Constraining Scalar Doublet and Triplet Leptoquarks with Vacuum Stability and Perturbativity

TL;DR

This paper studies how scalar leptoquarks affect the stability of the Higgs vacuum and the perturbativity of couplings up to the Planck scale, providing constraints on their Yukawa and quartic couplings.

Contribution

It offers a detailed analysis of vacuum stability and perturbativity constraints on scalar leptoquarks with multiple generations, including Landau pole behavior and upper bounds on couplings.

Findings

Landau poles appear at high energies for certain leptoquark models.

Leptoquarks can stabilize the Standard Model vacuum.

Constraints on Yukawa and quartic couplings are derived up to the Planck scale.

Abstract

We investigate the constraints on the leptoquark Yukawa couplings and Higgs-leptoquark quartic couplings for scalar doublet leptoquark $\tilde{R}_2$, scalar triplet leptoquark $\vec S_3$ and their combination with both three generations and one generation from perturbative unitarity and vacuum stability. Perturbative unitarity of all the dimensionless couplings have been studied via one- and two-loop beta-functions. Introduction of new $SU(2)$ multiplets in terms of these leptoquarks fabricate Landau poles at two-loop level in the gauge coupling $g_2$ at $10^{19.7}$ GeV and $10^{14.4}$ GeV, respectively for $\vec S_3$ and $\tilde{R}_2+\vec S_3$ models with three generations. However, such Landau pole ceases to exist for $\tilde{R}_2$ and any of these extensions with both one and two generations till Planck scale. The Higgs-leptoquark quartic couplings acquire severe constraints to protect Planck scale perturbativity, whereas leptoquark Yukawa couplings get some upper bound in order to respect Planck scale stability of Higgs Vacuum. The Higgs quartic coupling at two-loop constraints the leptoquark Yukawa couplings for $\tilde{R}_2,\vec S_3, \,\tilde{R}_2+\vec S_3$ with values $\lesssim 1.30, 3.90, 1.00$ 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.