I know that when two particles are collided some new particles come into existence and i know that the new particles weren't inside of the original particles. I understand that the energy of the collision can vibrate other fields to make particles.
What I don't understand is "were those other fields nearby the collision site when the collision happen?"
I presume you are talking about Quantum Fields. Particles are basically disturbances in fields. When particles collide, they can release energy. This agitates quantum fields, leading to a particle. (The disturbance in the field is the particle). There is a new disturbance in the field, and so, a new particle is created.
These fields exist and permeate through the entire universe, and you can find these fields even in a pure vacuum. In other words, quantum fields exist everywhere in the universe.
So, yes, there are fields near the collision site, as the collision site and its surroundings are parts of the universe. The fields will exist before, during, and after the collision.
Think of tangled up wires on top of each other. Sometimes when you move one of them the right way it moves the other. Now let us say this movement is a vibration. You vibrate one and it vibrates the other. This is a cartoon picture of the mathematics. A disturbance in some field (particle A) can cause a disturbance in another field (particle B appearing seemingly from nowhere). At least according to the math.
I know that when two particles are collided some new particles come into existence and i know that the new particles weren't inside of the original particles.
Yes, there is extensive experimental evidence for this.
I understand that the energy of the collision can vibrate other fields to make particles.
The standard model of particle physics which describes with great accuracy the collision and predicts the future behavior is a mathematical model based on quantum field theory.
Each elementary particle in the table is assumed to be a field permeating all space, like a coordinate system. This field is mathematically represented at each (x,y,z,t) by the free particle solution of the corresponding equation,(Dirac for fermions for example). On these solutions creation operators ( differential operators) create a particle and annihilation operators destroy it. In this way a propagation, a "track" for an elementary particle can be envisaged, using wave packets with the appropriate energy and momentum and heisenberg uncertainty.
When two particles interact, the theory has specific rules which were developed to fit and predict the data, and are simply described for calculational purposes by the use of Feynman diagrams.
The energy of collision can allow creation operators to work on the underlying fields and create new particles which will propagate away from the collision, as long as energy, momentum, angular momentum and all quantum numbers that have to be conserved are respected.
Not vibrations, but creation and annihilation operators acting on underlying all permeating fields is the mathematical model which succeeds to describe the data.
