Flavor and CP Symmetries in the Standard Model Effective Field Theory

TL;DR

This paper uses flavor symmetries to organize and classify CP properties of SMEFT operators, reducing the number of independent parameters and elucidating the structure of CP violation within the effective field theory framework.

Contribution

It introduces a systematic classification of SMEFT operators based on flavor and CP symmetries, employing the Hilbert series and Young tensor methods, and applies the minimal flavor violation hypothesis.

Findings

Classification of dimension-6 and dimension-8 operators by CP properties.

Reduction of independent CP-violating phases using flavor symmetries.

Explicit flavor structures of SMEFT operators under MFV hypothesis.

Abstract

The CP properties of effective operators are closely related to the spacetime and internal symmetries, such as the flavor symmetry, in the standard model effective field theory (SMEFT). In this work, we utilize the flavor symmetry to organize and reduce numbers of independent Wilson coefficients of the SMEFT operators. We classify the dimension-6 and dimension-8 baryon/lepton-number-conserving operators based on their CP properties. The $U(1)^4$ rephasing symmetry is applied to distinguish CP-odd and CP-violating operators which leads to reduction of the independent CP-violating phases. The $U(3)^5$ and $U(2)^5$ flavor symmetries let us classify the CP-violating phases as the flavor invariants, which can be enumerated by the Hilbert series and obtained explicitly by the Young tensor method. Then after introducing the minimal flavor violation (MFV) hypothesis, we present the flavor structures of the dimension-6 and dimension-8 SMEFT operators under the MFV hypothesis utilizing the spurion method.