Addressing the Rτ/μ,e(D(∗)) puzzle through new physics four-fermion operators and their impact on Λb→Λcτντ decay

The Lepton Flavor Universality ratio [Formula: see text] poses a notable challenge to the Standard Model (SM), as results of the B-factory experiments, BaBar, Belle and the LHCb show [Formula: see text] deviations from their theoretical predictions. Utilizing the latest HFLAV averages and incorporating the branching ratio constraints [Formula: see text], [Formula: see text] and [Formula: see text] from the lifetime of the [Formula: see text] meson, we determine the values of the Wilson coefficients (WCs) for different New Physics (NP) four-fermion operator with specific Lorentz structures. Our analysis finds that the parametric region allowed for the WC scenario [Formula: see text] emerged as the most probable, yielding the maximum pull from the SM, and strongly influenced by the constraints of the branching ratio. Furthermore, we identify three degenerate solutions involving [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] as the second most probable NP scenarios. We then studied the influence of these NP operators on various physical observables in [Formula: see text] decay by using the Lattice QCD form factors. Our results highlighted [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and the three degenerate scenarios involving [Formula: see text], [Formula: see text] and [Formula: see text] as strong indicators of NP. The correlation of different physical observables shows a direct correlation between [Formula: see text] and [Formula: see text] for WC [Formula: see text]; and between [Formula: see text] and [Formula: see text] for three degenerate WCs involving [Formula: see text]. We hope that the measurements of these observables on some ongoing and future experiments will help us to scrutinize these constraints on the various NP couplings.