My Sigma 70-200mm fell on the ground, how serious could it be?

As the title says, my Sigma 70- fell on the ground as it was attached to my Nikon, I bent over and it seems I pushed the button on the camera with my body and the lens detached it fell down from like 50- onto the tiles… The AF doesn't work and so doesn't the ring from MF.

I'm wondering if there's a chance that it's fixable?

Sure it is. Needs to go back to sigma. I'd say you're looking at 400 euros worth of damage.

Sure you can have it repaired but it will cost you some rather large $$$

You not only pressed the lens release button, but you had to twist the camera lenses to remove it.

I seems clear that you still do not know how to use your fine camera and lens if this is an issue

Spend some time with your cameras user manual and practice removing and adding lenses to it as well as how to use the cameras light meter in the manual mode

I've never heard of or seen a lens fall off a camera. You would need to "accidentally" press the button AND twist the lens. To me it sounds more like it wasn't attached properly.

Anyway, it probably is fixable but it will cost a lot. You might as well buy another one (maybe used).
You can check with Sigma first and see how much it would cost.

Are you sure you are attaching the lens to the camera properly? The fact that is just fell off says to me that you neglected to mount it correctly in the first place. Try reading your user manual, ensure it is fitted correctly, THEN try the AF again.

If it doesn't work then I would simply suggest selling it as spares/repair on eBay and buying a new one, perhaps second hand. The cost of repairing it will likely be more than buying a new one.