As I understand your question, it is ill-posed, or at least inconsistent with normal semantics. What we refer to as particles are excitations on some background. The background corresponds to a minimum of the effective potential. The masses of the particles are given by the second derivative of the effective potential.
If you are not at a minimum of the potential, I'm not sure what you even mean by a particle. I can poke my system somewhere and produce some stuff, but how do I know what part of that stuff to call a particle and what part to say is just evolution of the system (which is constantly rolling towards the minimum.)
If you have slow-rolling field (which I suspect is the case you are interested in) then maybe you can do some sort of adiabatic approximation. But that is a somewhat more specific question.
This post imported from StackExchange Physics at 2014-05-04 11:38 (UCT), posted by SE-user BebopButUnsteady