The purpose of ABS pipe in an irrigation manifold

I'd try to go through the slab and then below it. Most slabs are 6" thick with gravel underneath.

You can rent a concrete core drill for around $60 from home depot. Stick a hole in your slab.

Then you can use something called a 'sidewalk sleever' to tunnel under the slab. Then install pipe (a little tricky due to the elbow, and fill your hole back up with gravel.

The end result will be much prettier and do less damage to your slab.

The black sprinkler pipe is probably HDPE and not PVC so you need a different connection method than with PVC.

Your best bet is to check with a local sprinkler supply company that can give you the right option for local requirements. Around here they use hose barbs and hose clamps but other places may require different connectors when transitioning from HDPE to PVC.