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<p>A flavor-unified theory based on the simple Lie algebra of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25922_Article_IEq2.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="fraktur">su</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathfrak{su} \)</EquationSource> </InlineEquation>(8) was previously proposed to generate the observed three-generational Standard Model quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern due to their non-universal symmetry properties. A level-1 affine Lie algebra of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25922_Article_IEq3.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi mathvariant="italic">su</mi> <mo stretchy="true">̂</mo> </mover> <msub> <mfenced close=")" open="("> <mn>8</mn> </mfenced> <mrow> <msub> <mi>k</mi> <mi>U</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">\( \hat{su}{(8)}_{k_U=1} \)</EquationSource> </InlineEquation> with the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25922_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 1 supersymmetric extension is found to unify three gauge couplings through the maximally symmetry breaking pattern.</p>

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The unification in an \( \hat{su}{(8)}_{k_U=1} \) affine Lie algebra

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月8日

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  • Ning Chen,
  • Zhanpeng Hou,
  • Zhaolong Teng

摘要

A flavor-unified theory based on the simple Lie algebra of su \( \mathfrak{su} \) (8) was previously proposed to generate the observed three-generational Standard Model quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern due to their non-universal symmetry properties. A level-1 affine Lie algebra of su ̂ 8 k U = 1 \( \hat{su}{(8)}_{k_U=1} \) with the N \( \mathcal{N} \) = 1 supersymmetric extension is found to unify three gauge couplings through the maximally symmetry breaking pattern.