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Your fantasy picture of the standard Higgs mechanism is off.

The field d.o.f. metaphorically "absorbed" by the Ws and Z would have been Goldstone particles, in the absence of coupling to would-be-gauge fields, but are "now" bonafide d.o.f. of massive vector fields, propagating as such in an asymmetric vacuum, without bonafide goldstons, massless scalars in the spectrum.

So there is no meaningful background "give-and-take" stochastic fluctuation process, as you are conjuring up. (Where did this fantasy come from? Stochastic quantization? Not there.) There are no such Goldstone degrees of freedom in the vacuum or the theory's spectrum any more: they have been solidly reassigned to the vector bosons. The only d.o.f. remaining out of the original Higgs doublet is the Higgs boson, a massive excitation. No massless d.o.f. left over, beyond the escapee photon.

While people find it instructive to consider the "duck in the wolf's belly", Nuc Phys B261 (1985) 379-431, the so-called Equivalence theorem relating in high energies the longitudinal components of vector bosons to their associated would-be Goldstone bosons, it is counterproductive to imagine this morphing as a real statistical process and infer spurious consequences.

Im' not sure if you are asking about vector boson bound states in your last subquestion, but binding as a shortage of edible goldstons in a degenerate vacuum makes no sense.

Your fantasy picture of the standard Higgs mechanism is off.

The field d.o.f. metaphorically "absorbed" by the Ws and Z would have been Goldstone particles, in the absence of coupling to would-be-gauge fields, but are "now" bonafide d.o.f. of massive vector fields, propagating as such in an asymmetric vacuum, without bonafide goldstons, massless scalars in the spectrum.

So there is no meaningful background "give-and-take" stochastic fluctuation process, as you are conjuring up. (Where did this fantasy come from? Stochastic quantization? Not there.) There are no such Goldstone degrees of freedom in the vacuum or the theory's spectrum any more: they have been solidly reassigned to the vector bosons. The only d.o.f. remaining out of the original Higgs doublet is the Higgs boson, a massive excitation. No massless d.o.f. left over, beyond the escapee photon.

While people find it instructive to consider the "duck in the wolf's belly", Nuc Phys B261 (1985) 379-431, the so-called Equivalence theorem relating in high energies the longitudinal components of vector bosons to their associated would-be Goldstone bosons, it is counterproductive to imagine this morphing as a real statistical process and infer spurious consequences.

Im' not sure if you are really asking about vector boson bound states in your last subquestion, but binding as a shortage of edible goldstons in a degenerate vacuum makes no sense. Individually, mass does not vary in interactions with other particles.

Your fantasy picture of the standard Higgs mechanism is off.

The field d.o.f. metaphorically "absorbed" by the Ws and Z would have been Goldstone particles, in the absence of coupling to would-be-gauge fields, but are "now" bonafide d.o.f. of massive vector fields, propagating as such in an asymmetric vacuum, without bonafide goldstons.

So there is no meaningful background "give-and-take" stochastic fluctuation process, as you are conjuring up. (Where did this fantasy come from? Stochastic quantization? Not there.) There are no such Goldstone degrees of freedom in the vacuum or the theory's spectrum any more: they have been solidly reassigned to the vector bosons. The only d.o.f. remaining out of the original Higgs doublet is the Higgs boson, a massive excitation. No massless d.o.f. left over, beyond the escapee photon.

While people find it instructive to consider the "duck in the wolf's belly", Nuc Phys B261 (1985) 379-431, the so-called Equivalence theorem relating in high energies the longitudinal components of vector bosons to their associated would-be Goldstone bosons, it is counterproductive to imagine this morphing as a real statistical process and infer spurious consequences.

Im' not sure if you are asking about vector boson bound states in your last subquestion, but binding as a shortage of edible goldstons in a degenerate vacuum makes no sense.

Your fantasy picture of the standard Higgs mechanism is off.

The field d.o.f. metaphorically "absorbed" by the Ws and Z would have been Goldstone particles, in the absence of coupling to would-be-gauge fields, but are "now" bonafide d.o.f. of massive vector fields, propagating as such in an asymmetric vacuum, without bonafide goldstons, massless scalars in the spectrum.

So there is no meaningful background "give-and-take" stochastic fluctuation process, as you are conjuring up. (Where did this fantasy come from? Stochastic quantization? Not there.) There are no such Goldstone degrees of freedom in the vacuum or the theory's spectrum any more: they have been solidly reassigned to the vector bosons. The only d.o.f. remaining out of the original Higgs doublet is the Higgs boson, a massive excitation. No massless d.o.f. left over, beyond the escapee photon.

While people find it instructive to consider the "duck in the wolf's belly", Nuc Phys B261 (1985) 379-431, the so-called Equivalence theorem relating in high energies the longitudinal components of vector bosons to their associated would-be Goldstone bosons, it is counterproductive to imagine this morphing as a real statistical process and infer spurious consequences.

Im' not sure if you are asking about vector boson bound states in your last subquestion, but binding as a shortage of edible goldstons in a degenerate vacuum makes no sense.

Your fantasy picture of the standard Higgs mechanism is off.

The field d.o.f. metaphorically "absorbed" by the Ws and Z would have been Goldstone particles, in the absence of coupling to would-be-gauge fields, but are "now" bonafide d.o.f. of massive vector fields, propagating as such in an asymmetric vacuum, without bonafide goldstons.

So there is no meaningful background "give-and-take" stochastic fluctuation process, as you are conjuring up. (Where did this fantasy come from? Stochastic quantization? Not there.) There are no such Goldstone degrees of freedom in the vacuum or the theory's spectrum any more: they have been solidly reassigned to the vector bosons. The only d.o.f. remaining out of the original Higgs doublet is the Higgs boson, a massive excitation. No massless d.o.f. left over, beyond the escapee photon.

While people find it instructive to consider the "duck in the wolf's belly", Nuc Phys B261 (1985) 379-431, the so-called Equivalence theorem relating in high energies the longitudinal components of vector bosons to their associated would-be Goldstone bosons, it is counterproductive to imagine this morphing as a real statistical process and infer spurious consequences.

Im' not sure if you are asking about vector boson bound states in your last subquestion.

Your fantasy picture of the standard Higgs mechanism is off.

The field d.o.f. metaphorically "absorbed" by the Ws and Z would have been Goldstone particles, in the absence of coupling to would-be-gauge fields, but are "now" bonafide d.o.f. of massive vector fields, propagating as such in an asymmetric vacuum, without bonafide goldstons.

So there is no meaningful background "give-and-take" stochastic fluctuation process, as you are conjuring up. (Where did this fantasy come from? Stochastic quantization? Not there.) There are no such Goldstone degrees of freedom in the vacuum or the theory's spectrum any more: they have been solidly reassigned to the vector bosons. The only d.o.f. remaining out of the original Higgs doublet is the Higgs boson, a massive excitation. No massless d.o.f. left over, beyond the escapee photon.

While people find it instructive to consider the "duck in the wolf's belly", Nuc Phys B261 (1985) 379-431, the so-called Equivalence theorem relating in high energies the longitudinal components of vector bosons to their associated would-be Goldstone bosons, it is counterproductive to imagine this morphing as a real statistical process and infer spurious consequences.

Im' not sure if you are asking about vector boson bound states in your last subquestion, but binding as a shortage of edible goldstons in a degenerate vacuum makes no sense.