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We present a detailed study of the total $p p$ cross section for scalar Higgsproduction to next-to-next-to leading order in $\alpha_s$ at LHC energies, andof the $p\bar p$ cross section at the Tevatron, combining an implementation ofthe solutions of the parton evolution equations at the 3-loop order with thecorresponding hard scatterings, evaluated at the same perturbative order. Oursolutions of the DGLAP equations are implemented directly in $x$-space andallow the study of the dependence of the results on the factorization ($\mu_F$)and renormalization scales $(\mu_R)$ typical of a given process, together withthe stability of the perturbative expansion. The input sets for the partonevolutions are those given by Martin, Roberts, Stirling and Thorne and byAlekhin. Results for K-factors are also presented. The NNLO corrections can bequite sizeable at typical collider energies. The stability region of theperturbative expansion is found when $\mu_R > m_H\sim\mu_F$.Comment: 35 pages, 55 figure

On the scale variation of the total cross section for Higgs production at the LHC and at the Tevatron