Axial Currents from CKM Matrix CP Violation and Electroweak Baryogenesis

TL;DR

The paper investigates whether CP violation from the CKM matrix can generate axial quark currents sufficient for electroweak baryogenesis during a first-order electroweak phase transition. Employing a first-principles Kadanoff-Baym gradient expansion within the Schwinger-Keldysh framework, it derives CP-violating sources from a complex mass term and evaluates SM and two-Higgs-doublet-model scenarios. It finds that thermal self-energies can boost CKM-induced CP-violating effects by several orders of magnitude but remain inadequate to account for the observed BAU in the SM; however, two-Higgs-doublet models can provide larger CP-violating sources and a strong first-order transition, potentially enabling successful baryogenesis. The study clarifies the limitations of SM CP violation for electroweak baryogenesis and highlights extended scalar sectors as viable alternatives for generating the BAU at electroweak scales.

Abstract

The first principle derivation of kinetic transport equations suggests that a CP-violating mass term during the electroweak phase transition can induce axial vector currents. Since the important terms are of first order in gradients there is a possibility to construct new rephasing invariants that are proportional to the CP phase in the Cabibbo-Kobayashi-Maskawa matrix and to circumvent the upper bound of CP-violating contributions in the Standard Model, the Jarlskog invariant. Qualitative arguments are given that these new contributions still fail to explain electroweak baryogenesis in extensions of the Standard Model with a strong first order phase transition.

Figures (6)

• Figure 1: Leading contributions to the nondiagonal term in the self-energy at one and at two loop level.
• Figure 2: Dependence of $h_2$ on the Higgs vev$\langle\Phi\rangle$ in % of its value $v=246~{\rm GeV}$ at $T=0$. The external energies and momenta are fixed at $\omega=105$ GeV to $\omega=120$ GeV, $k=100$ GeV, the mass of the quark in the loop is $m_u=100$ GeV.
• Figure 3: Same as fig. (\ref{['fig1']}); mass of the quark in the loop is $m_u=10$ GeV.
• Figure 4: Same as fig. (\ref{['fig1']}); mass of the quark in the loop is $m_u=1$ GeV.
• Figure 5: Dependence of $h_2^\prime$ on the Higgs vev with an on-shell external quark of mass $m_e=4$ GeV and an internal quark mass in the range 1 GeV to 170 GeV.