https://doi.org/10.1140/epjc/s10052-021-09587-7
Regular Article - Theoretical Physics
Integrating out heavy fields in the path integral using the background-field method: general formalism
Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104, Freiburg, Germany
c
maximilian.stahlhofen@physik.uni-freiburg.de
Received:
13
April
2021
Accepted:
30
August
2021
Published online:
17
September
2021
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.
© The Author(s) 2021
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