When does a particle go through the Higgs Field?

This is a short and simple question...

I have been reading my book on particle physics and quantum physics when I had thought of a question that it failed to answer: "Does a particle enter/interact with the Higgs Field when created, or at some other time? And if the answer is neither of these two, does it constantly go through/react with the Higgs Field?"

I have been looking for this everywhere (here, Wikipedia and other sites) and haven't found an answer yet. Does anyone know that answer (or possible answers) to this?

Answer

Does a particle enter/interact with the Higgs Field when created, or at some other time?

After reading your question a couple of times as well as your comments, it occurs to me that you're picturing something like this: a massless particle is created, interacts once with the Higgs field to acquire a permanent classical like mass which it then 'keeps'.

But, this isn't a valid picture at all. A much better picture is to make an analogy with how photons become 'massive' within a superconductor.

Essentially, in this picture, space is an electroweak superconductor with the apparent mass of particles due to continuous interaction with the superconducting 'fluid'. From the Wikipedia article "Higgs Mechanism":

The Higgs mechanism is a type of superconductivity which occurs in the vacuum. It occurs when all of space is filled with a sea of particles which are charged, or, in field language, when a charged field has a nonzero vacuum expectation value. Interaction with the quantum fluid filling the space prevents certain forces from propagating over long distances (as it does in a superconducting medium; e.g., in the Ginzburg–Landau theory).

There's much more to this but hopefully this gets you pointed in the right direction.