Vacuum Stability and Perturbativity of SU(3) Scalars

Abstract

We calculate the vacuum stability conditions and renormalisation group equations for the extensions of standard model with a higher colour multiplet scalar up to the representation $15^{\prime }$ that leaves the strong interaction asymptotically free. In order to find the vacuum stability conditions, we calculate the orbit spaces for the self-couplings of the higher multiplets, which for the representations $15$ and $15^{\prime }$ of $SU(3{)}_c$ are highly complicated. However, if the scalar potential is linear in orbit space variables, it is sufficient to know the convex hull of the orbit space. In contrast to the self-couplings of other multiplets, we find that the scalar quartic couplings of the representations $3$ and $8$ walk rather than run, remaining nearly constant and perturbative over a vast energy range. We describe the conditions for walking couplings using a schematic model. With these technical results at hand we revise earlier results of generation of new scales with large $SU(3{)}_c$ scalar multiplets. Our results are easily extendable to models of new physics with additional $SU(3)$ or SU($N$) gauge symmetries.

arXiv comment26 pages, 6 figures, 2 tables

References in corpus (17)

• Flavor Changing Neutral Currents, an Extended Scalar Sector, and the Higgs Production Rate at the LHC
• Massive color-octet bosons and pairs of resonances at hadron colliders
• PyR@TE: Renormalization Group Equations for General Gauge Theories
• Softened Gravity and the Extension of the Standard Model up to Infinite Energy
• Electroweak Symmetry Breaking via QCD
• Multicomponent Dark Matter from Gauge Symmetry
• Color Sextet Scalars in Early LHC Experiments
• Geometric minimization of highly symmetric potentials
• PyR@TE 2: A Python tool for computing RGEs at two-loop
• A minimal model for $\mathrm{SU}(N)$ vector dark matter
• Di-higgs enhancement by neutral scalar as probe of new colored sector
• A Sommerfeld Toolbox for Colored Dark Sectors
• Pair production of 125 GeV Higgs boson in the SM extension with color-octet scalars at the LHC
• Two Higgs doublet models augmented by a scalar color octet
• SO(10) grand unification in light of recent LHC searches and colored scalars at the TeV-scale
• $\mathcal{C}\mathcal{P}$ violation with an unbroken $\mathcal{C}\mathcal{P}$ transformation
• Colour Octet Extension of 2HDM

Cited by in corpus (9)

• Algorithmic Boundedness-From-Below Conditions for Generic Scalar Potentials
• Renormalizable SU(5) Completions of a Zee-type Neutrino Mass Model
• Scheme dependence of asymptotically free solutions
• Vacuum Stability in Inert Higgs Doublet Model with Right-handed Neutrinos
• Asymptotic freedom in $Z_2$-Yukawa-QCD models
• Constraining the Higgs Trilinear Coupling from an $SU(2)$ Quadruplet with Bounded-from-Below Conditions
• Vacuum Stability and Radiative Symmetry Breaking of the Scale-Invariant Singlet Extension of Type II Seesaw Model
• Is our vacuum global in a 331 model with three triplets?
• Vacuum Stability Conditions for New $SU(2)$ Multiplets