Abstract
The Standard Model Effective Field Theory (SMEFT) is an established theoretical framework that parametrises the impact a UV theory has on low-energy observables. Such parametrization is achieved by studying the interactions of SM fields encapsulated within higher mass dimensional (≥ 5) operators. Through judicious employment of the tools of EFTs, SMEFT has become a source of new predictions as well as a platform for conducting a coherent comparison of new physics (beyond Standard Model) scenarios. We, for the first time, are proposing a diagrammatic approach to establish selection criteria for the allowed heavy field representations corresponding to each SMEFT operator. We have elucidated the links of a chain connecting specific CP conserving dimension-6 SMEFT operators with unique sets of heavy field representations. The contact interactions representing each effective operator have been unfolded into tree- and (or) one-loop-level diagrams to reveal unique embeddings of heavy fields within them. For each case, the renormalizable vertices of a UV model serve as the building blocks for all possible unfolded diagrams. Based on this, we have laid the groundwork to construct observable-driven new physics models. This in turn also prevents us from making redundant analyses of similar models. While we have taken a predominantly minimalistic approach, we have also highlighted the necessity for non-minimal interactions for certain operators.
Highlights
Standard Model Effective Field Theory (SMEFT) is the bottom-up extension of the Standard Model which consists of 59 operators at dimension-6 considering only a single flavour of fermions1 and brings to light several interesting features not encountered at the renormalizable level
Instead of starting with a different BSM Lagrangian each time and comparing the various subsets of SMEFT each of them leads to, it is more economical if we approach this issue in a retrograde manner, where based on the observables under study we first identify the necessary operators and attempt to enumerate the specific list of heavy fields that can generate the particular operator(s). This allows us to conduct our analysis in a minimal sense and highlights which combinations of heavy fields may lead to redundant contributions. This operator-driven BSM model building is what we have addressed in this work, i.e., our primary aim has been to identify the possible UV roots of each SMEFT operator when considering 1-particle-irreducible (1PI) diagrams up to one-loop-level built of interactions
We realise that the SMEFT operators may receive radiative corrections of the SM as well as heavy fields but accounting for such corrections would require us to delve deeper into the incorporation of a renormalization prescription which is beyond the scope of the current work and such analysis will form a part of our future objectives
Summary
We intend to highlight a generalizable procedure using which, provided a complete and independent set of operators, we can trace the origin of each operator from candidate UV theories containing specific heavy fields. In figure 2, we have collected schematic representations of Lorentz invariant operator classes that constitute a complete and independent set at dimension-6, popularly dubbed as the Warsaw basis in the context of SMEFT [3]. The important step is the “unfolding” of the effective operators, shown, using the renormalizable vertices depicted, through tree- and oneloop-level diagrams. This has been done for each class and the results have been shown in figures 3–10. Within the loops, we have kept open the possibility of having light as well as heavy propagators, but it must be understood that there is at least one heavy field
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