consideration that there are entire classes of world lines which never become entwined in convergent or divergent paths through higher dimensions, but only those of quantized charges. It is the partial alignment of these time lines for charges with time in the large scale that provides mass for charges. By the time line I mean the direction of the spacetime dilation that makes up the substance of the particle in Einstein-Davis and Kaluza-Klein theory. And this all holds even though the time lines for charges are tachyonic and hidden by event horizons. Quantization ensures that this alignment is not entirely relative.
So geometry implies rather strongly that Higgs bosons are not distinct entities.
Michael J. Burns