Two-loop renormalization in the Standard Model. Part I: Prolegomena

Abstract

In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and twoloop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles.

NNLO computational techniques: The cases and

“…The tadpole-renormalization prescription used in this paper will be the β t scheme, thoroughly discussed in section 2.3 of Ref. [42]. Following notation and conventions of Ref.…”

“…[42,43,44]. After assembling diagrams we perform the usual canonical tests to ensure that our result is correct, checking all possible unrenormalized Ward-Slavnov-Taylor (WST) identities.…”

Low energy behaviour of standard model extensions

“…For a complete analysis of tadpole terms we refere to ref. [24], in particular section (2.2) and eq. (6).…”

“…[24]). Further, we keep M as the W bare mass and add a new mass, M s , which will play the role of cut-off scale Λ. Also,…”

“…As an example we derive the h 2 Z 2 (mixed-loop) vertex 24) where the scalar three-point function is given in eq. (A.5).…”