- First of all, I'm happy that you use mu=3 GeV for the renormaization scale of the charm quark mass. mu=mc is too small, as you also write in the document. - In 4.2 you mention that you use "three-loop MS-on-shell conversion" as "highest available perturbative order" but later you refer to [1] where 4-loop corrections have been computed. - In 4.4 you propose to compute mb^pole from mb(mb)=4.18 GeV using the 4-loop OS-MSbar conversion from [1]. Note that for the bottom quark there is no convergence: the 4-loop term is not much smaller than the 3-loop and 2-loop coefficients. I assume that the dependence of \sigma(pp->Hbbar) on mb^pole is weak and \pm 100 MeV in mb^pole are not relevant. Then the procedure is OK. - Do you also need the top quark MSbar mass? In that case the the 4-loop conversion formula behaves well.