Does yukawa potential of two particles have effect on each other?

Question

Okay,a novice here.Suppose two particle interact with Higgs field.Does The Yukawa potential created by each of them affect each other or the interaction in any way.If so,what is it physical significance?

Answer 1

In fact, your question is not so clear. I try my best. The Yukawa potential is an exchange potential, so it is based on the particle which is exchanged between 2 interacting particles. So if that particle (a boson) is coupled to the Higgs boson, it will get mass and the potential between the 2 interacting particles should change from U(r)~1/r to U(r)~ exp(-mr)/r where m is the mass of the exchange particle.

However, one should be aware of that the photon does not couple to the Higgs field, its attributed potential does not change. Gluons don't couple neither to the Higgs. Pions get mostly their mass from chiral symmetry breaking, whereas the electroweak exchange bosons W and Z get indeed their mass from the Higgs boson so the potential attributed to them should change. But as their mass is so large, it mainly changes to a point interaction at least at low energy.

However, the 2 particles which exchange the boson, for instance two electrons which get mass from the Higgs boson, their interaction does not change at all (if only photon exchange is considered). The exchange particle between the electrons, the photon is not coupled to the Higgs. In particular the electromagnetic coupling constant of 2 electrons does not depend on their mass. The coupling constant is the same for zero mass electrons as well as for massive electrons. Therefore the interaction does not change. However, if the interaction of the electrons is realised by the Z-boson the Higgs field (if it exists or not) has an effect on the Yukawa potential of the Z via the mass attribution of the Z-boson whereas the coupling constant does not change.

May be you are thinking of the Higgs boson as an exchange particle. That's indeed a Yukawa-potential, it has a strong coupling constant if we take top quarks as interacting particles. We could instead imagine neutrinos which are almost massless, the coupling constant would be very weak, but the mass parameter of the Yukawa potential is actually the mass of the Higgs boson and not the mass of the interacting particles. So the mass parameter of this Yukawa potential does not change with the mass of the interacting particles (top's or electrons or neutrinos).

Finally I remind that most (if not all) interactions are determined by the product of the coupling constant $g^2$ (as 2 particles interacting) and the (Yukawa or not) potential $g^2U(r)$.

Answer 2

I'm not sure what you're asking, but it's not really true to say that particles interact with the Higgs field. A quantum field like the electron field interacts with the Higgs field and the result is that the electron field is massive i.e. its excitations (electrons) have a mass.

If you consider the Higgs boson, rather than the Higgs field, then the interaction of particles with the Higgs boson does indeed create a force called the Higgs force. This is discussed in the question Why isn't Higgs coupling considered a fifth fundamental force?.