Constraining scalar doublet and triplet leptoquarks with vacuum stability and perturbativity

Abstract

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 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.