Effective description of general extensions of the Standard Model: the complete tree-level dictionary (1711.10391v2)

Abstract: We compute all the tree-level contributions to the Wilson coefficients of the dimension-six Standard-Model effective theory in ultraviolet completions with general scalar, spinor and vector field content and arbitrary interactions. No assumption about the renormalizability of the high-energy theory is made. This provides a complete ultraviolet/infrared dictionary at the classical level, which can be used to study the low-energy implications of any model of interest, and also to look for explicit completions consistent with low-energy data.

• The paper presents a comprehensive tree-level UV/IR mapping that translates general BSM extensions into SMEFT dimension-six operators using Wilson coefficients.
• It systematically categorizes contributions from spin-0, spin-1/2, and spin-1 fields, distinguishing between tree-level and loop-level effects.
• The framework offers practical tools for model builders to interpret collider data and explore new physics scenarios beyond the Standard Model.

Overview of the Paper on Extensions of the Standard Model

The paper "Effective Description of General Extensions of the Standard Model: The Complete Tree-Level Dictionary" presents a comprehensive analysis of the low-energy implications of various extensions to the Standard Model (SM). By examining a general set of new hypothetical scalars, fermions, and vector bosons, the authors develop a tree-level ultraviolet (UV)/infrared (IR) dictionary for the Standard Model Effective Field Theory (SMEFT) up to dimension-six operators. This work is valuable for theorists working on beyond the Standard Model (BSM) scenarios who utilize effective field theories to interpret collider data where direct observations of new particles are beyond reach.

The paper acknowledges the extensive searches conducted at the Large Hadron Collider (LHC) in uncovering physics beyond the Standard Model, given the discovery of the Higgs boson and the subsequent shift in focus towards new physics. Despite impressive efforts, no significant departures from the SM have been directly observed, necessitating effective field theories (EFTs) for interpreting experimental data through a model-independent paradigm.

Key Contributions and Numerical Results

1. Dimensional Basis and Operator Matching: The paper constructs a systematic tree-level mapping from the UV complete theories to the SMEFT. The authors derive expressions for the Wilson coefficients—a pivotal tool in the matching procedure—at the leading order, assuming non-renormalization of the fundamental high-energy theory. This approach allows for a detailed classification of potential BSM particles and their interactions, constrained by current experimental data.
2. Comprehensive Field Consideration: Incorporating a variety of spin-0, spin-1/2, and spin-1 field extensions, the work outlines the possible tree-level contributions to the dimension-six SMEFT operators. These encompass various BSM scenarios, covering a wide spectrum of additional particle multiplets and their associated couplings. The constructed dictionary can compute IR Wilson coefficients for any BSM model's parameters.
3. Tree-Level Cleavage and Loop Identification: The analysis distinguishes between tree and loop-generated operators, emphasizing relevant tree-level diagrams and identifying operators requiring loop-level computation in UV completions. This characterization is crucial for understanding the scale of new physics and potential radiative corrections.
4. Numerical Implications for Various Operators: The paper provides detailed results for numerous dimension-six operators, elucidating their contributions from new particles. Notably, operators associated with four-fermion, bosonic, and boson-fermion interactions were meticulously catalogued, and their contributions were computed.

Practical and Theoretical Implications

On the practical front, this dictionary serves as a valuable resource for model builders aiming to explain anomalies or propose new physics scenarios by correlating low-energy observables with specific BSM parameters. The insights gained from this research have implications on how experimental data, such as that from the LHCb anomalies, is interpreted in terms of new physics.

Theoretically, the framework reinforces the SMEFT as a robust tool for analyzing potential extensions of the SM. The methodology detailed in the paper allows for future investigations into higher-dimensional operators and loop-level corrections, broadening the scope of theory-experiment comparisons. Additionally, these results could facilitate the automation of EFT matching calculations, further integrating theoretical models with empirical data.

Future Directions

Looking ahead, the research opens up pathways for considering higher-dimension operators and one-loop corrections, inviting further investigations into strongly-coupled UV completions and their implications on phenomena at higher energy scales. Future work might also explore automation advancements for dealing with a vast array of BSM theories using the dictionary framework established herein.

In summary, this paper provides a pivotal advancement in the understanding of how BSM scenarios interact with the SM under the framework of effective field theories, offering an in-depth resource to bridge theoretical advancements with experimental realities.