We demonstrate that the observed baryon asymmetry in the Universe can be accommodated in the extended Standard Model with sequential fourth generation fermions (SM4). We first construct the dimension-6 effective operators of the type <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mo>−</mo> <mi>i</mi> <mfenced close=")" open="("> <mrow> <msup> <mi mathvariant="normal">Φ</mi> <mo>†</mo> </msup> <mi mathvariant="normal">Φ</mi> </mrow> </mfenced> <msub> <mover accent="true"> <mi>F</mi> <mo stretchy="true">¯</mo> </mover> <mi>L</mi> </msub> <mi mathvariant="normal">Φ</mi> <msub> <mi>f</mi> <mi>R</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$ -i\left({\Phi}^{\dagger}\Phi \right){\overline{F}}_L\Phi {f}_R $</EquationSource> </InlineEquation> induced by fourth generation quarks, which carry the CP violation (CPV) source from the 4 × 4 Cabibbo-Kobayashi-Maskawa (CKM) matrix, Φ (FL, fR) being a Higgs double (left-handed fermion doublet, right-handed fermion singlet). The required inputs of the fourth generation fermion masses were derived in our previous dispersive analyses on heavy quark decays and neutral meson mixing. The similar framework allows the determination of the 4 × 4 CKM matrix elements <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>V</mi> <mrow> <mi>i</mi> <msup> <mi>b</mi> <mo>′</mo> </msup> </mrow> </msub> </math></EquationSource> <EquationSource Format="TEX">$ {V}_{i{b}^{\prime }} $</EquationSource> </InlineEquation>, i = u, c and t, such that the strength of the CPV source can be evaluated unambiguously. The dimension-6 operators associated with fourth generation leptons, as implemented into the formalism for the electroweak baryogenesis in the literature, lead to the baryon-over-entropy ratio ηB ≈ 10−10.

Lepton sourced baryon asymmetry in the fourth generation model

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2026年6月17日

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Hsiang-nan Li

摘要

We demonstrate that the observed baryon asymmetry in the Universe can be accommodated in the extended Standard Model with sequential fourth generation fermions (SM4). We first construct the dimension-6 effective operators of the type $- i (Φ^{†} Φ) {\bar{F}}_{L} Φ f_{R}$ $ -i\left({\Phi}^{\dagger}\Phi \right){\overline{F}}_L\Phi {f}_R $ induced by fourth generation quarks, which carry the CP violation (CPV) source from the 4 × 4 Cabibbo-Kobayashi-Maskawa (CKM) matrix, Φ (F_L, f_R) being a Higgs double (left-handed fermion doublet, right-handed fermion singlet). The required inputs of the fourth generation fermion masses were derived in our previous dispersive analyses on heavy quark decays and neutral meson mixing. The similar framework allows the determination of the 4 × 4 CKM matrix elements $V_{i b^{'}}$ $ {V}_{i{b}^{\prime }} $ , i = u, c and t, such that the strength of the CPV source can be evaluated unambiguously. The dimension-6 operators associated with fourth generation leptons, as implemented into the formalism for the electroweak baryogenesis in the literature, lead to the baryon-over-entropy ratio η_B ≈ 10⁻¹⁰.