Muon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:math> and a type-X two-Higgs-doublet scenario: Some studies in high-scale validity
Atri Dey, Jayita Lahiri, Biswarup Mukhopadhaya
Abstract
We study the high-scale validity of a type-X two Higgs doublet scenario, which provides an explanation of the observed value of muon ($g\ensuremath{-}2$). This region allows a pseudoscalar physical state, which is well below the observed 125-GeV scalar in mass. A second neutral scalar particle can be both above and below 125 GeV in such a scenario. Admissible regions in the parameter space are obtained by using the most recent data on muon ($g\ensuremath{-}2$), theoretical constraints such as low-scale perturbativity and vacuum stability, and also all experimental constraints, including the available LHC results. Among other things, both the aforesaid orders of $CP$-even neutral scalar masses are included in our benchmark studies. Two-loop renormalization group equations are used to predict the values of various couplings at high scales, and the regions in the space spanned by low-scale parameters, which retain perturbative unitarity as well as vacuum stability up to various scales are identified. We thus conclude that such a scenario, while successfully explaining the observed muon ($g\ensuremath{-}2$), can be valid up to energy scales ranging from ${10}^{4}\text{ }\text{ }\mathrm{GeV}$ to the Planck scale, thus opening up directions of thought on its ultraviolet completion.