Lepton sourced baryon asymmetry in the fourth generation model

TL;DR

The paper investigates whether the baryon asymmetry of the Universe can be explained within the Standard Model extended by a sequential fourth generation (SM4) by invoking lepton-sourced CP violation arising from a $4\times4$ CKM matrix. It constructs dimension-6 CPV operators $-i(\Phi^\dagger\Phi)\bar{F}_L\Phi f_R/\Lambda^2$ induced by fourth-generation quarks, deriving their coefficients via three-loop heavy-quark diagrams (pseudoscalar penguin and self-energy) and fixes the matching scale $\Lambda \approx 16$ TeV with a restoration scale $\Lambda_s \approx 22$ TeV. The $4\times4$ CKM matrix is determined from dispersive constraints on neutral-quark mixing, yielding the fourth-column elements and a Jarlskog invariant $J \approx -3.3\times 10^{-6}$, consistent with BAU requirements. Using the EFT-based EWBG framework, the paper shows that the leptonic CPV from the heavy fourth-generation leptons $(\tau', \nu')$ produces a baryon-to-entropy ratio $\eta_B \approx 10^{-10}$, while tau-sourced BAU is insufficient at the higher scale. Overall, SM4 can simultaneously realize a first-order EWPT and the observed BAU through heavy-quark dynamics and lepton CPV, with testable implications for collider searches and precision flavor/PMNS studies.

Abstract

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 $-i(Φ^\daggerΦ)\bar F_LΦf_R$ induced by fourth generation quarks, which carry the $CP$ violation (CPV) source from the $4\times 4$ 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 $4\times 4$ CKM matrix elements $V_{ib'}$, $i=u$, $c$ 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 $η_B\approx 10^{-10}$.

Figures (4)

• Figure 1: Diagram for producing the dimension-6 effective operator $\phi^6/(8M^2)$, where a dashed (solid) line represents a Higgs boson (heavy scalar).
• Figure 2: (a) One-loop diagram and (b) three-loop diagram for the effective operator $\phi\bar{f}\gamma_5 f$, where an arrowed solid line denotes a heavy quark and a wavy line denotes a charged scalar.
• Figure 3: (a) Vertex correction and (b) self-energy correction contained in the pseudoscalar penguin.
• Figure 4: Matching of RG evolutions of the Yukawa couplings $g_Q^2$ (dotted), $g_L^2$ (dashed) and $g_t^2$ (solid) at (a) $x_s=8.0$ and (b) $x_s=5.5$.