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We study the phenomenological constraints and consequences in the flavorsector, of introducing a new fourth generation $\mathcal{Z}_{2}$ oddvector-like lepton doublet along with a Standard Model (SM) singlet scalar andan $SU(2)_{L}$ singlet scalar leptoquark carrying electromagnetic charge of$+2/3$, both odd under a $\mathcal{Z}_{2}$. We show that with little finetuning among the various Yukawa couplings in the new physics (NP) Lagrangianalong with the CKM parameters, the model is able to push the theoretical valueof $R(D^{*})^{th}$ from $0.252 \pm 0.003$ to $0.263 \pm 0.051$ and $R(D)^{th}$from $0.300 \pm 0.008$ to $0.313 \pm 0.158$ compared to the SM value.Especially the NP contributions are able to reduce the discrepancy betweenexperiment and theory of $R(D^{*})$ substantially compared to SM. This is quiteimpressive given that the model satisfy all other very stringent constrainscoming from neutral meson oscillations and precision $Z$-pole data.

Implications of a vector-like lepton doublet and scalar Leptoquark on $R(D^{(*)})$