Which is inertial mass of Higgs boson? Idea that Higgs boson is giving inertial mass to particles (photos and gluons excluded) open question which is inertial mass of the Higgs boson itself.
The (inertial) mass of the Higgs has been measured at the LHC: 125.09 ± 0.21 (statistical error) ± 0.11 (systematic error) GeV, cf. http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.191803
Within the Standard Model it is defined through the Higgs potential, which relates it to the Higgs self-coupling constant and its vacuum expectation value.
An elementary yet not standard question : it is stated that Higgs boson is responsible for mass of leptons, - then what is responsible for the inertial mass ... of the itself Higgs boson?
Fantastically!- I found your work as a weird breakthrough... Yet its physical backgrounds, being separated from math formulas, should be much more elaborated and argued!
Once more: the mass of the Higgs boson itself is proportional to the Higgs self-coupling and the Higgs vacuum expectation value--it's determined by the curvature of the Higgs potential at its minimum.
The inertial mass of unstable particles, while not exactly trivial to define can be defined and its effects can be measured-an example is the mass of the top quark that could be deduced from the radiative corrections to processes measured at LEP.
The inertial mass is the same-it's the non-relativistic limit of the energy-momentum tensor of the object. The way it reacts with the gravitational field of a planet is controlled by the Schwarzschild metric, that contains, as parameter, the mass of the planet. And these statements are consistent with the fact that the inertial mass is equal to the gravitational mass.
One shouldn't confuse inertial mass with force. In the Newtonian approximation m_i (d^2x/dt^2) = m_g g and it's an additional assumption-confirmed by experiment-that m_i=m_g. In general relativity it's a consequence of the fact that the coupling of matter to gravity is through the energy-momentum tensor and that only the metric determines spacetime. The force on Earth is 9.81 Newtons and on Mars less-but that's, once more, due to the metric, not the mass of the object-that, in general relativity, is defined through the flux of the energy-momentum tensor at infinity, assuming the spacetime is asymptotically flat.
No-the energy density of the vacuum is not affected by the creation and annihilation of particles-unless it's unstable, e.g. in the presence of an electric field. Curvature of spacetime implies that the vacuum of quantum excitations isn't uniquely defined-that's what Hawking found and used to deduce that black holes radiate.
A quantum vacuum is Lorentz invariant, or invariant under general coordinate transformations, so its excitations cannot be labeled only by time. In a curved spacetime, the vacuum isn't unique and energy isn't uniquely defined. The gravitational constant is related to the Schwarzschild radius (they're proportional), they're not independent. Variations of the metric are coherent superpositions of gravitons in any case-and particles, such as the Higgs, are excitations of a vacuum. All this is presented in textbooks on quantum field theory and general relativity.
I'm very sorry, but what do you mean saying "inertial mass"? Is it _really_ different from the square root of the particle 4-momentum squared? (Note that the energy of a particle in rest is nothing but a component of its 4-vector of momentum). Reminder: the length of a pencil does not depend of its orentation, despite its projection on your desk may be of any value, from 0 to a maximum, defined by the pencil's length.