SMEFT atlas of \u2206F = 2 transitions

Abstract

We present a model-independent anatomy of the ∆F = 2 transitions K0− {overline{K}}^0 , Bs,d− {overline{B}}_{s,d} and D0− {overline{D}}^0 in the context of the Standard Model Effective Field Theory (SMEFT). We present two master formulae for the mixing amplitude [M12]BSM. One in terms of the Wilson coefficients (WCs) of the Low-Energy Effective Theory (LEFT) operators evaluated at the electroweak scale μew 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 μew 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 [M12]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.