Renormalization group improved implications of semileptonic operators in SMEFT

TL;DR

This paper investigates how renormalization group effects influence semileptonic operators in SMEFT, revealing their potential to cause observable effects at low energies and setting bounds on new physics scales.

Contribution

It provides a detailed analysis of RG running effects on semileptonic operators in SMEFT, highlighting their phenomenological implications and deriving bounds on new physics.

Findings

RG running can induce sizable effects in electroweak observables

Lower bounds on NP scale mbda are established for semileptonic operators

Allowed Wilson coefficient ranges are provided at mbda=3 TeV

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 \emph{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 phenomenological 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 the new physics (NP) scale $\Lambda$ 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 $\Lambda=3$ TeV.