Dimension-8 Operators in the Standard Model Effective Field Theory (2005.00059v6)

Abstract: We present a complete basis of dimension-8 operators in the Standard Model Effective Field Theory. Attention is paid to operators that vanish in the absence of flavor structure. There are dimension-8 SMEFT 44,807 operators. We also briefly discuss a few aspects of phenomenology involving dimension-8 operators, including light-by-light scattering and electroweak precision data.

Dimension-8 Operators in the Standard Model Effective Field Theory by Christopher W. Murphy

This manuscript undertakes the construction of a comprehensive basis for dimension-8 operators within the framework of the Standard Model Effective Field Theory (SMEFT). Considering the standard model (SM) as an effective field theory (EFT) valid below a certain cutoff scale, this research extends the SMEFT by incorporating dimension-8 operators, thus providing a more intricate description of potential phenomena beyond the perturbative SM.

Overview and Context

The SMEFT expands the SM Lagrangian by adding gauge invariant operators of all mass dimensions. It systematically counts and describes the interactions at mass dimension greater than four, assuming no additional light particles exist beyond the SM, apart from the Higgs as an $SU(2)_w$ doublet. Historically, the SMEFT operator bases have been well studied up to dimension-7, but the dimension-8 terms provide a pivotal leap in understanding interactions that manifest beyond leading-order corrections.

The paper meticulously enumerates and classifies 44,807 dimension-8 operators when flavor structures are considered. With $n_g = 3$ generations of fermions, the paper highlights scenarios where dimension-8 effects become particularly relevant, for instance, in processes like light-by-light scattering and electroweak precision data, which exhibit contributions that first arise at this dimension.

Structure and Classification

The classification process for these operators leans heavily on both previous literature and novel computational methods. The work extensively utilizes computational tools developed for operator counting and classification, such as $\mathtt{BasisGen}$ and $\mathtt{Sym2Int}$, facilitating a systematic generation of operators. Nonetheless, explicit forms and selections of the bases required meticulous diligence to ensure no redundancies exist, utilizing integration by parts and equations of motion to that end.

The dimension-8 operator basis is sensitive to the inclusion of scenarios like suppressed or vanishing interferences between the SM and dimension-6 contributions. This subtlety has been addressed through methodical hierarchical bases construction, extending beyond prior stochastic assessments available within literature.

Phenomenological Implications

Dimension-8 operators impact various phenomenological areas. Their effects can be more pronounced compared to dimension-6 operators when specific interference or precision scenarios suppress leading terms. The paper evaluates their role in light-by-light scattering, an interaction where no lower-dimension operators contribute directly within the SMEFT context. Likewise, contributions to the electroweak precision observables, specifically regarding the parameter U, reinforce their necessity, as leading corrections appear at this dimension for observables binding quantum loop effects.

Furthermore, exampling scalar $SU(2)_w$ quartets, the paper demonstrates model-specific scenarios where dimension-8 terms meaningfully enhance our physical descriptions, possibly reshaping expected signal sizes in experiments like the LHC when related to processes with currently constrained sensitivities (e.g., double Higgs production).

Renormalization Group Aspects

Together with operator classification, the paper explores implications for renormalization group evolution (RGE) within SMEFT at the dimension-8 level. Here, the research underscores that certain RGE contributions would be co-leading, given equivalent dimension insertions belong to differing operator dimensions. This presents interesting opportunities for precise SMEFT analysis, relying on subtleties of algebraic no-go theorems that limit mixing within SMEFT's anomalous dimension matrix.

Conclusion

This paper significantly advances the SMEFT by delivering a robust framework for dimension-8 operators, preparing grounds for subtle physical explorations beyond traditional phenomenological horizons. Its painstaking detailed approach to counting, classification, phenomenology, and implications on RGE signifies an essential resource for theorists exploring the domain of high-energy physics, steering experimental outlooks towards new horizons for testing models extending the SM.