> Do we have studies for this

For many values of 'this' in the medical domain, yes.

> Don't fotget about "accidents" that spread Polio by vaccination

Err, the Cutter incident spread Polio via live polio virus rather than by Polio vaccination.

Absolutely an example of a serious and deadly Quality Control f*ckup that led to a complete change in how vaccine production was approached.

Please, link those studies.

> Do we have studies for this that compare two controlled groups in same environment?

are you questioning the link between vaccines and polio almost entirely disappearing from all but about 4 countries on the planet?

what alternative "theory" do you have in this case?

Increasing wealth and overall hygiene.

99% polio cases are nowadays in developing countries.

What mechanism would you suggest connects wealth with polio?

I'm not sure if I understand a question. You mean how could wealth help with disapearing of polio?

Still nothing?