Inertial mass, gravitational mass, and the Higgs

[technobot]

If we explain the origin of inertial mass with the Higgs mechanism, how do we explain the origin of gravitational mass? In other words, how does the Higgs mechanism contribute to the gravitational field of a particle?

(Note: the closest thread I've found to this is http://www.physicsforums.com/showthread.php?t=300653 , but it doesn't answer my question and seems to go in a different direction)

[atyy]

At low energies, gravity is spin-two field, and "gravitational mass" is the stress-energy tensor of matter, where matter is simply a bunch of other fields, such as the electromagnetic field, the electron field etc - the Higgs field is just another field.

[tom.stoer]

If you calculate the stress-energy tensor for the Higgs coupling to some other field, then the term contributing to the "mass energy density" of that field will look like the coupling term between the Higgs and the field in the Lagrangian.

It's like deriving the Hamiltonian H from the Lagrangian. The Hamiltonian density and T°° are identical.

[technobot]

In other words, the higgs mechanism contributes directly to the stress-energy of the particle - did I understand correctly?

If so, allow me to refine my understanding with another question. In the higgs model, does the contribution to the inertial mass and the contribution to the gravitational mass appear as separate terms, or one and the same?

[tom.stoer]

In other words, the higgs mechanism contributes directly to the stress-energy of the particle - did I understand correctly?
Yes (of course it becomes more difficult if you want to include quantum corrections).

... In the higgs model, does the contribution to the inertial mass and the contribution to the gravitational mass appear as separate terms, or one and the same?
???
Ordinary QFT is always formulated in the framework of special relativity. Mass is mass. It can be calculated by integration T°° over three-space for fixed time.
If you want to understand how it looks like in general relativity I have to admit that I have no idea how this can be formulated. Of course T°° will have only one term (not two) coming from the Higgs interaction, and in principle you would again try integrate T°° over a spatial slice of four-dim. spacetime.
But definition of mass is tricky in GR. The reason is that you expect that the integral over T°° is energy that means the 0-component of a four vector. But this is not always true!