SMEFT predictions for semileptonic processes

The $SU(2)_L\times U(1)_Y$ invariance of the Standard Model Effective Field Theory (SMEFT) predicts multiple restrictions in the space of Wilson coefficients of $U(1)_{em}$ invariant effective lagrangians such as the Low-energy Effective Field Theory (LEFT), used for low-energy flavor-physics observables, or the Higgs Effective Field Theory (HEFT) in unitary gauge, appropriate for weak-scale observables. In this work, we derive and list all such predictions for semileptonic operators up to dimension 6. We find that these predictions can be expressed as 2223 linear relations among the HEFT/LEFT Wilson coefficients, that are completely independent of any assumptions about the alignment of the mass and flavor bases. These relations connect diverse experimental searches such as rare meson decays, high-$p_T$ dilepton searches, top decays, $Z$-pole observables, charged lepton flavor violating observables and non-standard neutrino interaction searches. We demonstrate how these relations can be used to derive strong indirect constraints on multiple Wilson coefficients that are currently either weakly constrained from direct experiments or have no direct bound at all. These relations also imply, in general, that evidence for new physics in a particular search channel must be accompanied by correlated anomalies in other channels.