SMEFT ATLAS of $Delta F=2$ Transitions

We present a model-independent anatomy of the $Delta F=2$ transitions $K^0-bar K^0$, $B_{s,d}-bar B_{s,d}$ and $D^0-bar D^0$ in the context of the Standard Model Effective Field Theory (SMEFT). We present two master formulae for the mixing amplitude $big[M_{12} big]_text{BSM}$. One in terms of the Wilson coefficients (WCs) of the Low-Energy Effective Theory (LEFT) operators evaluated at the electroweak scale $mu_text{ew}$ and one in terms of the WCs of the SMEFT operators evaluated at the BSM scale $Lambda$. The coefficients $P_a^{ij}$ entering these formulae contain all the information below the scales $mu_text{ew}$ and $Lambda$, 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 $big[M_{12}big]_text{BSM}$ can be considered as the SMEFT ATLAS of $Delta F=2$ 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 ($Z^prime$, $G^prime$) and corresponding heavy scalars.