Cosmological decay of Higgs-like scalars into a fermion channel

Abstract

We study the decay of a Higgs-like scalar Yukawa coupled to massless fermions in post-inflationary cosmology, combining a non-perturbative method with an adiabatic expansion. The renormalized survival probability ${\mathcal{P}}_{\Phi }(t)$ of a (quasi) particle ``born'' at time $t_b$ and decaying at rest in the comoving frame, ${\mathcal{P}}_{\Phi }(t)=[\frac{t}{t_b}{]}^{-\frac{Y^2}{8{\pi }^2}}{e}^{\frac{Y^2}{4{\pi }^2}(t/t_b{)}^{1/4}}{e}^{-{\Gamma }_0(t-t_b)}{\mathcal{P}}_{\Phi }(t_b)$, with ${\Gamma }_0$ the decay rate at rest in Minkowski space-time. For an ultrarelativistic particle we find ${\mathcal{P}}_{\Phi }(t)=e^{-\frac{2}{3}{\Gamma }_0{t}_{nr}(t/t_{nr}{)}^{3/2}}{\mathcal{P}}_{\Phi }(t_b)$ before it becomes non-relativistic at a time $t_{nr}$ as a consequence of the cosmological redshift. For $t\gg t_{nr}$ we find ${\mathcal{P}}_{\Phi }(t)=\left[\frac{t}{t_{nr}}{]}^{-\frac{Y^2}{8{\pi }^2}}{e}^{\frac{Y^2}{4{\pi }^2}(t/t_{nr}{)}^{1/4}}\right[\frac{t}{t_{nr}}{]}^{{\Gamma }_0{t}_{nr}/2}{e}^{-{\Gamma }_0(t-t_{nr})}{\mathcal{P}}_{\Phi }(t_{nr})$. The extra power is a consequence of the memory on the past history of the decay process. We compare these results to an S-matrix inspired phenomenological Minkowski-like decay law modified by an instantaneous Lorentz factor to account for cosmological redshift. Such phenomenological description \emph{under estimates the lifetime of the particle}. For very long lived, very weakly coupled particles, we obtain an \emph{upper bound} for the survival probability as a function of redshift $z$ valid throughout the expansion history ${\mathcal{P}}_{\Phi }(z)\gtrsim e^{-\frac{{\Gamma }_0}{H_0}{\rm Y}(z,z_b)}{\mathcal{P}}_{\Phi }(z_b)$, where ${\rm Y}(z,z_b)$ only depends on cosmological parameters and $t_{nr}$.

published version

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