# Why isn't Higgs coupling considered a fifth fundamental force?

When I first learned about the four fundamental forces of nature, I assumed that they were just the only four kind of interactions there were. But after learning a little field theory, there are many other kinds of couplings, even in the standard model. So why isn't the Yukawa Higgs coupling considered a fifth fundamental force? To be a fundamental force, does there need to be a gauge boson mediating it?

• I think you're more or less right; what have been (sociologically) canonized as the fundamental forces (minus gravity) roughly correspond to the factors $U(1)$, $SU(2)$, and $SU(3)$ in the famous "$U(1)\times SU(2)\times SU(3)$" gauge symmetry of the standard model. But this is really a historical question, in my opinion. – j.c. Nov 18 '10 at 18:40
• Doesn't look like this has been mentioned yet: intuitively, forces are vectors and impart momentum, whereas the Higgs field is a scalar field that generates mass. If a fundamental interaction isn't mediated by a gauge boson, then it loses it's most force-like quality of being a vector field. – David H Mar 28 '13 at 4:09
• For absolutely no good reason at all. – tparker Mar 15 '20 at 14:44

## 7 Answers

The Higgs exchange between matter particles can certainly be called a force. Whether it can be viewed a fundamental force, is a matter of taste. But there is one important distinction between the force due to the Higgs exchange and the usual fundamental interactions. The strong and electroweak interactions are described as gauge interactions. It means that they are not put by hand but arise automatically when you require that the matter fields be invariant under local certain internal transformations (phase rotations, color transformations, etc.). In contrast to that, the "Higgs force" is put into the model by hand, as its presence is not driven by any symmetry consideration. You can equally nicely consider a model with zero Yukawa coupling.

• The catch here being that the symmetries themselves are "put into the model by hand." The Higgs coupling is driven by experimental results, and so while you could consider a model with no coupling, you'd have to explain spontaneous symmetry breaking some other way. Is your suggestion that some higher energy theory may in fact have some further symmetry that at low energy gives us the Higgs interaction, and that the higher level symmetry is the fundamental force, making the Higgs in some sense non-fundamental (like electric and magnetic separately) – user542 Nov 18 '10 at 20:50
• Concerning putting by hand, let's consider electromagnetism. You start from free field theory with complex field describing matter. Complex fields are put by hand, but after quantum mechanics this is not that unnatural. The lagrangian has the global U(1) invariance, so that the global phase is unobservable. This is rather expected. What you ask in addition is to make the phase unobservable locally. This also seems a rather reasonable requirement. That's it, the electromagnetic interactions follow. For non-abelian groups I agree that the initial global symmetry is put by hand. – Igor Ivanov Nov 18 '10 at 21:34
• As for the second question, I just say that you can construct a theory with Higgs bosons but zero Yukawa couplings (no "direct Higgs force"), but you cannot construct a locally U(1) invariant theory without electromagnetic interactions. – Igor Ivanov Nov 18 '10 at 21:38
• You can certainly send the gauge coupling to zero. Notice also that you can write down theories in which the Higgs comes from additional components of gauge fields in extra dimensions. Given that, it is hard to argue that there is a fundamental difference between these interactions. – user178876 Dec 17 '17 at 3:21
• @IgorIvanov: Really? Are you sure you can't zero out the charges on all fundamental particles? – Joshua May 27 '18 at 20:09

Forces and interactions are similar, so maybe for the purposes of this discussion we should define force as "interaction with a massless particle," as this gives the possibility of macroscopic-range "forces" (barring impeding effects such as confinement or symmetry breaking). After all, gravity is a massless but non-Yang-Mills force (mediated by spin-2, not spin-1, particle). There are some constraints on which spins (representations) of massless particles are possible in quantum field theory, but I'm not familiar enough to try to cite them off-hand, sorry.

Scalar fields do transfer momentum in classical physics. Just take a look at acoustic signals in a gas. A strong sound can cause your windows to rattle. A well known example of energy transference by means of sound (pressure waves) is demonstrated with tuning forks. Quantum theory speaks of sound as particles (phonons), the discrete quanta of quantized mechanical vibrations of a christal lattice, whose longitudinal mode corresponds to our macroscopic perception of sound. In quantum field theory all fields need to be quantized in the end. If I've understood it correctly, the Higgs particle represents the discrete quanta of the quantized Higgs field. Since the Higgs field is a scalar field, its quanta are bosons. They carry kinetic energy, and this energy can be transmitted to all quantum fields that the Higgs field interacts with. You just need to take a look at the Lagrangian to see all the fields that the Higgs interacts with. Alternatively, look for the various Feynman diagrams that include Higgs lines. You can then easily see all the particles it interacts with.

• Exactly the same can be said about all 4 fundamental forces: they make waves which transfer energy and momentum, they are quantized and make particles, also bosons (though of other spins, 1 and 2, as they are vector and tensor fields). – firtree Aug 27 '14 at 14:33

The theory of particle physics is mathematically organized as a gauge theory with the group structure of SU(3)xSU(2)xU(1). These have exchange bosons, which before weak symmetry breaking have a zero mass, and after symmetry breaking have been associated with the three fundamental forces , electromagnetism, weak, strong. This association comes from the mathematical continuity that is necessary going from the microscopic frame of quantum mechanics to the macroscopic of classical electrodynamics, extended to the strong and weak forces.

A force in the micro world of Feynman diagrams is any dp/dt, momentum transfer, in an interaction exchanging particles, for example in this Compton scattering diagrams which is for calculating the crossection of a photon scattering off an electron: There is a dp/dt, and the virtual exchange particle is the electron. It is an electromagnetic interaction because the incoming vertex is electromagnetic and has the coupling constant of electromagnetism. The electron exchange between vertices is not a fundamental force.

Fundamental are the exchanges associated with the gauge bosons, as the lower order diagrams which give most of the probability for the interaction are the simple exchange of a gauge boson, when it is allowed by quantum numbers. It is the simple exchange of virtual photons that will build up the classical electric and magnetic potentials of the classical electromagnetic interaction.

The Higgs field which is associated with the existence of the mass of the elementary particles does not transfer momentum, and thus is not a force; the exchanges of the Higgs boson are on the same level as for example the exchanges of electrons, (as seen in the diagram above,) in the appropriate diagrams, i.e. a simple transfer of dp/dt. Thus the Higgs mechanism is not related to a new fundamental force.

At the quantum level it is the coupling constants that define the type of interaction and are fundamental. The Higgs boson is in the electroweak sector and, as a neutral elementary particle, interacts only with the weak coupling constant at the vertices.

• There is a Higgs-exchange force, as discussed here. – benrg Jan 18 at 17:57
• @benrg interesting, nevertheless it is not counted in the three fundamental forces of the standard model. In a sense all virtual particle exchanges in a Feynman diagram carry a dp/dt and can be called a "force", imo – anna v Jan 18 at 18:18

The Higgs field is not a vector field like, say, the vector potential of EM is. It arises from the observed coupling of massive particles to the weak field. So the Higgs boson is not a force-exchanging gauge boson in the same way as the other bosons of the Standard Model.

• The gravition wouldn't be a vectorial (it would have spin 2), but I would still be a force boson. Right? – jinawee Nov 14 '13 at 16:12

I agree with tparker's comment: it's for absolutely no good reason at all.

As discussed in this Résonaances blog post, there is a Higgs-mediated force between particles, which is a bit like scalar gravity, but with a weak-force-like range. Its Feynman diagrams look just like those for other forces. I can't see any good reason to deny fundamental-force status to this interaction in light of the fact that:

• The nuclear force, which is carried by non-gauge bosons (pions), is called a force. Not a fundamental force, since pions aren't fundamental, but it's similar to the Higgs force otherwise. There's even a pion version of the Higgs mechanism.

• The electromagnetic force is called fundamental even though its force carrier is a weird mixture of the fundamental SU(2) and U(1) gauge fields.

• The weak force is called a fundamental force even though it barely has the qualities you'd normally associate with a force, and its force carriers are weird mixtures of the fundamental SU(2) and U(1) gauge fields and the fundamental Higgs field.

The Higgs force shares the weak force's weakness of not being quite fundamental because the Higgs that we see isn't quite the fundamental Higgs field. But it's not a composite particle either. I'm inclined to say that gravity, SU(3), SU(2), U(1), and the fundamental Higgs force are the five fundamental forces of our current standard model, and electromagnetism, the weak force, and the low-energy Higgs force should be classified as "dwarf fundamental forces".

• Right, I find it laughable when people say the Higgs doesn't qualify when three components of the Higgs field literally make up some of the degrees of freedom of the W and Z. I would also point out that Higgs mediated interactions are one of the primary targets of dark matter direct detection experiments, so if the Higgs doesn't count as a force... what would one say these experiments are looking for? – kaylimekay Jan 18 at 18:00

If gravity is a fundamental force, then the Higgs mechanism is also. This is is true whether they are related or not. The Higgs mechanism is certainly the source of the inertial mass that inspired Newton to quantify what a force is, and how it behaves.

Gravity, like the Higgs mechanism, can add mass/energy to matter in bulk (like constant acceleration), bend or even confine other force carrying bosons (photons) in space. This happens in the event horizon of black holes.

Not only is the Higgs mechanism a fundamental force, but the way it interacts is unquestionably unique among the fundamental forces. It slows down and limits the range of electroweak force carriers (W,Z) by breaking local symmetry, giving them mass without violating conservation of mass/energy.

• The Higgs mechanism is certainly a source of the inertial mass, but the only source it is not. A rare occasion where English helps to get a thought precisely, a correct one or not. – Incnis Mrsi Oct 24 '14 at 18:59