There must be a refutation... (Paulsen Sicilian, without ...Nf6)

Here is an opening I played (as White) in a recent game.

Black's 5th move looks laughable, but after thinking for a while, I played the even more laughable 6.Qd3 (I won, but after such a blunderfest from both sides that I would be ashamed to post it), seeing neither how not to lose a pawn otherwise, nor what compensation I could get for it.

Suggestions... ?

I can hardly believe this is a refutation of my 5.c4, is that ?

This trick often wins a pawn on e4 in a variety of openings (Scotch Game, English Defense, etc.), but perhaps here White has compensation after Nxc6 Qxe4+ Be2 Qxc6 O-O?   I dunno, looks sort of sketchy. :)

Or, er, what pfren suggests.

I'm guessing your threw out some lines where you got doubled pawns or maybe even lost a pawn.  Look a little more, with a move like Qh4 you may zoom ahead in development for such a small price.  It would help you posted a sample line that was troubling you.

Although pfren already gave an answer.

Being a former Taimanov player, Black can get a slight advantage with the line White played.  5.c4 is a mistake.  Black can take advantage of it with 5...Bb4+.

If White wants to play a Maroczy Bind against the Taimanov, which is perfectly fine, but he gets no advantage, then he should play 5.Nb5 first, virtually forcing 5...d6, and only then, play 6.c4, when 6...Bb4+ is impossible because the d-pawn now blocks in the Dark-Squared Bishop.  Black will often end up playing a Hedgehog structure here.

Neither of them understood chess 

Huh ?

After 6.Bd2 I cannot see any problem for White. Exchanging the bishops or even worse 6...Nxd4 7.Bxb4 gives Black nothing apart weak squares.

Post edited to see the loss / sacrifice of a pawn in all the lines, none of them looked very promising to me.

Thanks for the suggestions, pfren and Gargleblaster. I begin to see why Black plays ...a6 in some lines, even if b5 will never be pushed with a pawn on c4.