Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence

Abstract: We calculate the complete order y^2 and y^4 terms of the 59 x 59 one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory, where y is a generic Yukawa coupling. These terms, together with the terms of order lambda, lambda^2 and lambda y^2 depending on the Standard Model Higgs self-coupling lambda which were calculated in a previous work, yield the complete one-loop anomalous dimension matrix in the limit of vanishing gauge couplings. The Yukawa contributions result in non-trivial flavor mixing in the various operator sectors of the Standard Model effective theory.

• The paper derives the complete one-loop anomalous dimension matrix for SM dimension-six operators, focusing on Yukawa contributions.
• It employs naive dimensional analysis and extensive one-loop diagrams to streamline flavor-dependent perturbative calculations.
• The study reveals crucial implications for flavor-changing processes and non-standard Higgs couplings, guiding future experimental explorations.

Renormalization Group Evolution of the Standard Model Dimension Six Operators: Yukawa Dependence

The research paper by Jenkins, Manohar, and Trott explores the renormalization group (RG) evolution of dimension-six operators within the Standard Model (SM) effective field theory framework. This study specifically focuses on the contributions of Yukawa couplings, showcasing their implications on flavor dynamics within the SM. Building upon previous work on gauge-independent contributions, the authors provide a comprehensive analysis of the complete one-loop anomalous dimension matrix for these operators, emphasizing Yukawa terms while leaving gauge terms to future discussions.

Theoretical Foundation and Formalism

The authors address a critical component of the effective field theory approach to beyond Standard Model (BSM) physics by incorporating higher dimensional operators, with particular emphasis on dimension-six operators. By doing so, they retain the predictive power of the SM at energies below a new physics scale $\Lambda$, while acknowledging potential BSM effects. The analysis builds on the existence of 59 independent dimension-six operators that respect baryon number conservation, categorizing them into eight classes based on field content and derivative order. These operators lead to potential modifications in SM observables—most notably in the Higgs sector—which are captured through an extensive anomalous dimension matrix, detailed comprehensively in the paper.

Key Contributions and Computational Techniques

The Yukawa-dependent contributions to the anomalous dimensions highlight potential flavor-changing processes in the Higgs sector, with implications such as non-standard Higgs to fermion couplings and flavor-violating processes like $\mu \rightarrow e \gamma$. The work encompasses calculations stemming from a vast array of one-loop diagrams involving these operators—specifically underlining the challenges of calculating full flavor dependencies. The authors utilize naive dimensional analysis to efficiently streamline the coupling constant dependence in their calculations, thereby simplifying perturbative order classifications within the RG evolution equations.

Implications and Future Directions

The implications of this research are substantial within the context of both theoretical predictions and experimental verification. The nuanced flavor dynamics arising from Yukawa contributions present potentially observable phenomenological impacts at current and future experiments exploring Higgs physics and flavor violation. Notably, the work suggests that incorporating these RG effects can refine interpretations of experimental results, even in instances where no deviations from SM predictions are found. Such insights might guide exploration into symmetry-based solutions or flavor structures like minimal flavor violation.

This paper exemplifies a rigorous enhancement to the ongoing development of the SM effective field theory, enabling precise descriptions of BSM physics. Continued exploration into uncharted territories of gauge contributions in subsequent research rounds out the authors' ambition to fully delineate the RG evolution within a high-fidelity theoretical framework, which holds promise for extensive applications in precision particle physics. Thus, the study effectively bridges a significant gap between current experimental capabilities and theoretical expectations, while paving the way for future advancements in understanding potential new physics.