Universal One-loop Effective Action Research Articles

One-loop effective action up to dimension eight: Integrating out heavy fermion(s)

We present the universal one-loop effective action up to dimension eight after integrating out heavy fermion(s) using the Heat-Kernel method. We have discussed how the Dirac operator being a weak elliptic operator, the fermionic operator still can be written in the form of a strong elliptic one such that the Heat-Kernel coefficients can be used to compute the fermionic effective action. This action captures the footprint of both the CP conserving as well as violating UV interactions. As it does not rely on the specific forms of either UV or low energy theories, can be applicable for a very generic action. Our result encapsulates the effects of heavy fermion loop through Yukawa couplings only.

The universal one-loop effective action with gravity

We complete the so-called Universal One-Loop Effective Action (UOLEA) with effects of gravity and provide a systematic approach to incorporate higher dimensional operators in curved spacetime. The functional determinant stemming from the path integral is computed using the Covariant Derivative Expansion (CDE), in a momentum representation that does not rely on a specific choice of coordinate to be defined, as it often is. This efficient approach manifests an interesting novelty as it allows to integrate out chiral fermions in curved spacetime in a direct manner leading to new operators involving the curvature, and provides a new alternative to the use of Feynman diagrams in that regard. The method presented would very well fit in a code that performs CDE, offering the possibility to integrate out at one-loop fields on a curved spacetime background, including spin-2 fields, like the graviton. Eventually these results should provide an interesting way to study low energy effects of UV completions of gravity.

Universal scalar leptoquark action for matching

In this study we present a universal effective action for one-loop matching of all scalar leptoquarks. We use both the Universal One-Loop Effective Action (UOLEA) and covariant diagrams to evaluate the Wilson coefficients directly in the Green basis for up to dimension-6 operators. On the technical side, we use the newly developed method of evaluating supertraces, to further validate the results stemming from the use of covariant diagrams. As an application, we perform a fully functional matching onto Standard Model Effective Field Theory (SMEFT) of a model with two scalar leptoquark fields: a weak isospin singlet and a doublet. We demonstrate its use by calculating several observables, such as lepton magnetic and electric dipole moments, neutrino masses, proton decay rate, while we comment upon fine tuning issues in this model. Apart from its phenomenological interest, this model generates the majority of dimension-6 operators and provides an EFT benchmark towards future matching automation.

Integrating out new fermions at one loop

We present the fermionic universal one-loop effective action obtained by integrating out heavy vector-like fermions at one loop using functional techniques. Even though previous approaches are able to handle integrating out heavy fermions with non-chiral interactions, i.e. vanishing γ5 interaction terms, the computations proceed in a tedious manner that obscures a physical interpretation. We show how directly tackling the fermionic functional determinant not only allows for a much simpler and transparent computation, but is also able to account for chiral interaction terms in a simple, algorithmic way. Finally, we apply the obtained results to integrate out at one loop the vector-like fermions appearing in a toy model and in a fermionic model that exhibits strong cosmological phase transitions.

The fermionic universal one-loop effective action

Recent development of path integral matching techniques based on the covariant derivative expansion has made manifest a universal structure of one-loop effective Lagrangians. The universal terms can be computed once and for all to serve as a reference for one-loop matching calculations and to ease their automation. Here we present the fermionic universal one-loop effective action (UOLEA), resulting from integrating out heavy fermions (Dirac or Majorana) with scalar, pseudo-scalar, vector and axial-vector couplings. We also clarify the relation of the new terms computed here to terms previously computed in the literature and those that remain to complete the UOLEA. Our results can be readily used to efficiently obtain analytical expressions for effective operators arising from heavy fermion loops [13].

Singlet night in Feynman-ville: one-loop matching of a real scalar

A complete one-loop matching calculation for real singlet scalar extensions of the Standard Model to the Standard Model effective field theory (SMEFT) of dimension- six operators is presented. We compare our analytic results obtained by using Feynman diagrams to the expressions derived in the literature by a combination of the universal one-loop effective action (UOLEA) approach and Feynman calculus. After identifying contributions that have been overlooked in the existing calculations, we find that the pure diagrammatic approach and the mixed method lead to identical results. We highlight some of the subtleties involved in computing one-loop matching corrections in SMEFT.

Completing the scalar and fermionic universal one-loop effective action

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.

Extending the universal one-loop effective action by regularization scheme translating operators

We extend the universal one-loop effective action (UOLEA) by operators which translate between dimensional reduction (DRED) and dimensional regularization (DREG). These regularization scheme translating operators allow for an application of the UOLEA to supersymmetric high-scale models matched to non-supersymmetric effective theories. The operators are presented in a generic, model independent form, suitable for implementation into generic spectrum generators.

Extending the Universal One-Loop Effective Action: heavy-light coefficients

The Universal One-Loop Effective Action (UOLEA) is a general expression for the effective action obtained by evaluating in a model-independent way the one-loop expansion of a functional path integral. It can be used to match UV theories to their low-energy EFTs more efficiently by avoiding redundant steps in the application of functional methods, simplifying the process of obtaining Wilson coefficients of operators up to dimension six. In addition to loops involving only heavy fields, matching may require the inclusion of loops containing both heavy and light particles. Here we use the recently-developed covariant diagram technique to extend the UOLEA to include heavy-light terms which retain the same universal structure as the previously-derived heavy-only terms. As an example of its application, we integrate out a heavy singlet scalar with a linear coupling to a light doublet Higgs. The extension presented here is a first step towards completing the UOLEA to incorporate all possible structures encountered in a covariant derivative expansion of the one-loop path integral.

Mixed heavy–light matching in the Universal One-Loop Effective Action

Recently, a general result for evaluating the path integral at one loop was obtained in the form of the Universal One-Loop Effective Action. It may be used to derive effective field theory operators of dimensions up to six, by evaluating the traces of matrices in this expression, with the mass-dependence encapsulated in the universal coefficients. Here we show that it can account for loops of mixed heavy-light particles in the matching procedure. Our prescription for computing these mixed contributions to the Wilson coefficients is conceptually simple. Moreover it has the advantage of maintaining the universal structure of the effective action, which we illustrate using the example of integrating out a heavy electroweak triplet scalar coupling to a light Higgs doublet. Finally we also identify new structures that were previously neglected in the universal results.

The universal one-loop effective action

We present the universal one-loop effective action for all operators of dimension up to six obtained by integrating out massive, non-degenerate multiplets. Our general expression may be applied to loops of heavy fermions or bosons, and has been checked against partial results available in the literature. The broad applicability of this approach simplifies one-loop matching from an ultraviolet model to a lower-energy effective field theory (EFT), a procedure which is now reduced to the evaluation of a combination of matrices in our universal expression, without any loop integrals to evaluate. We illustrate the relationship of our results to the Standard Model (SM) EFT, using as an example the supersymmetric stop and sbottom squark Lagrangian and extracting from our universal expression the Wilson coefficients of dimension-six operators composed of SM fields.