246 GeV is the measured ``vacuum expectation value'' of the Higgs field. If it were zero, at the classical level, the Higgs boson could acquire a mass, nevertheless-this was found in 1973 by S. Coleman and E. Weinberg (no relation to S. Weinberg!) Article Radiative Corrections as the Origin of Spontaneous Symmetry Breaking

The Higgs boson mass does depend on the Higgs vev-but the relation is quite complex. And what's interesting is that, even if in the ``classical'' theory the vacuum expectation value of the Higgs vanishes, quantum effects won't keep it zero-that's the upshot.

If the measured vacuum expectation value of the Higgs were much larger than 246 GeV, then perturbation theory wouldn't be valid and this would have led to significant new effects at the LHC. In fact the measurement of the properties of the Higgs boson at the LHC, that indicate that its vacuum expectation value is 246 GeV imply that there must exist new particles, whose, hitherto unkown, interactions with the known particles keep the vacuum expectation value low enough that perturbation theory seems sufficient. The reason is that the contribution of only the known particles to the vacuum expectation value of the Higgs would lead, generically, to it taking a value much larger than 246 GeV.

Dear Amitabh,

The mass of the boson is related with the spontaneous breaking of symmetry which happens if the vacuum

ϕ(x)=v+h(x)

isn't at ϕ=0 but ϕ=v. The expansion of the dynamical field h(x) can be made perturbatively around the vacuum in x=0. Thus the shift v is going to be in all couplings where ϕ(x) were defined and its value obviously is going to appear. Therefore the Higgs boson mass depends on the vev as you ask in your question.

The vacuum expectation value of the Higgs field is the value of the minimum of its (effective) potential; the mass (squared) of the Higgs particle is the value of the curvature of the (effective) potential at its minimum. They are independent quantities.

The system is unestable at x=0 and it is necessary to define a new vev at ϕ = v which is stable, i.e. the ground state of the Higgs field is degenerate. And the mass of the Higgs boson is directly related with this v shift and with other parameter \lambda. Experimentally it is found a value of 246 GeV/c2 . Obviously the mass has to be defined at the minimum of the potential and this is the reason to make the new definition of the Higgs field in v instead in zero.

Some people say that the Higgs gives the other particles mass, but that’s inaccurate (at best). The Higgs gives only about 2% of the mass of the matter around us in everyday live. The rest is provided by the spontaneous breaking of chiral symmetry and the trace anomaly in QCD. Within the standard model of elementary particles the condensate of the Higgs field provides mass to the quarks and leptons.

The Higgs field itself has a generic mass term by its own, but with the “wrong sign”, so that the local SU(2) x U(1) gauge symmetry is broken to U(1). The great discovery of Brout and Englert, Higgs, and Guralnik, Hagen, Kibble (all three articles in PRL 13, 1964) was that in the case of such a spontaneous breaking of a local gauge symmetry is an exception to Goldstone’s theorem that applies to global gauge symmetries only. In the case of a spontaneously broken local gauge symmetry the “would-be Goldstone bosons” are lumped into the gauge fields of the broken part of the symmetry group and thus provide the longitudinal third component of a massive vector boson, i.e., these gauge bosons become massive. In the case of the electroweak standard model that means that the SU(2) weak-isospin gauge bosons become massive (these are the three W and Z bosons), while the unbroken electromagnetic U(1) keeps its massless gauge boson (the photon). Excitations of the Higgs field above its vacuum expectation value (VEV) appear as physical particles in the theory, and that’s the Higgs boson. It gets its mass from the generic mass term and part of the Higgs-self interaction around the VEV. This leads to an effective mass term for the Higgs boson with the right sign. For the usual choice of a “minimal Higgs sector”, where the Higgs field is a SU(2) weak-isospin doublet (4 real field-degrees of freedom, of which 3 are providing the longitudinal components of the W and Z bosons and 1 describes Higgs-boson particles after spontaneous symmetry breaking).

In the original version of the Standard Model, the fermions are massless. When you try to add a mass term by hand, it violates gauge invariance. If there is a Higgs boson, there would have to be an interaction term between the Higgs boson and the fermions, and that interaction term has the same mathematical form as a mass term for the fermions would have, if there were a mass term, and so therefore you can use the interaction term between the Higgs boson and the fermions for the mass term for the fermions, and thus you end up with a mass term for the fermions.

https://www.youtube.com/watch?v=VtItBX1l1VY

The Higgs boson mass is given by mH = √ λ/2 v, where λ is the Higgs self-coupling parameter and v is the vacuum expectation value of the Higgs field, v = (√ 2G_F )^ {−1/2} ≈ 246 GeV, fixed by the Fermi coupling G_F , which is determined with a precision of 0.6 ppm from muon decay measurements. λ is presently unknown. Therefore, the Higgs boson mass depend on the Higgs VeV.

Experimental value is near 125 GeVs. (See attached figure from CERN courier Aug 23, 2012) Because it a microscopic particle we have to interpret this result in terms of a "theoretical model", simply because we cannot "see" it by our own eyes as we see a star or a galaxy. Because standard model is very successful in explaining experimental data, Higgs mass can be interpreted in terms of this model; it is thus a "microscopic reality". Then, in terms of standard model parameters, at the tree level, Higgs mass depends on the product of the quartic scalar coupling with the VEV of Higgs field.

When we were Ph.D. students in early nineties, there were competing models describing experimental data emerging from colliders. For example there was technicolor models which described electroweak symmetry breaking in terms of new gauge interactions that becomes strong at the electroweak scale forming fermion condensates. Such models did not invoke Higgs field at all. Experimental discovery of Higgs bosons have ruled out these models.

ref: http://cerncourier.com/cws/article/cern/50566

Higgs mass depends theoretically on VEV. Numerical value has to be found experimentally.

It is doubtful that quantized time could appear on the fundamental level.