Coulomb cross section and PDFs

Hi everyone, there is a computation I've done in MG5 I find rather puzzling. First, the non-puzzling one. If I compute the cross section for, say, ta- b > b ta- /z h QED=2, in sm-full, for a "free" b quark, and in the entire phase space (no cuts), I obtain a non-sensical result: ME gives an absurdly large cross section and it apparently refuses to compute all of the events. This is as it should be, since the cross section for Coulomb scattering does not exist. The same thing happens if I set the PDF for the b quark to 1 (proton) and choose, say, CTEQ6m.

On the other hand, if I replace the b quark for a c quark, without the PDF the cross section blows up, but when I set the PDF to 1, the result seems convergent: ME evaluates all of the events and gives a result of order 10^4 which is apparently meaningful. Is this apparently convergent result just a numerical artifact?

But the problem is this: if I put a cut off on the scattering angle or the momentum transfer, as I make the cut off smaller the cross section should grow without bounds. This is so in the case of the b quark. But for the c quark the total cross section, being finite, puts an upper bound on the growth of the cut-off cross section. As far as I understand, this is incorrect.

It seems I'm not understanding this properly... Any hing would be greatly appreciated.