The QCD axion is investigated within the minimal supersymmetric SO(10) grand unified theory, where the Yukawa sector involves Higgs multiplets 10 and <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mn mathvariant="bold">126</mn> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ \overline{\textbf{126}} $</EquationSource> </InlineEquation>. The relative phase between the VEVs of (10, 1, 3) ⊂ <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mn mathvariant="bold">126</mn> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ \overline{\textbf{126}} $</EquationSource> </InlineEquation> and (<InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mn mathvariant="bold">10</mn> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ \overline{\textbf{10}} $</EquationSource> </InlineEquation>, 1, 3) ⊂ 126 under SU(4)C × SU(2)L × SU(2)R is identified with the axion. The axion is dominantly the relative phase between ∆R and <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mover accent="true"> <mtext>∆</mtext> <mo stretchy="true">¯</mo> </mover> <mi>R</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$ {\overline{\Delta }}_R $</EquationSource> </InlineEquation>, with a small 10-Higgs component due to the VEV hierarchy. The Peccei-Quinn and B − L symmetry breaking scales coincide through <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mfenced close="|" open="|"> <mfenced close="〉" open="〈"> <msub> <mi mathvariant="normal">Δ</mi> <mi>R</mi> </msub> </mfenced> </mfenced> <mo>=</mo> <mfenced close="|" open="|"> <mfenced close="〉" open="〈"> <msub> <mover accent="true"> <mi mathvariant="normal">Δ</mi> <mo stretchy="true">¯</mo> </mover> <mi>R</mi> </msub> </mfenced> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ \left|\left\langle {\Delta}_R\right\rangle \right|=\left|\left\langle {\overline{\Delta}}_R\right\rangle \right| $</EquationSource> </InlineEquation>. The scalar partner of the lightest right-handed neutrino plays the role of the inflaton, realizing hybrid inflation consistent with the observed CMB density fluctuations. After inflation, both fields acquire VEVs, and the domain-wall problem is resolved through the Lazarides-Shafi mechanism, which naturally restricts the model to three generations.

Axion in the minimal SO(10) GUT

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2026年3月13日

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Takeshi Fukuyama

摘要

The QCD axion is investigated within the minimal supersymmetric SO(10) grand unified theory, where the Yukawa sector involves Higgs multiplets 10 and $\bar{126}$ $ \overline{\textbf{126}} $ . The relative phase between the VEVs of (10, 1, 3) ⊂ $\bar{126}$ $ \overline{\textbf{126}} $ and ( $\bar{10}$ $ \overline{\textbf{10}} $ , 1, 3) ⊂ 126 under SU(4)_C × SU(2)_L × SU(2)_R is identified with the axion. The axion is dominantly the relative phase between ∆_R and ${\bar{∆}}_{R}$ $ {\overline{\Delta }}_R $ , with a small 10-Higgs component due to the VEV hierarchy. The Peccei-Quinn and B − L symmetry breaking scales coincide through $|〈Δ_{R}〉| = |〈{\bar{Δ}}_{R}〉|$ $ \left|\left\langle {\Delta}_R\right\rangle \right|=\left|\left\langle {\overline{\Delta}}_R\right\rangle \right| $ . The scalar partner of the lightest right-handed neutrino plays the role of the inflaton, realizing hybrid inflation consistent with the observed CMB density fluctuations. After inflation, both fields acquire VEVs, and the domain-wall problem is resolved through the Lazarides-Shafi mechanism, which naturally restricts the model to three generations.