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As SMEFT is a framework of growing importance to analyze high-energy data,understanding its parameter space is crucial. The latter is commonly split intoCP-even and CP-odd parts, but this classification is obscured by the fact thatCP violation is actually a collective effect that is best captured byconsidering flavor-invariant combinations of Lagrangian parameters. First weshow that fermion rephasing invariance imposes that several coefficientsassociated to dimension-six operators can never interfere with operators ofdimension $\leq4$ and thus cannot appear in any physical observable at$\order{1/\Lambda^2}$. For those that can, instead, we establish a one-to-onecorrespondence with CP-odd flavor invariants, all linear with respect to SMEFTcoefficients. We explicitly present complete lists of such linear CP-oddinvariants, and carefully examine their relationship to CP breaking throughoutthe parameter space of coefficients of dimension $\leq 4$. Requiring that theseinvariants all vanish, together with the Jarlskog invariant, the strong-CPphase, and the 6 CP-violating dimension-6 bosonic operators, provides$699(+1+1+6)$ conditions for CP conservation to hold in any observable atleading order, $\cO$1/\Lambda^2$$.

Beyond Jarlskog: 699 invariants for CP violation in SMEFT