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Why do you want to adding a product to cart with quantity 0? Having a product with quantity 0 in your cart is the same as NOT having that product in the cart. Or, in reverse logic, you'd already have every single product in your cart, but with the quantity 0. lol

But besides that, you probably want to use the hook 

actionBeforeCartUpdateQty

or

actionCartSave

There is more discussion about appropriate hooks here: 

https://stackoverflow.com/questions/43316822/ps-1-6-module-trigger-event-on-ajax-add-to-cart

Why do you want to adding a product to cart with quantity 0? Having a product with quantity 0 in your cart is the same as NOT having that product in the cart. Or, in reverse logic, you'd already have every single product in your cart, but with the quantity 0. lol

But besides that, you probably want to use the hook 

actionBeforeCartUpdateQty

There is more discussion about appropriate hooks here: 

https://stackoverflow.com/questions/43316822/ps-1-6-module-trigger-event-on-ajax-add-to-cart