Penetration is a function of velocity, stiffness/hardness & sharpness of the projectile, and sectional density, which the latter is in turn a function of length, width and mass.
So in theory a narrower arrow has a higher sectional density given the same mass, than a thicker one. But this is virtually irrelevant because the shaft is BEHIND the broadhead which makes entrance first. So the width of the broadhead is the key component in determining sectional density, along with the weight of the total arrow/broadhead projectile. That means you want a smallish cutting area (either 3/4ths" or 7/8ths" - or at most 1.0"), such as with a Muzzy or one of many others that are not massively wide (such as those giving a 1.25", 1.5", 2.0", or larger cutting area. Also, a two-blade broadhead (such as an Easton) will penetrate better than an 3-blade or 4-blade. The 3-blade Muzzy would be preferable to the 4-blade in your situation. Also, obviously, the sharper the better - they need to be razor sharp. And since heavier is better for sectional density, a 125 grain or heavier broadhead is what you want.
So, although a thinner arrow won't HELP you very much (since it's path is being paved by the broadhead in front of it), it certainly won't hurt you and if anything, it can help you a little bit, provided it is heavy-ish (thick-walled), in providing penetration.
So, thin=good. But light=bad. You want a thin (9/32nds or 5/16ths), but heavy-ish arrow such as the Easton Axis ST - something up around 9.5 to 10 gpi (grains per inch), with a lighter draw weight such as your (45 lbs) in my opinion.
But yes, in general, carbon arrows rock - they are superior to aluminum and wood in several ways. I shoot carbons even with a traditional bow.
Oh another thing - important - on your field points - you need to definitely ditch the ones that are wider than your arrows, and replace them. You want field points that are the same or *narrower* than your arrow shaft; otherwise, it is hell pulling them out of your field point target.
Another thing, on flex, with that light of a draw weight, you want a shaft this is pretty flex-y, depending on the arrow length. You'll need to consult the charts, but I believe you'll want a *minimum* flex of 400 (and possibly 500) for that draw weight with a 28-30" shaft, and you will almost certainly need a 500 high flex if your arrow is only 25-27".