Copositivity for a Class of Fourth-Order Symmetric Tensors Given by Scalar Dark Matter

Song, Yisheng; Li, Xudong

doi:10.1007/s10957-022-02086-z

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Co-positivity Criteria1

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Cited by 5 publications

(1 citation statement)

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“…The co-positivity of a symmetric real tensor has been used to the SM in literature to obtain vacuum stability conditions in Refs. [13,17,[24][25][26][27]. A 4th-order n-dimensional symmetric real tensor T = (t ijkl ) is co-positive [28][29][30][31][32][33] if for all non-negative vectors…”

Section: Co-positivity Criteriamentioning

confidence: 99%

Vacuum stability conditions of the general two-Higgs-doublet potential

Song¹

2023

Preprint

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Section: Co-positivity Criteriamentioning

confidence: 99%

Vacuum stability conditions of the general two-Higgs-doublet potential

Song¹

2023

Preprint

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Vacuum stability conditions of the general two-Higgs-doublet potential

Song

2023

Mod. Phys. Lett. A

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In this paper, we present the novel analytical expressions for the bounded-from-below or the vacuum stability conditions of scalar potential for a general two-Higgs-doublet model by using the concepts of co-positivity and the gauge orbit spaces. More precisely, several sufficient conditions and necessary conditions are established for the vacuum stability of the general 2HDM potential, respectively. We also give an equivalent condition of the vacuum stability of the general 2HDM potential in theory, and then, apply it to derive the analytical necessary conditions of the general 2HDM potential. Meanwhile, the semi-positive definiteness is proved for a class of 4th-order two-dimensional complex tensor.

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Co-positivity of tensors and boundedness-from-below conditions of CP conserving two-Higgs-doublet potential

Song

2023

Int. J. Mod. Phys. A

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In this paper, the analytic sufficient and necessary conditions are obtained for the CP conserving two-Higgs-doublet potential to be bounded from below by using the co-positivity of tensors. This is achieved by treating the potential as a fourth-order homogeneous polynomial about the moduli of the two Higgs doublet fields, where the “angles” is described as the misalignment of the two doublets, then solving three minimum problems with respect to the misalignment. Finally, the analytic conditions are established with the help of the corresponding theory and methods of higher-order tensors.

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Copositivity for a Class of Fourth-Order Symmetric Tensors Given by Scalar Dark Matter

Cited by 5 publications

References 46 publications

Vacuum stability conditions of the general two-Higgs-doublet potential

Vacuum stability conditions of the general two-Higgs-doublet potential

Vacuum stability conditions of the general two-Higgs-doublet potential

Co-positivity of tensors and boundedness-from-below conditions of CP conserving two-Higgs-doublet potential

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