[Paper Review] Towards the one loop IR/UV dictionary in the SMEFT: one loop generated operators from new scalars and fermions

Guilherme Guedes, P. Olgoso+1 more|arXiv (Cornell University)|Jan 1, 2023

Black Holes and Theoretical Physics1 citations

TL;DR

This paper presents the first systematic classification of one-loop generated dimension-6 operators in the Standard Model Effective Field Theory (SMEFT) from weakly coupled new physics models containing additional scalars and fermions. Using a novel Mathematica package called SOLD, the authors compute the complete one-loop matching for operators not generated at tree level—such as those with three gauge field strengths, two field strengths with scalars, and dipole operators—providing a foundational step toward a full one-loop IR/UV dictionary in SMEFT.

ABSTRACT

Effective field theories offer a rationale to classify new physics models based on the size of their contribution to the effective Lagrangian, and therefore to experimental observables. A complete classification can be obtained, at a fixed order in perturbation theory, in the form of IR/UV dictionaries. We report on the first step towards the calculation of the one loop, dimension 6 IR/UV dictionary in the SMEFT. We consider dimension-six operators in the SMEFT that cannot be generated at tree level in weakly coupled extensions of the Standard Model. This includes operators with three gauge field strength tensors, operators with two field strength tensors and two scalar fields and dipole operators. We provide a complete classification of renormalizable extensions of the Standard Model with new scalar and fermion fields that contribute to these operators at one loop order, together with their explicit contribution. Our results are encoded in a exttt{Mathematica} package called exttt{SOLD} (SMEFT One Loop Dictionary), which includes further functionalities to facilitate the calculation of the complete tree level and one loop matching of any relevant model via an automated interface to exttt{matchmakereft}. All operators in our list are indeed generated at the one loop order in the extensions considered with the exception of CP-violating ones with three field-strength tensors.

Motivation & Objective

• To establish a systematic classification of one-loop contributions to SMEFT dimension-6 operators from new scalar and fermion fields.
• To identify all renormalizable UV extensions of the SM that generate specific classes of dimension-6 operators not accessible at tree level.
• To develop a computational framework (SOLD) that automates the matching of any such model to the SMEFT at one-loop order.
• To provide a complete and explicit list of one-loop matching coefficients for non-tree-level operators, including corrections from evanescent operators.
• To lay the groundwork for a full one-loop, dimension-6 IR/UV dictionary in SMEFT, enabling model-independent phenomenological analysis.

Proposed method

• Focus on dimension-6 operators in the SMEFT that cannot be generated at tree level in weakly coupled SM extensions, including those with three gauge field strengths, two field strengths and two scalars, and dipole operators.
• Systematically classify all renormalizable UV models with new scalar and fermion fields that contribute to these operators at one loop.
• Compute one-loop matching coefficients using standard quantum field theory techniques, including loop integrals and regularization in dimensional regularization.
• Account for evanescent operators in the calculation, particularly for dipole-type operators, using known results from prior work.
• Implement the results in a Mathematica package called SOLD, which provides automated interfaces to matchmakereft for model matching.
• Use the Warsaw basis and handle redundant and evanescent operators via explicit projection and redefinition procedures.

Experimental results

Research questions

• RQ1 Which renormalizable UV extensions of the SM generate dimension-6 operators at one loop that are not accessible at tree level?
• RQ2 What are the complete one-loop matching coefficients for operators involving three gauge field strengths, two field strengths with scalars, and dipole operators?
• RQ3 How do evanescent operator contributions affect the physical matching coefficients of dipole operators in the SMEFT?
• RQ4 Can a systematic, automated framework be built to compute one-loop matching for any new physics model in the SMEFT?
• RQ5 What is the structure of the one-loop IR/UV dictionary for SMEFT, and how does it extend the existing tree-level dictionary?

Key findings

• The authors provide a complete classification of one-loop generated dimension-6 operators in the SMEFT from new scalar and fermion fields, excluding only CP-violating three-gauge-boson operators.
• The matching coefficients for all listed operators are computed explicitly, with closed-form expressions derived for the X3 class (e.g., α3V for non-Abelian gauge groups).
• The evanescent operator contributions to dipole operators are quantified and included in the final results, with explicit shifts in the matching coefficients involving Yukawa couplings and the ξrp parameter.
• The SOLD package successfully automates the one-loop matching process, enabling efficient computation of SMEFT matching for any model with new scalars and fermions.
• The results confirm that all operators in the list are indeed generated at one loop in the considered UV models, with the exception of CP-violating three-field-strength operators.
• The framework provides a critical foundation for extending the SMEFT IR/UV dictionary to one-loop order, enabling model-independent phenomenological analyses at next-to-leading order in perturbation theory.