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  • Open Access

Flavor and CP symmetries in the standard model effective field theory

Hao Sun2,3,* and Jiang-Hao Yu1,2,3,4,†

  • *Contact author: sunhao@itp.ac.cn
  • †Contact author: jhyu@itp.ac.cn
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Phys. Rev. D 112, 075022 – Published 14 October, 2025

DOI: https://doi.org/10.1103/cngm-rc2x

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-violating and CP-odd 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.

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Phys. Rev. D 112, 075022– Published 14 October, 2025
  • Received 17 July 2025
  • Accepted 9 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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