- The paper identifies 20 independent dimension-7 operators in SMEFT, establishing a complete classification under strict gauge invariance rules.
- It employs rigorous hypercharge and Lorentz invariance constraints along with classical equations of motion to streamline the operator set.
- The study highlights significant lepton and baryon number violations, providing new avenues for exploring baryogenesis and leptogenesis in BSM physics.
Extending the Standard Model Effective Field Theory with Dimension-7 Operators
In the pursuit of understanding physics beyond the Standard Model (BSM), effective field theories provide a robust framework for systematically exploring deviations from established models. This paper by Landon Lehman contributes to the Standard Model Effective Field Theory (SMEFT) by identifying and categorizing the complete set of dimension-7 operators within the SMEFT framework. These operators are constructed using the degrees of freedom from the Standard Model while ensuring gauge invariance under the Standard Model’s symmetry groups, specifically SU(3)C​⊗SU(2)W​⊗U(1)Y​.
Main Findings
The author has cataloged a total of 20 independent dimension-7 operators, a significant reduction from the 63 operators noted at dimension 6. This reduction reflects the stringent conditions imposed by gauge invariance and the dimensional criteria. One of the striking features of these operators is their ubiquitous involvement of fermion fields, resulting from the absence of viable fermion-free operators of odd dimensions. Furthermore, these 20 operators are characterized by lepton number violation, and a subset of 7 also exhibit baryon number violation, thus contributing to possible mechanisms for baryogenesis and leptogenesis.
Methodological Approach
The classification methodology hinges on hypercharge constraints and Lorentz invariance conditions. The paper employs rules derived from these constraints, specifically noting that no scalar or tensor fermion currents possess zero hypercharge and no vector currents possess hypercharge ±1/2. These rules serve as critical filters to streamline the operator list, accompanied by classical equations of motion to simplify certain constructs further.
Implications and Future Directions
The identification of these dimension-7 operators opens pathways for theoretical inquiries into the nature of BSM physics. For instance, the lepton and baryon number violating operators can be instrumental in developing new models of matter-antimatter asymmetry. In practical terms, these operators can guide experimental physicists in establishing new search strategies at collider experiments such as the LHC, focusing on specific channels where deviations from the Standard Model might manifest.
The author suggests several extensions and modifications that could further enrich the SMEFT framework, including the addition of multiple Higgs doublets or right-handed neutrinos to the Standard Model. Such extensions could potentially yield more operators and inform corrections at even larger dimensions.
Speculations on Future AI Developments
As these theoretical frameworks evolve, there is an anticipation that AI could play a significant role in accelerating both theory and experimental validation. AI technologies, especially those capable of handling large datasets and predicting complex quantum field interactions, might become invaluable in testing the practical implications of these newly defined operators.
In summary, this paper provides a comprehensive classification of dimension-7 operators within the SMEFT, paving the way for deeper exploration into BSM theories. The systematic approach and rigorous classification contribute substantially to a universal understanding of potential deviations from the Standard Model, offering fertile ground for both theoretical advancements and experimental investigations in modern physics.
