Opportunistic CP violation

In the electroweak sector of Standard Model, CP violation arises through a very particular interplay between three quark generations, as described by Cabibbo--Kobayashi--Maskawa (CKM) mechanism and single Jarlskog invariant $J_4$. Once generalized to Model Effective Field Theory (SMEFT), this peculiar pattern gets modified higher-dimensional operators, whose associated Wilson coefficients are usually split into CP-even odd parts. However, at dimension four, i.e., lowest order in EFT expansion, blurs distinction: any coefficient can interfere with $J_4$ mediate violation. paper, we study such interferences first SMEFT $\mathcal{O}(1/\Lambda^2)$, capture their parameter space via set 1551 linear CP-odd flavor invariants. This construction describes both new, genuinely CP-violating quantities well interference CP-conserving ones. We call latter possibility \textit{opportunistic violation}. Relying on an appropriate extension matrix rank Taylor expansions, which dub \emph{Taylor rank}, define procedure organize invariants terms magnitude, so retain only relevant ones given precision. explore how characterization changes when different assumptions made structure coefficients. Interestingly, some turn out be less suppressed than $J_4$, even they opportunistic CPV, demonstrating that CP-violation SM, 4, is \textit{accidentally small.}