A few comments from a naive member (me). I'm looking to more knowledgeable members to correct any errors and fill in accurately.
say_cheese said:
Now we are presumably creating (?) Higgs Bosons in the collider. But the universe is permeated already by the Higgs field and Higgs bosons.
Actually, the universe is permeated by the Higgs field, but not Higgs bosons, due to their extremely short lifetime. They decay so rapidly, detecting the Higgs boson at the LHC is actually done by the confirmation/detection of particles the Higgs has already decayed into.
When the colliders make an "artificial" Higgs, what conservation laws (in addition to energy, momentum, charge, isospin, baryon number etc.)are obeyed?
It's not artificial - it's the real deal. The enourmous energy levels the LHC provides are required to create the particle. All conservation laws are obeyed as far as I'm aware.
In other words, is there a disturbance in the existing Higgs field in that collider space? Are the particles in the collider affected by this disturbance. Above all, is this a wrong and improper question in some way. If yes, how?
Here's where I was initially confused when I first became interested in the quest for the Higgs: I read the Higgs was all about giving other particles their mass (requiring a proportionate force to accelerate them, for example). BUT, as I searched to learn further, I found that it's more about the Higgs field than the boson. It's the Higgs field that is all around and associated with giving certain particles their mass.
If I understand correctly, all fields are associated with corresponding particles. The particles are excitations of their field. (I think) For example, photons are the carriers of the EM (electromagnetic) field. Now then, the big deal about creating a Higgs boson was because it's the particle the Standard Model predicted to be associated with the Higgs field. Physicists had pretty good ideas of the attributes it would have and the high energy required to create one. Confirming the Higgs particle was a confirmation of the Higgs field.
Hope what I've written is 'mostly' correct

and helps to fill in some of the picture.