Mexican hat potentials

I've been getting my head round the Higgs mechanism. I'm not there yet but here's a summary of some of the stuff that I have heard. There is a Higgs field throughout the Universe. The potential associated with it has the shape of the sombrero hat above. The wooden sphere is a particle. It is just about possible to balance the sphere on the top of the hat. Then there will be perfect symmetry. But it is not stable. If it were stable, we'd have a mass-less Universe. However, it isn't stable and symmetry gets broken. The particle looks for a local minimum. Now there is some form of symmetry in the ability of the sphere to roll around the brim. That could be analogous to the massless photons which are the exchange particles for electromagnetism. I followed the lecture about that far. It was then suggested that if the sphere were to try to go up and down the slope, that would account for the W and Z bosons of the weak interaction having mass. It's beginning to make sense to me but we are not there yet!