Resonant relaxation in electroweak baryogenesis

We compute the leading, chiral charge-changing relaxation term in the quantum transport equations that govern electroweak baryogenesis using the closed time path formulation of nonequilibrium quantum field theory. We show that the relaxation transport coefficients may be resonantly enhanced under appropriate conditions on electroweak model parameters and that such enhancements can mitigate the impact of similar enhancements in the $CP$-violating source terms. We also develop a power counting in the time and energy scales entering electroweak baryogenesis and include effects through second order in ratios $ϵ$ of the small and large scales. We illustrate the implications of the resonantly enhanced $\mathcal{O}({ϵ}^2)$ terms using the Minimal Supersymmetric Standard Model, focusing on the interplay between the requirements of baryogenesis and constraints obtained from collider studies, precision electroweak data, and electric dipole moment searches.

Figure 1

Contributions to the relevant self-energies from scattering of particles from the spacetime varying Higgs vevs.

Figure 2

Contributions to the relevant self-energies from Yukawa interactions.

Figure 3

Representative contributions to self-energies from (super)gauge interactions.

Figure 4

Left panel: $CP$-violating Higgsino source ${\widehat{S}}_{\tilde{H}}=-S_{\tilde{H}}^{CP}/(v^2\dot{\beta }\sin {\varphi }_{\mu })\cos $, as a function of $|\mu |$. Right panel: relaxation rate $R_{\Gamma }=({\Gamma }_h+{\Gamma }_M^{-})/({\Gamma }_h+{\Gamma }_m{)}_{\mathrm{H}.\mathrm{N}.}$, normalized to the value used in 10, as a function of $|\mu |$. We have taken $M_2=200\mathrm{GeV}$, and the values of all other parameters as indicated in the text.

Figure 5

Left panel: Higgsino contribution to $Y_B$ (Cf. Eq. (87)), normalized to the observed value. $F_1$ displays residual resonant behavior for $|\mu |\sim M_2$. All other input parameters are given in the text. Right panel: Stop contribution to $Y_B$ (Cf. Eq. (87)) normalized to the observed value. The upper curve is for $M_{{\tilde{b}}_L}=M_{{\tilde{t}}_L}$, while the lower one is for $M_{{\tilde{b}}_L}\gg M_{{\tilde{t}}_L}$. We have taken here $M_{{\tilde{t}}_R}=100\mathrm{GeV}$, $|\mu |=200\mathrm{GeV}$, and have allowed $M_{{\tilde{t}}_L}$ to reach unrealistically low values to explore the size of the squark resonance. For realistic input parameters $F_2\ll F_1$.

Figure 6

Allowed band in the $|\sin {\varphi }_{\mu }|$–$|\mu |$ plane, obtained by requiring successful electroweak baryogenesis. All other MSSM parameters are given in the text. The light-shaded narrow band corresponds to the experimental input from WMAP, while the two bands combined [$\mathrm{\text{dark}}+\mathrm{\text{light}}$] correspond to input from Big Bang Nucleosynthesis.

Figure 7

Allowed bands in the ${\varphi }_{\mu }$–${\varphi }_A$ plane implied by consistency with the 95% C.L. limits on electron EDM ($|d_e|<1.9\times {10}^{-27}e·\mathrm{cm}$ [34]), mercury EDM ($|d_{\mathrm{Hg}}|<2.1\times {10}^{-28}e·\mathrm{cm}$ [35]), and baryogenesis. The shaded [dark and light combined] EWB band corresponds to BBN input [2], while the narrow light-shaded band on the left corresponds to WMAP input [3]. In the left panel we use $|\mu |=M_2=200\mathrm{GeV}$ (resonance peak), while in the right panel we use $M_2=200\mathrm{GeV}$ and $|\mu |=250\mathrm{GeV}$ (off resonance). In both cases the other supersymmetric masses are as specified in the text.