Constraining scalar doublet and triplet leptoquarks with vacuum stability and perturbativity

We investigate the constraints on the leptoquark Yukawa couplings and the Higgs-leptoquark quartic couplings for scalar doublet leptoquark $$\widetilde{R}_2$$, scalar triplet leptoquark $$\varvec{S}_3$$ and their combination with both three generations and one generation with respect to perturbative unitarity and vacuum stability. The perturbative unitarity of all the dimensionless couplings is studied via one- and two-loop beta functions. New $$SU(2)_L$$ multiplets in terms of these leptoquarks are introduced to fabricate Landau poles at the two-loop level in the gauge coupling $$g_2$$ at $$10^{19.7}$$ GeV and $$10^{14.4}$$ GeV, respectively, for the $$\varvec{S}_3$$ and $$\widetilde{R}_2+\varvec{S}_3$$ models with three generations. However, such Landau poles cease to exist for $$\widetilde{R}_2$$ and any of these extensions with both one and two generations up to Planck scale. The Higgs-leptoquark quartic couplings acquire severe constraints to protect Planck scale perturbativity, whereas leptoquark Yukawa couplings acquire some upper bound in order to respect Planck scale stability of Higgs vacuum. The Higgs quartic coupling at the two-loop level constrains the leptoquark Yukawa couplings for $$\widetilde{R}_2,\varvec{S}_3, \,\widetilde{R}_2+\varvec{S}_3$$ with values ≲ 1.30, 3.90, 1.00 with three generations. In the effective potential approach, the presence of any of these leptoquarks with any number of generations pushes the metastable vacuum of the Standard Model to the stable region