Kinetic description of fermion flavor mixing and CP-violating sources for baryogenesis

TL;DR

The paper develops a kinetic description of fermion flavor mixing with a spacetime-dependent mass matrix, using Schwinger-Keldysh/Kadanoff-Baym formalism in Wigner space and a gradient expansion to derive transport equations without forcing a single-flavor semiclassical limit. By transforming to a chiral basis and employing flavor rotations, the authors decouple diagonal and transverse densities, revealing distinct on-shell structures for off-diagonal densities while diagonal modes obey standard dispersion relations. They introduce a Q-based CP operation to cleanly extract CP-violating sources, identifying both local (transverse, second-order) and nonlocal (diffusion-influenced) contributions, and apply the formalism to the MSSM chargino sector to obtain explicit expressions for CP-violating currents. Numerical results with a fluid Ansatz show how diagonal and off-diagonal contributions compete across parameter space, indicating regimes where diagonal second-order sources can dominate and potentially drive baryogenesis, while acknowledging limitations due to simplified damping and collision treatments and outlining plans for a full BAU calculation.

Abstract

We derive transport equations for fermionic systems with a space-time dependent mass matrix in flavor space allowing for complex elements leading to CP violation required for electroweak baryogenesis. By constructing appropriate projectors in flavor space of the relevant tree level Kadanoff-Baym equations, we split the constraint equations into "diagonal" and "transversal" parts in flavor space, and show that they decouple. While the diagonal densities exhibit standard dispersion relations at leading order in gradients, the transverse densities exhibit a novel on-shell structure. Next, the kinetic equations are considered to second order in gradients and the CP-violating source terms are isolated. This requires a thorough discussion of a flavor independent definition of charge-parity symmetry operation. To make a link with baryogenesis in the supersymmetric extension of the Standard Model, we construct the Green functions for the leading order kinetic operator and solve the kinetic equations for two mixing fermions (charginos). We take account of flavor blind damping, and consider the cases of inefficient and moderate diffusion. The resulting densities are the CP-violating chargino currents that source baryogenesis.

Figures (6)

• Figure 1: Bubble wall: The higgs vev profile (\ref{['H']}) and $\beta$ (\ref{['beta']}) as a function of $z$.
• Figure 2: Dependence of the current for a typical source on the number of momenta $N$ used.
• Figure 3: The CP-violating currents of first order $j^0$, $j^0_5$ and of second order ${j_5^0}^{(2)}$. $M_2=200$ GeV. $\mu_c=205$ GeV, $\Lambda/T_c^2 \in [0.22, 4.0]$.
• Figure 4: The CP-violating currents of first order $j^0$, $j^0_5$ and of second order ${j_5^0}^{(2)}$. $M_2=200$ GeV. $\mu_c=220$ GeV, $\Lambda/T_c^2 \in [0.93, 4.2]$.
• Figure 5: The CP-violating currents of first order $j^0$, $j^0_5$ and of second order ${j_5^0}^{(2)}$. $M_2=200$ GeV. $\mu_c=250$ GeV, $\Lambda/T_c^2 \in [2.4, 5.1]$.