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 is enhanced by a factor of roughly 9 with respect to the Standard Model value. Tevatron experimental data can place stringent exclusion limits for the Higgs mass in this model.