SMEFT atlas of ∆F = 2 transitions

Abstract

Abstract We present a model-independent anatomy of the ∆F = 2 transitions K0−$$ {\overline{K}}^0 $$ K ¯ 0 , Bs,d−$$ {\overline{B}}_{s,d} $$ B ¯ s , d and D0−$$ {\overline{D}}^0 $$ 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 $$ {P}_a^{ij} $$ 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.