SMEFT atlas of ∆F = 2 transitions

A bstract We present a model-independent anatomy of the ∆ F = 2 transitions K 0 − K ¯ 0 , B s,d − B ¯ s , d and D 0 − D ¯ 0 in the context of the Standard Model Effective Field Theory (SMEFT). We present two master formulae for the mixing amplitude [ M 12 ] BSM . One in terms of the Wilson coefficients (WCs) of the Low-Energy Effective Theory (LEFT) operators evaluated at the electroweak scale μ ew and one in terms of the WCs of the SMEFT operators evaluated at the BSM scale Λ. The coefficients P a ij entering these formulae contain all the information below the scales μ ew and Λ, respectively. Renormalization group effects from the top-quark Yukawa coupling play the most important role. The collection of the individual contributions of the SMEFT operators to [ M 12 ] BSM can be considered as the SMEFT atlas of ∆ F = 2 transitions and constitutes a travel guide to such transitions far beyond the scales explored by the LHC. We emphasize that this atlas depends on whether the down-basis or the up-basis for SMEFT operators is considered. We illustrate this technology with tree-level exchanges of heavy gauge bosons ( Z′ , G′ ) and corresponding heavy scalars.