The Indo-European component of the core Persian population is very, very small.
The question now is when were these people conquered by a small group of Indo-Europeans who then imposed their language on the hapless captive population.
Arabs and Persians are considered "Caucasion".
Haitian Creole is a Romance language, but the average Haitian probably doesn't have much Roman DNA.
'Arabs and Persians are considered "Caucasion"'
Well, Arabs are considered Semitic. Their language is not in the Indo-European family.