Evolution of cosmological baryon asymmetries. II. The role of Higgs bosons

The time evolution of the baryon asymmetry of the universe due to superheavy Higgs bosons is obtained by integrating the Boltzmann equations. The interactions included are decays, inverse decays, and annihilations of the Higgs bosons. The minimal SU(5) model is used to calculate the interactions, although our results are more generally applicable. Decays and inverse decays of these bosons damp preexisting asymmetries by $\exp \mathrm{}(-0.3K)\mathrm{}$ to $\exp \mathrm{}(-2.0K)\mathrm{}$ where $K=2.9\mathrm{}\times {10}^{17}{\alpha }_H\frac{\mathrm{GeV}}{M_H}$ (${\alpha }_H$ and $M_H$ are the coupling strength and mass of the Higgs boson). If both $C$ and $\mathrm{CP}$ are violated, then in an initially symmetrical universe a baryon asymmetry evolves and its value depends upon $K$ and $\frac{{\alpha }^2}{{\alpha }_H}$ ($\alpha$ is the gauge coupling strength). For $K\ll \frac{{\alpha }_H}{{\alpha }^2}$ the asymmetry produced is $\frac{k{n}_B}{s}\simeq 2\times {10}^{-3\mathrm{}}\epsilon$, and for $K\gg 1$ it is $\frac{k{n}_B}{s}\simeq 2\times {10}^{-3\mathrm{}}\epsilon {\mathrm{}\left(3K\right)\mathrm{}}^{-1.2\mathrm{}}$ ($\frac{\epsilon }{2}$=the baryon excess produced by the decay of a pair of $H$, $\overline{H}$ bosons). In SU(5) for $M_H\gtrsim 3\times {10}^{13}$ GeV preexisting asymmetries are not damped and the observed asymmetry $\frac{k{n}_B}{s}={10}^{-9.8\mathrm{}\pm 1.6}$ can be produced if $\epsilon \simeq {10}^{-7\mathrm{}}$. In a companion paper the role of gauge bosons is considered.