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<p>Existing literature shows that the vacuum stability of a general scalar potential is equivalent to the strict copositivity of its corresponding coupling tensor. In order to judge the copositivity of a coupling tensor, we provide two criteria of a strict copositive tensor, and show their correctness and effectiveness via two practical examples by checking the vacuum stability of a general scalar potential for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10440_2025_739_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>3</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$\mathbb{Z}_{3}$</EquationSource> </InlineEquation> scalar dark matter.</p>

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Criteria of a Copositive Tensor with Application to Check Vacuum Stability of a General Scalar Potential

  • 期刊论文

  • 发表日期：

    2025年8月25日

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  • Chunye Wang,
  • Jianxing Zhao

摘要

Existing literature shows that the vacuum stability of a general scalar potential is equivalent to the strict copositivity of its corresponding coupling tensor. In order to judge the copositivity of a coupling tensor, we provide two criteria of a strict copositive tensor, and show their correctness and effectiveness via two practical examples by checking the vacuum stability of a general scalar potential for Z 3 $\mathbb{Z}_{3}$ scalar dark matter.