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arXiv · 2507.17870

On the addition of an $SU(2)$ quadruplet of scalars to the Standard Model

Darius Jurčiukonis·Luís Lavoura
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Abstract

We consider the extension of the Standard electroweak Model through an $SU(2)$ quadruplet of scalars with hypercharge either $3/2$ or $1/2$ (with an additional reflection symmetry in the latter case). We establish, through $\textit{exact analytical equations}$, the boundaries of the phase spaces of the gauge-invariant terms that appear in the (renormalizable) scalar potentials. We devise procedures for the determination of necessary and sufficient bounded-from-below conditions on those potentials; we emphasize that one mostly needs to scan the scalar potential over a few $\textit{lines}$, instead of $\textit{surfaces}$, in order to establish the boundedness-from-below; this fact allows one $\textit{to reduce by three orders of magnitude the computational time}$ devoted to that establishment.

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Darius Jurčiukonis, Luís Lavoura. 2025-07-23. On the addition of an $SU(2)$ quadruplet of scalars to the Standard Model. https://doi.org/10.21468/scipostphyscore.9.2.022

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