Abstract
In the electroweak sector of the Standard Model, CP violation arises through a very particular interplay between the three quark generations, as described by the Cabibbo-Kobayashi-Maskawa (CKM) mechanism and the single Jarlskog invariant J4. Once generalized to the Standard Model Effective Field Theory (SMEFT), this peculiar pattern gets modified by higher-dimensional operators, whose associated Wilson coefficients are usually split into CP-even and odd parts. However, CP violation at dimension four, i.e., at the lowest order in the EFT expansion, blurs this distinction: any Wilson coefficient can interfere with J4 and mediate CP violation. In this paper, we study such interferences at first order in the SMEFT expansion, 𝒪(1/Λ2), and we capture their associated parameter space via a set of 1551 linear CP-odd flavor invariants. This construction describes both new, genuinely CP-violating quantities as well as the interference between J4 and CP-conserving ones. We call this latter possibility opportunistic CP violation. Relying on an appropriate extension of the matrix rank to Taylor expansions, which we dub Taylor rank, we define a procedure to organize the invariants in terms of their magnitude, so as to retain only the relevant ones at a given precision. We explore how this characterization changes when different assumptions are made on the flavor structure of the SMEFT coefficients. Interestingly, some of the CP-odd invariants turn out to be less suppressed than J4, even when they capture opportunistic CPV, demonstrating that CP-violation in the SM, at dimension 4, is accidentally small.
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Acknowledgments
We thank G. Branco, V. Cortés, J. Kley, A. Trautner, N. Weiner and C. Yao for inspiring discussions. This work is supported by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy EXC 2121 “Quantum Universe” - 390833306. JTR is supported by National Science Foundation grants PHY-19154099 and PHY-2210498, and by an award from the Alexander von Humboldt Foundation. EG is supported in part by the National Science Foundation under Grant No. NSF PHY-1748958 and by the Collaborative Research Center SFB1258 and the Excellence Cluster ORIGINS, which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2094-390783311. QB is supported by the Office of High Energy Physics of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. CG and JTR performed part of this work at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-2210452.
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Bonnefoy, Q., Gendy, E., Grojean, C. et al. Opportunistic CP violation. J. High Energ. Phys. 2023, 141 (2023). https://doi.org/10.1007/JHEP06(2023)141
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DOI: https://doi.org/10.1007/JHEP06(2023)141