# Do massive particles exchange Higgs bosons?

Do massive particles exchange virtual Higgs bosons between themselves?

If they do does the resulting Higgs force decay exponentially with distance?

• – John Rennie Aug 27 '14 at 11:12

Yes, massive particles such as W-bosons, Z-bosons, quarks, and leptons couple to the Higgs field via the cubic (Yukawa) interaction, so they may also exchange the virtual Higgs. Yes, because the virtual particle is massive, one gets the Yukawa potential that includes the exponential dumping with distance.

This "Higgs force" is much less fundamental and important than the four fundamental interactions (strong and weak nuclear forces, electromagnetism, gravity) because

1. it's not made inevitable by any local/gauge/diffeomorphism symmetry
2. the Yukawa coupling is tiny so the force is extremely weak even before it drops exponentially with distance for stable particles such as electrons
3. the Yukawa coupling and the force is only strong for heavy enough particles such as the top quarks but those particles are unstable so before one may measure this weak, highly localized force, the particle decays.

The third point is related to the fact that unlike electrostatic, magnetostatic, and gravitational static forces, the Higgs exchange doesn't become "more important" when some objects are at rest. Instead, the Feynman diagrams with the Higgs exchange are examples among many and they're usually important primarily for very quickly moving particles. When the speeds are close to the speed of light, one has to use the full quantum field theory and the concept of "force", relevant only in mechanics, becomes inadequate.

• You say that the Higgs force is less fundamental than four other interactions. How do you define the "degree of fundamentality" here? I think that the Higgs interaction is part of the SM Lagrangian on an equal footing with four other interactions. If it is less fundamental, then maybe it can be the outward manifestation of some more fundamental yet unknown part of model? What can it be or look like? If it would not, then the level of fundamentality should be the same? Or my interpretation of your words is wrong? – firtree Aug 27 '14 at 12:23

In my analysis, the complex Higgs doublet $(\phi^0, \phi^+)$ can be transformed by $SU(2)$ only to $(0, \phi^0+i\phi^+)$, which is not real. By coupling to gravity in the first order formalism $(e,w)$, a local conformal symmetry exists while gravity remains non-dynamic.

Therefore, the electroweak gauge can be spontaneously broken by fixing a conformal scale, and the complex Higgs doublet reduces to $(0, \mu+iH)$. The Yukawa couplings to fermions are now absent, and there is no Higgs exchange. The only remaining Higgs interaction other than to gravity is to the vector bosons as $(\mu^2+H^2)$, which contributes to their mass renormalisation.

Such a theory avoids the complications of adding an imaginary mass term to the Higgs Lagrangian, and the real Higgs mass emerges naturally from the $|\mu+iH|^4$ term. Higgs resonances can still be realized at high energies for the vector boson tadpole diagrams, but there is no Higgs force.

• So how do fermions get their mass? Is there a paper or website where the equations of this alternative theory of the Higgs are set out? – Mitchell Porter Aug 29 '18 at 3:00