Horizontal drain pipe through 2x4s

For our DIY kitchen remodel project, we're moving the kitchen sink from one wall to another. The new location has a window just in front of the sink. This is a single-story house in CA with crawl space (although crawl space is not easily accessible).

My question is, without going vertical into the crawl space, can I horizontally (with proper downward angle) install the drain pipe (and connect to previous drainage)? My hesitation comes from the studs -- this is an external wall (load bearing) and studs are 2x4. Not sure if the smallest diameter drain pipe for the sink would allow 5/8" on each side of the hole.

All the books I've read are talking about 2x6 studs to allow for easier drain pipe installation -- none addresses the situation with 2x4s.

Sink will be in the center of 8' wall with the window, meaning, I will be drilling holes in half of the studs (I think 4 or 5 of them) to get this done. I appreciate any suggestions (for example, if the outer diameter is of critical importance, I'm ok to use a different material for the drain, like copper if that's appropriate)

Thanks.

If the holes are only in studs that are under the window, those studs are not load bearing even if that wall is. The load is redirected to the studs on either side of the window, the concept is that a glass window obviously can't carry a load.
Check with the codes in your city but I think with a non-bearing exterior wall the maximum boring is 40%. So in a 3 1/2 wide 2x4 that is about 1 3/8" on other non-bearing walls the max boring is 60% or about 2 1/8". If the studs are doubled then you can bore to 60% even on bearing studs but not through more than two pairs when they are doubled.

holes

I have always bored through the studs as needed and have never had an inspector question it. Obviously, you would want to check with your inspector before doing it.

The answer given by JDKIMES is correct. I am no engineer, but you may be able to add Simson brand heavy duty stud reinforcments which are made specfically for holes in studs. Check with your inspector before drilling.