Dimension-Six Terms in the Standard Model Lagrangian (1008.4884v3)

Abstract: When the Standard Model is considered as an effective low-energy theory, higher dimensional interaction terms appear in the Lagrangian. Dimension-six terms have been enumerated in the classical article by Buchmueller and Wyler [3]. Although redundance of some of those operators has been already noted in the literature, no updated complete list has been published to date. Here we perform their classification once again from the outset. Assuming baryon number conservation, we find 15 + 19 + 25 = 59 independent operators (barring flavour structure and Hermitian conjugations), as compared to 16 + 35 + 29 = 80 in Ref.[3]. The three summed numbers refer to operators containing 0, 2 and 4 fermion fields. If the assumption of baryon number conservation is relaxed, 4 new operators arise in the four-fermion sector.

• The paper refines the classification of dimension-six operators by eliminating redundant terms through equations of motion.
• It identifies 59 independent operators under baryon number conservation, updating the previous 80-operator Buchmüller-Wyler basis.
• The analysis provides a robust framework for exploring beyond-SM physics and effective field theories in high-energy experiments.

An Analysis of Dimension-Six Terms in the Standard Model Lagrangian

The paper presented aims to refine the classification of dimension-six operators in the Standard Model (SM) when it is regarded as an effective field theory at low energies. By leveraging the Effective Field Theory (EFT) framework, the authors systematically revisit and update the operator basis initially compiled by Buchmüller and Wyler (1986).

Key Findings and Methodology

The paper's analysis hinges on the assumption of baryon number conservation, leading to the identification of 59 independent operators, which categorize as follows: 15 bosonic operators, 19 single-fermionic-current operators, and 25 four-fermion operators. This differs from the earlier catalog of 80 operators as outlined in Buchmüller and Wyler's work. If baryon number conservation is relaxed, four additional operators emerge in the four-fermion sector.

The authors engage in a thorough review of redundancies that arise when certain linear combinations of operators vanish by the Equations of Motion (EOMs). By eliminating such redundant operators, a leaner and more precise operator basis is achieved without relying on previous analyses.

Technical Approach and Results

1. EOM-Driven Reduction: The authors apply classical equations of motion to identify and eliminate operators that do not affect physical matrix elements, regardless of perturbative or non-perturbative context.
2. Re-evaluation of Prior Work: By revisiting Buchmüller and Wyler’s classification, they identify several operators that are redundant due to being representable as linear combinations of EOM-vanishing operators.
3. Novel Operator Identification: The work acknowledges missing operators in previous lists, such as the Q_lequ operator, correcting earlier limitations in operator characterization.
4. Systematic Enumeration: All operators are systematically categorized based on their field compositions and transformations under the SM gauge symmetries. The extensive listings in Tables 2 and 3 of the paper provide a refined framework for future analyses in various phenomenological contexts.

Implications and Speculations

This research provides a more robust foundation for exploring beyond-the-SM physics by delineating a precise operator basis for higher-dimensional corrections. These findings are critical for probing deviations from the SM in high-energy physics experiments, such as those at the Large Hadron Collider (LHC).

From a theoretical perspective, the updated operator list facilitates numerous computational simplifications and ensures consistent application across different beyond-SM scenarios, particularly where power-suppressed terms can have significant phenomenological implications.

Future Directions

The precision of this operator classification establishes a solid groundwork for ongoing and future phenomenological studies involving EFTs. As experimental techniques continue to evolve, enabling more precise measurements of SM parameters and potential deviations, the refined operator basis will likely guide interpretations and model extensions in particle physics.

Furthermore, the approach used in this paper sets a precedent for similar re-evaluations of operator definitions in other effective theories, ensuring that any theoretical analysis is firmly grounded on non-redundant, physically meaningful constructs.

In conclusion, the paper advances the understanding of dimension-six operators within the SM and rectifies existing discrepancies through rigorous analysis. It provides essential insights for future theoretical developments and experimental validations of the SM and its conceivable extensions.