The NNLO gluon fusion Higgs production cross-section with many heavy quarks

We consider extensions of the Standard Model with a number of additional heavy quarks which couple to the Higgs boson via top-like Yukawa interactions. We construct an effective theory valid for a Higgs boson mass which is lighter than twice the lightest heavy quark mass and compute the corresponding Wilson coefficient through NNLO. We present numerical results for the gluon fusion cross-section at the Tevatron for an extension of the Standard Model with a fourth generation of heavy quarks. The gluon fusion cross-section at NLO and in the approximation of infinitely heavy quarks is enhanced by a factor of 9 with respect to the Standard Model value. Tevatron experimental data can place stringent exclusion limits for the Higgs mass in this model. We find that the relative magnitude of the higher order QCD corrections with respect to the LO is similar to the Standard Model. Our result serves to carry out an exclusion analysis for a four-generation Standard Model with the same accuracy as in the Standard Model analysis.