2021/02/28 by Stefan Dittmaier, Sebastian Schuhmacher, Maximilian Stahlhofen
Physics and Astronomy · #Boson #Effective field theory #Eigenvalues and eigenvectors #Electroweak interaction #Formalism (music) #Higgs boson #Higgs sector #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Path integral formulation #Quantum Chromodynamics and Particle Interactions #Renormalization #hep-ph #hep-th
paper · pdf · doi:10.1140/epjc/s10052-021-09587-7
published as Eur. Phys. J. C 81, 826 (2021) · 42 pages; v2: journal version
openalex created_date 2021/03/01 · openalex publication_date 2021/09/01 · arxiv created 2021/10/19 · arxiv updated 2021/10/20 · openalex updated_date 2026/08/05
Abstract Building on an older method used to derive non-decoupling effects of a heavy Higgs boson in the Standard Model, we describe a general procedure to integrate out heavy fields in the path integral. The derivation of the corresponding effective Lagrangian including the one-loop contributions of the heavy particle(s) is particularly transparent, flexible, and algorithmic. The background-field formalism allows for a clear separation of tree-level and one-loop effects involving the heavy fields. Using expansion by regions the one-loop effects are further split into contributions from large and small momentum modes. The former are contained in Wilson coefficients of effective operators, the latter are reproduced by one-loop diagrams involving effective tree-level couplings. The method is illustrated by calculating potential non-decoupling effects of a heavy Higgs boson in a singlet Higgs extension of the Standard Model. In particular, we work in a field basis corresponding to mass eigenstates and properly take into account non-vanishing mixing between the two Higgs fields of the model. We also show that a proper choice of renormalization scheme for the non-standard sector of the underlying full theory is crucial for the construction of a consistent effective field theory.