It is well-known that in Sacks model there are P-points and even Ramsey ultrafilters, but what the usual (i.e. findable in the literature) proofs for these facts do is proving that ground model P-points (or Ramsey ultrafilters) are preserved by Sacks forcing (i.e. still generate an ultrafilter in the extension). Thus, the only examples of P-points or Ramsey ultrafilters that I know of in Sacks model are those that already existed in the ground model, hence they all have weight $\aleph_1$ (i.e. they are generated by $\aleph_1$ many elements, since the ground model satisfies CH). So my question is:

**Is it known whether there are P-points and/or Ramsey ultrafilters of weight $\aleph_2$ in Sacks model?** (actually my real question is: if yes, how are they constructed?, I guess)