*Higgs force*. I'm surprised why this PR-cool aspect is not explored in our outreach efforts. Higgs bosons mediate the Higgs force in the same fashion as gravitons, gluons, photons, W and Z bosons mediate the gravity, strong, electromagnetic, and weak forces. Just like gravity, the Higgs force is always attractive and its strength is proportional, in the first approximation, to particle's mass. It is a force in a common sense; for example, if we bombarded long enough a detector with a beam of particles interacting only via the Higgs force, they would eventually knock off atoms in the detector.

There is of course a reason why the Higgs force is less discussed: it has never been detected directly. Indeed, in the absence of midi-chlorians it is extremely weak. First, it shares the feature of the weak interactions of being short-ranged: since the mediator is massive, the interaction strength is exponentially suppressed at distances larger than an attometer (10^-18 m), about 0.1% of the diameter of a proton. Moreover, for ordinary matter, the weak force is more important because of the tiny Higgs couplings to light quarks and electrons. For example, for the proton the Higgs force is thousand times weaker than the weak force, and for the electron it is hundred thousand times weaker. Finally, there are no known particles interacting

*only*via the Higgs force and gravity (though dark matter in some hypothetical models has this property), so in practice the Higgs force is always a tiny correction to more powerful forces that shape the structure of atoms and nuclei. This is again in contrast to the weak force, which is particularly relevant for neutrinos who are immune to strong and electromagnetic forces.

Nevertheless, this new paper argues that the situation is not hopeless, and that the current experimental sensitivity is good enough to start probing the Higgs force. The authors propose to do it by means of atom spectroscopy. Frequency measurements of atomic transitions have reached the stunning accuracy of order 10^-18. The Higgs force creates a Yukawa type potential between the nucleus and orbiting electrons, which leads to a shift of the atomic levels. The effect is tiny, in particular it is always smaller than the analogous shift due to the weak force. This is a serious problem, because calculations of the leading effects may not be accurate enough to extract the subleading Higgs contribution. Fortunately, there may be tricks to reduce the uncertainties. One is to measure how the isotope shift of transition frequencies for several isotope pairs. The theory says that the leading atomic interactions should give rise to a universal linear relation (the so-called King's relation) between isotope shifts for different transitions. The Higgs and weak interactions should lead to a violation of King's relation. Given many uncertainties plaguing calculations of atomic levels, it may still be difficult to ever claim a detection of the Higgs force. More realistically, one can try to set limits on the Higgs couplings to light fermions which will be better than the current collider limits.

Atomic spectroscopy is way above my head, so I cannot judge if the proposal is realistic. There are a few practical issues to resolve before the Higgs force is mastered into a lightsaber. However, it is possible that a new front to study the Higgs boson will be opened in the near future. These studies will provide information about the Higgs couplings to light Standard Model fermions, which is complementary to the information obtained from collider searches.

## 19 comments:

I totally agree that the Higgs force is cool and wanted to find some applications for it before. Can you have a bound state held together by the force, for example?

"Just like gravity, the Higgs force is always attractive"

You only meant that it's attractive if the signs of the "Higgs charges" are the same, right? But antiparticles have the opposite signs of the charges, I thought. The top-antitop Higgs force is repulsive however, right? Unlike the masses (sources of gravity) which are never definite, the charges under the Higgs force have both signs, don't they?

"which are never definite" - I meant negative.

I think the Higgs force is always attractive in the SM. What may indeed happen is that if the sign of the Yukawa coupling yf1 is flipped compared to the SM, then the force between f1 and f2 (whose Yukawa coupling is assumed not to be flipped) will be repulsive.

I thought that in QFT forces represented by gauge symmetries and that the mediators are the generator of the group, so how can there be a Higgs force?

A TV commercial ago, Jester, I was writing a comment that it can't be the case that the sign is the same for top and antitop etc.

But now I think you must be right. It's very counterintuitive because when top-antitop pair is created from a photon, the "Higgs charge" discontinuously jumps from 0 to two top units. But it's no contradiction because the "Higgs charge" doesn't have to be conserved - there is no corresponding symmetry for such a conservation law.

Explicitly, the Yukawa equation

(Laplacian + m^2) Higgs = sources

has sources = yukawaconstant*psibar*psi. But the psibar*psi behaves "oppositely" under the exchange of psi with C(psi) - particles and particles - than psibar*gamma_mu*psi, the electromagnetic current. So because the latter changes the sign, psibar*psi shouldn't change the sign. By Dirac equation, psibar*psi behaves just like the stress-energy tensor (because the stress-energy tensor also contains the mass term, times g_mu,nu, among other things) when it comes to the signs under the charge conjugation, so the force indeed looks like attractive whether there top or antitops etc. on both sides.

Good to have fixed this misconception of myself.

Jester wrote: “in practice the Higgs force is always a tiny correction to more powerful forces that shape the structure of atoms and nuclei”. But, in the original article, they talk about an atomic Higgs force enhancement by a factor of 10^6.

Everybody knows that the Higgs force is the mediated force needed to create mass. But a deeper understanding of the Higgs boson couplings is required. Let's see how, in the next years, precision physics could help us.

Claudio,

“Higgs force” appears to be a misnomer if you take the traditional view that interactions in QFT strictly arise from local gauge symmetry and are mediated by vector bosons.

Yet in a classical context, the conservative force is the (minus) gradient of the potential term entering the Lagrangian. From this standpoint, the “Higgs force” acquires a different meaning as something that derives from the Higgs potential. By analogy with the dynamics of nonlinear oscillators, Higgs self-interaction does not require a mediating carrier and may be considered as primary source of the “Higgs force”. Broadening this interpretation, Yukawa couplings stem from EW symmetry breaking and may be viewed as consequence of the “Higgs force”.

Ervin, thanks for the explanation.

I think it's a question of definition. I understand "force" as momentum exchange between particles without changing their identity (that is, without annihilating or turning into other particles). According to this definition, every boson creates a force, whether a spin-0 scalar, or a spin-1 gauge boson associated to a local symmetry, or a spin-2 graviton associated to the local coordinate invariance. Note that spin-0 pions were originally introduced to describe nuclear forces, before a better picture was developed.

I disagree with the statement that the Higgs force couples to all matter. It does not couple to the photon and as far as we know does not couple to the graviton or gluon either. If you just define matter as the fermions you may be right. Although, we are not sure if the Higgs couples to the neutrinos.

In this context, i meant "matter around us", that is protons, electrons, etc. I modified the first two sentences to make that clear.

Super-cool. I hope you'll let us know if this kind of experiment is actually carried out at some point.

And by "experiment", I guess I mean "measurement".

Whilst in a straightforward way it may be considered a force by analogy, languages are rich with words and would consider not conflating the Force-as-gauge-redundancy with the Force-as-any-interaction-term-in-QFT. A Yukawa interaction is an interaction not a gauge redundancy. Are you going to claim a mass term is a force too, because it is a self interaction? The couplings/charges of forces arise quite differently from the Yukawa couplings. Long range forces can be Higgsed - can the Higgs force be Higgsed [the Higgs Higgses itself so to speak by being massive it becomes a short range force, but if massless would be long range]? There is more that is dismiliar than is similar in your analogy, but on reflection I now sit on the fence about this one.

I agree that there's no unique definition of a force. In my understanding, a force is an attraction or repulsion capable of changing trajectories of stable particles. The Higgs force satisfies this criterion (a mass term does not). Note that we could make the Higgs force long-ranged by taking the limit of zero Higgs mass.

The Higgs force is in fact similar in many respects to the weak force. One practical difference is that there exists neutrinos who feel only the weak force, while there is no known particles interacting only via the Higgs force. For this reason the existence of the former is much easier to demonstrate experimentally.

Hi Jester,

"I agree that there's no unique definition of a force. In my understanding, a force is an attraction or repulsion capable of changing trajectories of stable particles."

This definition sounds intuitively plausible, but is not really a good one, because of the general principle of relativity. If you want to fix the definition to be coordinate-independent, you end up with the force being defined as a curvature of a section in some suitable fiber bundle. This includes all four (traditional) forces, but excludes couplings (i.e. interactions) such as Higgs, Yukawa, and cosmological constant. The CC is actually a nice counterexample --- one could say that in a certain sense it "changes the trajectories of particles", but it is somehow awkward to call it a new force.

As far as terminology goes, I think we should distinguish "forces" and "interactions". An interaction is any term in the action that gives rise to nonlinearity of equations of motion (i.e. cubic or higher order term in the action). OTOH, a force is a geometric concept, the curvature of a fiber-bundle corresponding to a given gauge symmetry. That would be my proposal at least... :-)

Best, :-)

Marko

Hi Jester,

"I agree that there's no unique definition of a force. In my understanding, a force is an attraction or repulsion capable of changing trajectories of stable particles."

This definition sounds intuitively plausible, but is not really a good one, because of the general principle of relativity. If you want to fix the definition to be coordinate-independent, you end up with the force being defined as a curvature of a section in some suitable fiber bundle. This includes all four (traditional) forces, but excludes couplings (i.e. interactions) such as Higgs, Yukawa, and cosmological constant. The CC is actually a nice counterexample --- one could say that in a certain sense it "changes the trajectories of particles", but it is somehow awkward to call it a new force.

As far as terminology goes, I think we should distinguish "forces" and "interactions". An interaction is any term in the action that gives rise to nonlinearity of equations of motion (i.e. cubic or higher order term in the action). OTOH, a force is a geometric concept, the curvature of a fiber-bundle corresponding to a given gauge symmetry. That would be my proposal at least... :-)

Best, :-)

Marko

Perhaps we can hope a popular movie will be released with the title "The Interaction Awakens". ;)

Here is a talk at Moriond EW about this topic: https://indico.in2p3.fr/event/12279/session/7/contribution/149/material/slides/0.pdf

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