Consequences of DM/antiDM Oscillations for Asymmetric WIMP Dark Matter

TL;DR

This paper investigates how oscillations between dark matter (DM) and anti-DM, enabled by a Δ(DM)=2 mass term, impact the relic abundance in asymmetric DM scenarios. Using a density-matrix formalism that incorporating annihilations and elastic scatterings, the authors show that DM–antiDM oscillations can repopulate antiparticles, reactivate annihilations, and drive the final abundance in a way that decouples the relic density from a strict initial asymmetry. The main result is that EW-scale DM masses and larger annihilation cross sections can still yield the observed Ω_DM h^2 when δm is in the meV–eV range, significantly broadening viable parameter space. Cosmological and astrophysical constraints, particularly from the CMB and gamma-ray observations, are then analyzed to delineate the allowed regions, highlighting the interplay between early-universe dynamics and present-day indirect searches. The work provides a framework for exploring more general DM sectors where coherence and collisions dynamically shape the DM abundance.

Abstract

Assuming the existence of a primordial asymmetry in the dark sector, a scenario usually dubbed Asymmetric Dark Matter (aDM), we study the effect of oscillations between dark matter and its antiparticle on the re-equilibration of the initial asymmetry before freeze-out, which enable efficient annihilations to recouple. We calculate the evolution of the DM relic abundance and show how oscillations re-open the parameter space of aDM models, in particular in the direction of allowing large (WIMP-scale) DM masses. A typical wimp with a mass at the EW scale (\sim 100 GeV - 1 TeV) presenting a primordial asymmetry of the same order as the baryon asymmetry naturally gets the correct relic abundance if the DM-number-violating Delta(DM) = 2 mass term is in the \sim meV range. The re-establishment of annihilations implies that constraints from the accumulation of aDM in astrophysical bodies are evaded. On the other hand, the ordinary bounds from BBN, CMB and indirect detection signals on annihilating DM have to be considered.

Figures (7)

• Figure 1: Illustrative plots of the solutions of the evolution equations in the case of annihilations only (top left panel, discussed in Sec. \ref{['sec:annonly']}), annihilations with oscillations (top right panel, Sec. \ref{['sec:ann+osc']}) and in the case which includes elastic scatterings (bottom left panel, Sec. \ref{['sec:wscatterings']}). The blue (magenta) line represents the comoving population of $n^+$ ($n^-$), the black line their sum. The arrow points to the value of the primordial asymmetry, the green band is the correct relic abundance ($\pm\, 1 \sigma$).
• Figure 2: Left panel: illustration of the approximate relation in eq. (\ref{['xosc']}) and eq. (\ref{['xoscann']}), i.e. the value of $x$ at which oscillations start as a function of $\delta m$ for a few indicative values of the DM mass. The dotted lines trace the modification to that relation in the case where annihilations are active, see Sec. \ref{['sec:ann+osc']}. Right panel: graphical illustration of the approximate relation in eq. (\ref{['eq:ratio']}), i.e. the efficiency of oscillations in depleting the aDM excess (for definiteness, in the case of no elastic scatterings, i.e. $\xi = 0$, except for the dashed line marked by the label $\xi = 10^{-2}$). The crossings of the diagonal dotted lines with the four solid lines individuate the values of $\delta m$ for which $\Omega_{\hbox{\tiny \rm DM}}$ reproduces the correct abundance, for the indicated values of $m_{\hbox{\tiny \rm DM}}$.
• Figure 3: Some illustrative cases of the time evolution of the populations of DM particles and antiparticles. Notations are like in fig. \ref{['figannosc']}, i.e. the blue (magenta) line represents the comoving population of $n^+$ ($n^-$), the black line their sum. The arrow points to the value of the primordial asymmetry, the green band is the correct relic abundance ($\pm\, 1 \sigma$). Notice that some plots have linear scale while other have logarithmic ones, depending on structure which is necessary to show. See text for more details.
• Figure 4: Contour lines along which a correct $\Omega_{\hbox{\rm \tiny DM}}h^2$ can be obtained, for various values of the initial asymmetry $\eta_0$ (various colors) and several values of the oscillation parameter $\delta m$ (labelled lines marked by different dashings). The solid thick black line at the bottom represents the standard case ($\eta = 0, \delta m = 0$). The labelled points (A to F) refer to the cases shown in Fig. \ref{['results']}. Top panels: Oscillations and annihilations only, i.e. with $\xi = 0$. Bottom panels: Adding elastic scatterings, i.e. with $\xi = 10^{-2}$. The left panels consider initial asymmetries equal or close to the baryonic one. The right panels focus on large initial asymmetries. The faint gray lines correspond to the semi-analytic approximations in eq. (\ref{['anapproximationA']}) and eq. (\ref{['anapproximationB']}).
• Figure 5: Approximate illustration of the relevant parameter space in the scenarios we are considering, for the case without elastic scatterings (left panel) and for the case with scatterings (right panel). The upper left area shaded in grey corresponds to the region in which the evolution reduces to the standard freeze-out scenario. The white region refers to a regime in which oscillations recouple annihilations on cosmological scales and we always assume that a suitable value for the annihilation cross section is adopted for a given choice of $m_{\hbox{\tiny \rm DM}}$ and $\delta m$ such that we reproduce the correct relic abundance. The lower area shaded in pink/orange is excluded by the constraints discussed in Sec. \ref{['sec:constraints']} (red is for FERMI and orange for H.E.S.S., see Fig. \ref{['paramspacezoom']}) either because it requires a too high cross section in 'our' regime, or because the value of $\delta m$ is such that oscillations do not recouple annihilations on the cosmological scales, and we are back to a usual WIMP scenario. The fuzzy edge in the large $m_{\hbox{\tiny \rm DM}}$ portion indicates that it is not possible to individuate a single $\delta m$ in the area where the H.E.S.S. constraints matter. We stress that these figures only illustrate the approximate areas of interest on the basis of eq. (\ref{['deltammaxannscatt']}), while the results in all other plots in fig. \ref{['paramspace']} and \ref{['paramspacezoom']} are determined by the full numerical solutions.