Vacuum stability in an extended standard model with a leptoquark

We investigate the standard model (SM) with the extension of a charged scalar having fractional electromagnetic charge of $-1/3$ unit and with lepton and baryon number violating couplings at tree level. Without directly taking part in the electro-weak (EW) symmetry breaking, this scalar can affect stability of the EW vacuum via loop effects. The impact of such a scalar, i.e., a leptoquark on the perturbativity of SM dimensionless couplings as well as on new physics couplings has been studied at two-loop order. The vacuum stability of the Higgs potential is checked using one-loop renormalization group (RG) improved effective potential approach with two-loop beta function for all the couplings. From the stability analysis various bounds are drawn on parameter space by identifying the region corresponding to metastability and stability of the EW vacuum. Later we also address the Higgs mass fine-tuning issue via Veltman condition and the presence of such scalar increases the scale up to which the theory can be considered as reasonably fine-tuned. All these constraints give a very predictive parameter space for leptoquark couplings which can be tested at present and future colliders. Especially, a leptoquark with mass $\mathcal{O}\,$(TeV) can give rise to lepton-quark flavor violating signatures via decaying into the $t\, τ$ channel at tree level, which can be tested at the LHC or future colliders.