Eur. Phys. J. C (2006) 47: 703-721
https://doi.org/10.1140/epjc/s2006-02608-5

Theoretical Physics

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

¹ Dipartimento di Fisica, Università di Lecce and INFN sezione di Lecce, Via per Arnesano, 73100, Lecce, Italy
² Department of Physics, University of Crete, 71003, Heraklion, Greece
³ C.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York, 11794-3840, USA
⁴ NIKHEF, Postbus 41882, 1009 DB, Amsterdam, The Netherlands

^* e-mail: marco.guzzi@le.infn.it

Received: 17 October 2005
Revised: 18 May 2006
Published online: 21 July 2006

Abstract

We present a detailed study of the total pp cross section for scalar Higgs production to next-to-next-to-leading order in α_s at LHC energies, and of the pp̄ cross section at the Tevatron, combining an implementation of the solutions of the parton evolution equations at the three-loop order with the corresponding hard scatterings, evaluated at the same perturbative order. Our solutions of the DGLAP equations are implemented directly in x-space and allow for the study of the dependence of the results on the factorization (μ_F) and renormalization scales (μ_R) typical of a given process, together with the stability of the perturbative expansion. The input sets for the parton evolutions are those given by Martin, Roberts, Stirling and Thorne and by Alekhin. Results for K-factors are also presented. The NNLO corrections can be quite sizeable at typical collider energies. The stability region of the perturbative expansion is found when μ_R>m_H∼μ_F.