Abstract
We extend the known Universal One-Loop Effective Action (UOLEA) by all operators which involve scalars and fermions, not including contributions arising from open covariant derivatives. Our generic analytic expressions for the one-loop Wilson coefficients of effective operators up to dimension six allow for an application of the UOLEA to a broader class of UV-complete models. We apply our generic results to various effective theories of supersymmetric models, where different supersymmetric particles are integrated out at a high mass scale.
Highlights
Of new particles are significantly above the electroweak scale
We extend the known Universal One-Loop Effective Action (UOLEA) by all operators which involve scalars and fermions, not including contributions arising from open covariant derivatives
Due to their generic structure, the expressions are well suited to be implemented into generic spectrum generators such as SARAH [19,20,21,22] or FlexibleSUSY [23, 24] or Effective Field Theories (EFTs) codes in the spirit of CoDEx [25, 26]
Summary
We briefly review the most important steps in the functional matching approach at one-loop level in a scalar theory and fix the notation for the subsequent sections. Using similar arguments for the Lagrangian of the EFT, LEFT[φ], which only depends on the light fields, the generator of 1PI Green’s functions in the EFT can be calculated at one-loop as. The functional determinants can be calculated using the relation log det A = Tr log A and calculating the trace This includes a trace in the Hilbert space as constructed in [27]. To derive the currently known form of the purely scalar UOLEA [8, 9] from (2.13), one expands the logarithm in a power series, which is evaluated up to terms giving rise to operators of mass dimension 6 and calculates the corresponding coefficients arising from the momentum integral. In order to keep gauge-invariance manifest in the resulting L1EFT a covariant derivative expansion [11, 12] is used, where P μ is kept as a whole and not split into a partial derivative and gauge fields
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