Hi There,
Recursive descent parsing is actually a technique. It cannot handle left-recursion because it is a top-down parsing technique, and top-down parsers cannot handle left recursion. This is because in left recursion, for a rule conforming to: A -> Aἄ | β, the starting symbol is repeated immediately after the arrow; making the derivation refer to itself infinitely times.
This usually implies a follow up question, how do you get rid of left recursion?
For this, use your alpha/beta rules.