Can a Higgs Field Gradient Produce a Force?

[Benido]

How did you find PF?: Chat GPT

Could a spatial gradient in the Higgs vacuum expectation value exert a force on matter?

If the Higgs VEV varied with position, (v=v(x)), then for an elementary fermion,
$$m(x)=\frac{y,v(x)}{\sqrt{2}}$$
This appears to imply a spatial gradient in the particle's rest energy $E(x)=m(x)c^2$.

Would this produce an effective force
$$F=-\nabla E$$
and if so, how should this be treated correctly in Standard Model field theory?

 

[.Scott]

Welcome to these forums.
I like your question. The regular discussion about loss of the Higgs Field describes a bubble expanding at the speed of light and crushing galaxies and destroying all chemistry in the process. But I never considered the notion of an expanding bubble that restores the Higgs field. If that is possible, then, on the face of it, the combined effects of those two waves would present an interesting "conservation of matter/energy" problem.

This is not my area of expertise.

 

[PeterDonis]

how should this be treated correctly in Standard Model field theory?

I think the answer to this is that the Standard Model is not constructed to handle spatial variation in the Higgs VEV; it's assumed to be a constant everywhere in space, and does not change with time, at least not once the Electroweak Phase Transition is completed.

 

[renormalize]

I think the answer to this is that the Standard Model is not constructed to handle spatial variation in the Higgs VEV;

Actually, by its very construction the standard model incorporates an ultra-short-distance Yukawa force between leptons and quarks arising from the exchange of virtual Higgs bosons. See, for example Probing Atomic Higgs-like Forces at the Precision Frontier:

The characteristic range distance of the force potential (3) is $d=\hbar c/M_H=1.58\times 10^{-18}\,\text{m}\,$. Note that $d$ is only about $1/500\text{-th}$ the radius of a proton.

 

[PeterDonis]

by its very construction the standard model incorporates an ultra-short-distance Yukawa force between leptons and quarks arising from the exchange of virtual Higgs bosons.

But this is not due to the Higgs VEV, let alone a gradient in it; the VEV is constant and has no effect on the dynamics you're describing here. The Higgs bosons are what is "left over" after the VEV is determined at the electroweak phase transition.

 

[renormalize]

But this is not due to the Higgs VEV, let alone a gradient in it; the VEV is constant and has no effect on the dynamics you're describing here.

I certainly agree with you regarding the Higgs VEV. In my defense, my post was written in response to the title of the thread: "Can a Higgs Field Gradient Produce a Force?" (italics added by me). Clearly the answer is yes.

 

[PeterDonis]

I certainly agree with you regarding the Higgs VEV.

And as the OP of the thread makes clear, a gradient in the Higgs VEV is what is being asked about.

In my defense, my post was written in response to the title of the thread: "Can a Higgs Field Gradient Produce a Force?" (italics added by me). Clearly the answer is yes.

Even leaving aside the above, I'm not so sure. Interactions mediated by the exchange of virtual gauge bosons (which is itself a heuristic description) do not necessarily have a useful description in terms of gradients of a field.

 

[renormalize]

Even leaving aside the above, I'm not so sure. Interactions mediated by the exchange of virtual gauge bosons (which is itself a heuristic description) do not necessarily have a useful description in terms of gradients of a field.

Can you clarify your response? You mention gauge bosons (spin-1), but Higgs bosons are massive scalar (spin 0) particles which, to my understanding, always give rise to an attractive gradient force, just as in the original nuclear binding model of Yukawa based on the exchange of massive pions.

 

[PeterDonis]

You mention gauge bosons (spin-1)

AFAIK "gauge boson" is not limited to spin-1, it can be any boson that can participate in a virtual particle exchange interaction. I might be using the term too broadly; but in that case, just substitute "any boson that can participate in a virtual particle exchange interaction" for "gauge boson" in what I posted.

Higgs bosons are massive scalar (spin 0) particles which, to my understanding, always give rise to an attractive gradient force

I don't think an even spin exchange interaction has to be attractive--I think in the even spin case like charges attract and unlike charges repel, whereas in the odd spin case, like charges repel and unlike charges attract. In the case of the Higgs interaction you describe, the "charges" are basically the masses (or at least the mass numbers), so it's all like charges, hence an attractive interaction.

 

[MTDismuke]

How did you find PF?: Chat GPT

Could a spatial gradient in the Higgs vacuum expectation value exert a force on matter?

If the Higgs VEV varied with position, (v=v(x)), then for an elementary fermion,
$$m(x)=\frac{y,v(x)}{\sqrt{2}}$$
This appears to imply a spatial gradient in the particle's rest energy $E(x)=m(x)c^2$.

Would this produce an effective force
$$F=-\nabla E$$
and if so, how should this be treated correctly in Standard Model field theory?

The short answer to his Higgs question in standard physics is: yes, if the Higgs vacuum expectation value actually changed across space, it would create an effective force because it would change the rest energy. But mainstream model rules say the Higgs VEV is a flat, uniform constant everywhere, so it doesn't happen.

 

[Benido]

Thank you — that is exactly the sort of question I am trying to explore.

My thought is whether a local disturbance of the Higgs field could be followed by a restoring disturbance, effectively creating two boundaries rather than one permanently expanding bubble. If such a configuration were physically possible, the important question would be how energy and momentum are conserved across the two boundaries.

I realise this is speculative, but I think it may be an interesting direction to investigate.