Abstract
We study implications of the four-fermion semileptonic operators at the low-energy and at electroweak (EW) scale in the framework of Standard Model Effective Field Theory (SMEFT). We show how the renormalization group (RG) running effects can play an important role in probing the generic flavour structure of such operators. It is shown that at the 1-loop level, through RG running, depending upon the flavour structure, these operators can give rise to sizable effects at low energy in the electroweak precision (EWP) observables, the leptonic, quark, as well as the Z boson flavour violating decays. To this end, we isolate the phenomenologically relevant terms in the full anomalous dimension matrices (ADMs) and discuss the impact of the QED+QCD running in the Weak effective field theory (WET) and the SMEFT running due to gauge and Yukawa interactions on the dim-4 and dim-6 operators at the low energy. Considering all the relevant processes, we derive lower bounds on new physics (NP) scale Λ for each semileptonic operator, keeping a generic flavour structure. In addition, we also report the allowed ranges for the Wilson coefficients at a fixed value of Λ = 3 TeV.
Highlights
An interesting aspect of the Standard Model Effective Field Theory (SMEFT) is its built-in gauge symmetry
We study implications of the four-fermion semileptonic operators at the lowenergy and at electroweak (EW) scale in the framework of Standard Model Effective Field Theory (SMEFT)
We isolate the phenomenologically relevant terms in the full anomalous dimension matrices (ADMs) and discuss the impact of the QED+QCD running in the Weak effective field theory (WET) and the SMEFT running due to gauge and Yukawa interactions on the dim-4 and dim-6 operators at the low energy
Summary
The pattern of mixing between different operators due to running from Λ to the EW scale is very complex in nature Often this leads to the appearance of new operators at the EW scale, which can give rise to unpredictable correlations among low-energy observables. It is extremely important to systematically analyze these effects for all flavour structures of the operators of our interest This will allow us to identify all possible observables which are sensitive to these operators. We will identify all possible observables which can be used to constrain a given operator directly (at tree-level) or through the operators to which it mixes into, through the RG effects (at 1-loop level) Using this information, we will derive the lower bounds on the scale of each semileptonic operator assuming the presence of a single operator at the scale Λ
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