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We study theoretical constraints on a model whose scalar sector contains onecolor octet and one or two color singlet $SU(2)_L$ doublets. Using theunitarity of the theory, we constrain the parameters of the scalar potentialfor the first time at next-to-leading order in perturbation theory. We alsoderive new conditions guaranteeing the stability of the potential. We use theHEPfit package to single out the viable parameter regions at the electroweakscale and test the stability of the renormalization group evolution up to themulti-TeV region. Additionally, we set upper limits on the scalar masssplittings. All results are given for both cases, with and without a secondscalar color singlet.

New theoretical constraints on scalar color octet models