Idea behind sacrifice pawn I would like to know what compensation White gets after the pawn sacrifice 6. b4.



To me, giving back the pawn just for a tempo, i.e. Bb5, does not seem to be enough.
I simply do not agree with your computer there. It is probably a bit of the "horizon effect", which is when a computer plays a bad move because it puts the refutation beyond its ability to calculate, or "horizon".

White played this opening every passively, and really should be looking to break up black's center so he is not smothered, and b4 does not seem the way to do that. It is very short-sighted by white to try and keep c5, especially when it puts him behind in development. Per my computer, (quad-core 2.9Ghz with 24 GB of RAM), there are a bunch of moves there, and b4 is fourth on the list per Stockfish 10 on my computer. The other candidate moves are c4! (the best in my opinion), h3, and even Nb3 since e4 h3 is good for white.

6.b4?! Nxb4 5.Bb5? {h3, c4, or Rb1 are all still better per my beast) Nc6 6.h3 Bf3 7.Qf3 Bc5 8.c4 Nf6 and while white has some compensation for the pawn, it is not enough. Black is slightly better as white may win the pawn back soon, but black remains slightly better placed.

      [FEN ""]

     1. d4 d5 2. Nf3 c5 3. dxc5 Nc6 4. e3 Bg4 5. Nbd2 e5 6. b4?! (6. c4!) (6. h3) (6. Nb3 e4? 7. h3 Bxf3 8. gxf3 {and white is just a pawn up.}) Nxb4 7. Bb5+?! (7. c4!) (7. h3) (7. Rab1 {are all better}) Nc6 8. h3 Bxf3 9. Qxf3 Bxc5 10. c4 Nf6 11. cxd5 Qxd5 12. Qxd5 Nxd5 {Black's pieces are all very nicely placed here, and the Nd2 is passive.} 13. Bb2 O-O-O 14. Rc1? Bb4 {is the tactical justification.}