Correlation between \( {R}_{D^{\left(\ast \right)}} \) and top quark FCNC decays in leptoquark models

Some interpretations of $$ {R}_{D^{\left(\ast \right)}} $$ anomaly in B meson decay using leptoquark (LQ) models can also generate top quark decays through Flavor Changing Neutral Current (FCNC). In this work we focus on two LQs, i.e. scalar S1 and vector U1 which are both singlet under the SU(2)L gauge group in the Standard Model (SM). We investigate their implications on the 3-body top FCNC decays t → cℓiℓj at tree level and the 2-body t → cV at one-loop level, with ℓ being the SM leptons and V = γ, Z, g being the SM gauge bosons. We utilize the 2σ parameter fitting ranges of the LQ models and find that Br(t → cℓiℓj) at tree level can reach $$ \mathcal{O} $$(10−6) and Br(t → cV) at one-loop level can reach $$ \mathcal{O} $$(10−10). Some quick collider search prospects are also analyzed.