Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching (1709.04486v3)

Abstract: The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as $\Delta B= \pm \Delta L = \pm 1$, $\Delta L=\pm 2$, and $\Delta L=\pm 4$ operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order $1/\Lambda^2$ is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints.

• The paper systematically classifies gauge-invariant operators up to dimension six to connect low-energy EFT with SMEFT.
• The authors employ tree-level matching and one-loop anomalous dimensions to achieve leading-log precision in predicting new physics effects.
• The study establishes a structured power counting method that bridges theoretical predictions with experimental constraints from low-energy decay processes.

An Exploration of Low-Energy Effective Field Theory and Its Interface with the Standard Model

The paper "Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching" by Jenkins, Manohar, and Stoffer provides a comprehensive classification of gauge-invariant operators up to dimension six in the low-energy effective field theory (LEFT) below the electroweak scale. This analysis is pivotal for understanding the influence of physics beyond the Standard Model (SM) at low energies while maintaining consistency with observed high-energy constraints from the Large Hadron Collider (LHC) and other experiments.

The authors undertake a meticulous inventory of Hermitian dimension-five and dimension-six operators. They identify 70 dimension-five operators, which conserve baryon and lepton numbers, and 3631 dimension-six operators, alongside operators that account for lepton- and baryon-number violation. These operators enable the parametrization of new physics through an Effective Field Theory (EFT) framework compatible with the Standard Model Effective Field Theory (SMEFT).

The paper leverages SMEFT to impose constraints on the coefficients of these low-energy operators, which are experimentally testable to verify whether the SM's electroweak gauge symmetry is indeed broken by a fundamental scalar doublet. This alignment is achieved through tree-level matching from SMEFT to LEFT up to order $1/\Lambda^2$.

By incorporating the one-loop anomalous dimensions of both the low-energy theory and SMEFT, the research permits calculations of new physics implications with leading-log accuracy. Consequently, experimental constraints acquired at low energies, from processes such as $B$ and $K$ decays, can be synthesized with high-energy constraints to evaluate new physics models systematically.

In presenting the implications for practical applications, the paper meticulously delineates the power counting in LEFT, emphasizing the dual expansion in $m/v$ and $v/\Lambda$, where $m$ represents low-energy masses, $v$ the electroweak scale, and $\Lambda$ the new physics scale. This results in predictable suppression patterns for higher-dimension operator contributions.

The implications of this research are profound both theoretically and experimentally. It highlights the necessity of maintaining theoretical models consistent across various energy scales and offers a structured methodology to explore the potential deviations from the SM. Future advancements in experimental precision might further restrict the coefficient space of these operators, providing tighter bounds on possible new physics scenarios.

As an academic contribution, this work exemplifies the synergy between theoretical development and experimental testing, underscoring the complexity and necessity of effective field theories in contemporary particle physics. The detailed classification and systematic approach to matching conditions are expected to be indispensable resources for subsequent studies aiming for precision tests of the SM and searches for new physics phenomena.

In conclusion, Jenkins et al.'s work not only classifies possible operators in a low-energy theory below the electroweak scale but also lays down concrete methodologies for bridging the gap between SMEFT and LEFT. This research augments our understanding of how to consistently interpret experimental data across varying energy scales and provides a robust framework to scrutinize the next frontier in particle physics.