A suggested at <Physics from Symmetry by Jakob Schwichtenberg (2015)> chapter 3.9 "Elementary particles", it appears that in the <Standard Model>, the behaviour of each particle can be uniquely defined by the following five numbers:
* due to <spacetime symmetries>:
  * <mass>
  * <spin (physics)>
* due to <internal symmetries>:
  * <electric charge>
  * <Weak charge>
  * <color charge>

E.g. for the <electron> we have:
* mass: $9.1 \times 10^{-31}$
* spin: 1/2
* electric charge: $1.6 \times 10^{-29}$
* weak charge: -1/2
* color charge: 0

Once you specify these properties, you could in theory just pluck them into the <Standard Model Lagrangian> and you could simulate what happens. 

Setting new random values for those properties would also allow us to create new particles. It appears unknown why we only see the particles that we do, and <parameters of the Standard Model>[why they have the values of properties they have].


 Defining properties of elementary particles