Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions

TL;DR

This paper calculates the one-loop anomalous dimensions of a comprehensive set of operators in the low-energy effective field theory below the electroweak scale, including dimension five and six operators, and discusses the renormalization group equations and operator ambiguities.

Contribution

It provides the first complete computation of anomalous dimensions for all relevant operators up to dimension six in the low-energy effective theory below the electroweak scale.

Findings

Computed anomalous dimensions for 70 dimension-five and 3631 dimension-six operators.

Derived renormalization group equations incorporating operator contributions.

Resolved operator ambiguity issues using field redefinitions.

Abstract

We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton masses and the QCD and QED gauge couplings are modified by dimension-five and dimension-six operator contributions. We compute the renormalization group equations from one insertion of dimension-five and dimension-six operators, as well as two insertions of dimension-five operators, to all terms of dimension less than or equal to six. The use of the equations of motion to eliminate operators can be ambiguous, and we show how to resolve this ambiguity by a careful use of field redefinitions.