Figure 1

Leading-order self-energy graphs that induce the collision terms in the Boltzmann equations, corresponding to (a) coherent forward scattering, and (b) nonforward scattering ($\varphi A\leftrightarrow \varphi A$) and annihilation ($\varphi {\varphi }^{†}\leftrightarrow AA$).Reuse & Permissions

Figure 2

Left panel: mass eigenvalues $m_{1,2}(t)$ as a function of time. Right panel: components of ${\overrightarrow{B}}_{\Sigma }$ as a function of time: $({\overrightarrow{B}}_{\Sigma }{)}_x$ (red, largest peak), $({\overrightarrow{B}}_{\Sigma }{)}_y$ (green, oscillatory line), $({\overrightarrow{B}}_{\Sigma }{)}_z$ (blue, smaller peak). Input parameters are as in Table .Reuse & Permissions

Figure 3

Evolution of flavor polarization and $CP$ asymmetry in the absence of collisions, starting from a $CP$-invariant, pure $L$-handed initial state. Left column: time dependence of the particle polarization vector components $p_x$ (red, darker oscillatory line), $p_y$ (green, lighter oscillatory line), and $p_z$ (blue, dark straighter line), for different values of ${\tau }_{\mathrm{w}}=40/T$, $20/T$, $10/T$, $5/T$ (from top to bottom). Middle column: time dependence of the antiparticle polarization vector components ${\tilde{p}}_x$ (red, darker oscillatory line), ${\tilde{p}}_y$ (green, lighter oscillatory line), and ${\tilde{p}}_z$ (blue, dark straighter line), for different values of ${\tau }_{\mathrm{w}}=40/T$, $20/T$, $10/T$, $5/T$ (from top to bottom). Right column: time dependence of the flavor-diagonal $CP$ asymmetry $n_L(k,t)$ for different values of ${\tau }_{\mathrm{w}}=40/T$, $20/T$, $10/T$, $5/T$ (from top to bottom). In all cases $k=3T$ and all other input parameters (except ${\tau }_{\mathrm{w}}$) are as in Table , corresponding to ${\tau }_{\mathrm{osc}}\simeq 35/T$ (at $t=0$).Reuse & Permissions

Figure 4

Maximum value of $CP$ asymmetry $|n_L(k,t)|$ for $k=3T$ as a function of ${\tau }_{\mathrm{osc}}(t=0)/{\tau }_{\mathrm{w}}$. Except for ${\tau }_{\mathrm{w}}$ that is varied, all other input parameters are as in Table .Reuse & Permissions

Figure 5

Evolution of flavor polarizations with no collisions, flavor-blind collisions, and flavor-sensitive collisions. We plot the components $p_x(k,t)$ (red, darker oscillatory line), $p_y(k,t)$ (green, lighter oscillatory line), and $p_z(k,t)$ (blue, dark straighter line) (left panels) and $n_L(k,t)$ (right panels), for $k=3T$, as a function of time in several regimes: no collisions (1st row); flavor-blind collisions, $y_L=y_R=1$, $g_{\mathrm{eff}}=200$ (2nd row); flavor-sensitive collisions with $y_L=1$, $y_R=0.8$, $g_{\mathrm{eff}}=200$ (3rd row); flavor-sensitive collisions with $y_L=1$, $y_R=0.5$, $g_{\mathrm{eff}}=200$ (4th row). In all cases we use equilibrium initial conditions at $t_{\mathrm{in}}=-15/T$. All other input parameters are as in Table . The dotted line in the 2nd row represents the nonzero density $n_L$ surviving at late times corresponding to a nonvanishing chemical potential ${\mu }_L$. In the 3rd and 4th rows, the late-time density goes to zero since $y_L\ne y_R$. See text for additional details.Reuse & Permissions

Figure 6

Dependence of solutions on the relative size of ${\tau }_{\mathrm{w}}$ and ${\tau }_{\mathrm{coll}}$. Keeping ${\tau }_{\mathrm{w}}$ fixed, we control ${\tau }_{\mathrm{coll}}$ by dialing the effective number of degrees of freedom $g_{\mathrm{eff}}$ in thermal bath. We plot the polarization vectors $p_x(k,t)$ (red, darker oscillatory line), $p_y(k,t)$ (green, lighter oscillatory line), and $p_z(k,t)$ (blue, dark straighter line) (left panels) and $n_L(k,t)$ (right panels), for $k=3T$, as a function of time with $y_L=1$, $y_R=0.5$ and all other input parameters are as in Table , for different values of $g_{\mathrm{eff}}$. $g_{\mathrm{eff}}=200$ (1st row); $g_{\mathrm{eff}}=1000$ (2nd row); $g_{\mathrm{eff}}=2000$ (3rd row). In all cases we use equilibrium initial conditions at $t_{\mathrm{in}}=-15/T$. See text for additional details.Reuse & Permissions

Figure 7

Dependence of the late time $L$-handed chemical potential ${\mu }_L$ on the mass parameter $m_L$, with $m_R/T=2$ and all other input parameters as in Table , with flavor-blind interaction $y_L=y_R=1$.Reuse & Permissions