Flavorful Lepton-Number-Violating SMEFT: Loop Mixing, $0\nu \beta \beta$ and Rare Meson Decays

We investigate how one-loop operator mixing reshapes the flavor sensitivity of lepton-number-violating dimension-7 SMEFT interactions. Using both bottom-up and top-down EFT approaches, we study the interplay of neutrinoless double beta decay ($0\nu \beta \beta$) and neutral current rare meson decays $K\to \pi \nu \nu$, and $B\to K^{(\ast )}\nu \nu$, which at tree level probe apparently disconnected quark- and lepton-flavor sectors. We show that loop mixing qualitatively changes this picture: flavor structures radiatively feed into one another, substantially extending the sensitivity to higher new-physics scales across operators and flavors. In the bottom-up EFT approach, this can make $0\nu \beta \beta$ highly sensitive even to operators involving heavier-generation quarks, while rare kaon and $B$ decays retain crucial complementary sensitivity to other flavor combinations. A top-down EFT approach example using a ultraviolet model involving scalar-leptoquark illustrates how the same effects can reorder the relative importance of different observables.