Abstract
As SMEFT is a framework of growing importance to analyze high-energy data, understanding its parameter space is crucial. The latter is commonly split into CP-even and CP-odd parts, but this classification is obscured by the fact that CP violation is actually a collective effect that is best captured by considering flavor-invariant combinations of Lagrangian parameters. First we show that fermion rephasing invariance imposes that several coefficients associated to dimension-six operators can never interfere with operators of dimension ≤ 4 and thus cannot appear in any physical observable at \( \mathcal{O} \)1/Λ2. For those that can, instead, we establish a one-to-one correspondence with CP-odd flavor invariants, all linear with respect to SMEFT coefficients. We explicitly present complete lists of such linear CP-odd invariants, and carefully examine their relationship to CP breaking throughout the parameter space of coefficients of dimension ≤ 4. Requiring that these invariants all vanish, together with the Jarlskog invariant, the strong-CP phase, and the 6 CP-violating dimension-6 bosonic operators, provides 699(+1 + 1 + 6) conditions for CP conservation to hold in any observable at leading order, \( \mathcal{O} \)(1/Λ2).
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Bonnefoy, Q., Gendy, E., Grojean, C. et al. Beyond Jarlskog: 699 invariants for CP violation in SMEFT. J. High Energ. Phys. 2022, 32 (2022). https://doi.org/10.1007/JHEP08(2022)032
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DOI: https://doi.org/10.1007/JHEP08(2022)032