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  1. A bstract 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 J 4 . 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 J 4 and mediate CP violation. In this paper, we study such interferences at first order in the SMEFT expansion, 𝒪(1 / Λ 2 ), 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 J 4 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 J 4 , even when they capture opportunistic CPV, demonstrating that CP-violation in the SM, at dimension 4, is accidentally small. 
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  2. A bstract The detection of massless kinetically-mixed dark photons is notoriously difficult, as the effect of this mixing can be removed by a field redefinition in vacuum. In this work, we study the prospect of detecting massless dark photons in the presence of a cosmic relic directly charged under this dark electromagnetism. Such millicharged particles, in the form of dark matter or dark radiation, generate an effective dark photon mass that drives photon-to-dark photon oscillations in the early universe. We also study the prospect for such models to alleviate existing cosmological constraints on massive dark photons, enlarging the motivation for direct tests of this parameter space using precision terrestrial probes. 
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  3. A bstract We look for relations among CKM matrix elements that are not consequences of the Wolfenstein parametrization. In particular, we search for products of CKM elements raised to integer powers that approximately equal 1. We study the running of the CKM matrix elements and resolve an apparent discrepancy in the literature. To a good approximation only A runs, among the Wolfenstein parameters. Using the Standard Model renormalization group we look for CKM relations at energy scales ranging from the electroweak scale to the Planck scale, and we find 19 such relations. These relations could point to structure in the UV, or be numerical accidents. For example, we find that |V td V us | = | $$ {V}_{cb}^2 $$ V cb 2 | , within 2% accuracy, in the 10 9 –10 15 GeV range. We discuss the implications of this CKM relation for a Yukawa texture in the UV. 
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