Ledger-Closure Constraints on the SMEFT: A Lattice-Theoretic Derivation of Operator Exclusions and Wilson-Coefficient Relations

This paper develops a basis-independent dimensional-closure framework for the Standard Model Effective Field Theory (SMEFT) using a five-dimensional integer ledger lattice. Each operator is assigned a ledger vector encoding its dimensional exponents. An operator is admissible only if its vector lies in the lattice sum
LQ+LCL_Q + L_CLQ+LC,
where LQL_QLQ is the span of a Quantized Dimensional Cell (QDC) of type L3F2L^3 F^2L3F2, and LCL_CLC is the sublattice generated by fundamental constants. A unimodular-invariance theorem ensures that the closure criterion is independent of basis choice.

Applying this framework to SMEFT through dimension eight, we derive a structural filter on the 2,499 Warsaw-basis operators. Several four-fermion contact families are shown to be forbidden as fundamental interactions, while gauge–Higgs and scalar operators admit classifications into fundamental, scale-suppressed, or mediator-generated classes. Ledger equivalence also induces algebraic relations among Wilson coefficients that are independent of gauge symmetries and reduce SMEFT’s free parameter space.

This work provides a dimensional-lattice constraint principle for effective field theory construction and complements symmetry-based SMEFT analyses. The mathematical foundations of the ledger lattice and closure criterion are developed in the companion paper, Dimensional Closure and Ledger Lattices in Effective Field Theories (Bourassa 2025).