Massive two-loop diagrams: The Higgs propagator Original Research Article

Formulae are provided to express any two-loop scalar integral with arbitrary masses and arbitrary external momenta in terms of an integral of one fairly simple function or of its derivatives. Such integrals can be calculated numerically with high precision. Good agreement is found with known analytical expressions of specific two-loop diagrams. To prove the effectiveness of these techniques, the two-loop self-energy of the Higgs boson to order (g2M2H/m2w)2 is calculated, and the correctness of the result is checked by using the unitarity of the S-matrix. This result allows one to disentangle the leading correction to the location of the Higgs resonance in fermion scattering, and to derive a perturbative bound of ∼1.2 TeV on the mass of the Higgs boson.