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.

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Different types of orthoses are available to clinicians for non-surgical treatment of acute ankle sprains. The goal of this study was to scientifically compare the movement restrictions in the sagittal and frontal plane during simulated walking between one adaptable semi-rigid brace (OrthoTri-Phase TM), four non-adaptable semi-rigid braces (OrthoStandard TM , MalleoLoc TM , MalleoSprint TM , VACOankle TM), and one rigid cast. Predefined time sequences of rotational moments and axial loading during gait were applied via an ankle joint simulator, with the pneumatic pressure inside the orthoses kept constant to ensure the same condition for different trials and orthoses. The peak ranges of motion (RoMs) in the frontal and sagittal plane during gait were analyzed for statistically significant differences using single-factorial ANOVA with post-hoc Bonferroni analysis. Significant differences in peak plantar-/dorsiflexion and in-/eversion RoM during gait were found between different types of orthoses. In the sagittal plane, the rigid cast most significantly restricted overall RoM followed by the Ortho Tri-Phase TM in Phase 1 and the Ortho Standard TM. The peak restriction in-/eversion RoM of the VACOankle TM came closest to the rigid cast, with a shift towards inversion. The VACOankle TM allowed for significantly larger dorsiflexion movement compared to all other orthoses. The present results may help clinicians in the decision-making process of finding the optimal orthosis for individual patients.

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