Coannihilation without chemical equilibrium

Chemical equilibrium is a commonly made assumption in the freeze-out calculation of coannihilating dark matter. We explore the possible failure of this assumption and find a new conversion-driven freeze-out mechanism. Considering a representative simplified model inspired by supersymmetry with a neutralinolike and sbottomlike particle we find regions in parameter space with very small couplings accommodating the measured relic density. In this region freeze-out takes place out of chemical equilibrium and dark matter self-annihilation is thoroughly inefficient. The relic density is governed primarily by the size of the conversion terms in the Boltzmann equations. Due to the small dark matter coupling the parameter region is immune to direct detection but predicts an interesting signature of disappearing tracks or displaced vertices at the LHC. Unlike freeze-in or superWIMP scenarios, conversion-driven freeze-out is not sensitive to the initial conditions at the end of reheating.

Figure 1

Left panel: Rates of annihilation (blue curves) and conversion (red curves) terms in the Boltzmann equation relative to the Hubble rate as a function of $x=m_{\chi }/T$ for $m_{\chi }=500\mathrm{GeV}$, $m_{\tilde{b}}=510\mathrm{GeV}$, ${\lambda }_{\chi }\approx 2.6\times {10}^{-7}$. Right panel: Evolution of the resulting abundance (solid curves) of $\tilde{b}$ (blue) and $\chi$ (red). The dashed curves denote the equilibrium abundances.

Figure 2

Relic density as a function of the coupling ${\lambda }_{\chi }$, for $m_{\chi }=500\mathrm{GeV}$, $m_{\tilde{b}}=510\mathrm{GeV}$. The dotted blue line is the result that would be obtained when assuming CE. The red line shows the full solution including all conversion rates; the gray dashed line corresponds to the solution when only decays are considered. The shaded areas highlight the dependence on initial conditions, $Y_{\chi }(1)=(0–100)\times Y_{\chi }^{\mathrm{eq}}(1)$. The central curves correspond to $Y_{\chi }(1)=Y_{\chi }^{\mathrm{eq}}(1)$.

Figure 3

Dependence on the initial conditions for $Y_{\chi }$ at $x=1$. We show solutions for the choices $Y_{\chi }(1)=[0,1,100]\times Y_{\chi }^{\mathrm{eq}}(1)$, and otherwise the same parameters as in Fig. 1.

Figure 4

Viable parameter space in the plane spanned by $m_{\chi }$ and $\mathrm{\Delta }{m}_{\chi \tilde{b}}=m_{\tilde{b}}-m_{\chi }$. We adjust ${\lambda }_{\chi }$ such that $\mathrm{\Omega }{h}^2=0.12$. Above the thick black curve CE holds, while below this curve CE breaks down and the freeze-out is conversion driven. The corresponding coupling ${\lambda }_{\chi }/{10}^{-7}$ (decay length $c\tau$) of the mediator is denoted by the thin green (gray) dotted lines. The blue dashed (dotted-dashed) curve shows our estimates for the limits from $R$-hadron searches at 8 (13) TeV. The constraint from monojet searches is shown as the red double-dotted-dashed curve.

Figure 5

Regions excluded at 95% C.L. by a reinterpretation of the searches for detector stable top-squark $R$-hadrons with CMS at the 8 TeV and 13 TeV LHC (tracker-only analysis).

Figure 6

Dependence of the final DM density on the regularization parameter $m_{\text{cut}}\in [0.1,0.5,5]\mathrm{GeV}$, for $m_{\chi }=500\mathrm{GeV}$, $m_{\tilde{b}}=510\mathrm{GeV}$.

Figure 7

Upper panel: Evolution for the resulting abundance of $\tilde{b}$ (blue) and $\chi$ (red) of the differential (solid) and integrated (dotted) Boltzmann equation. The dashed curves denote the equilibrium abundances. Lower panel: Ratio of the two abundances for $\chi$. The red solid line shows the converged result while the orange thick and thin curves denote the first and the following iterations, respectively. Only the decay term is considered.

Figure 8

Collision operator (normalized by the Hubble rate, green dotted-dashed curves) and the phase-space distribution of the differential (blue solid) and integrated (red dashed) solution as a function of the momentum mode $q$ for three different times, $x=15$, 63 and 100. The phase-space distribution is normalized to the integral over the differential solution, $q^2{f}_{\chi }/\int q^2{f}_{\chi }^{\text{diff}}\mathrm{d}q$. Only the decay term is considered.

Figure 9

Evolution of the abundance of $\tilde{b}$ (blue solid) and $\chi$ (red solid) for two different choices of the starting point of the iteration, shown in the two panels, respectively. Left panel: Initial mediator abundance set to the equilibrium abundance, $Y_{\tilde{b}}(x)=Y_{\tilde{b}}^{\mathrm{eq}}$. The thick and thin orange solid curves denote the first and the following iterations, respectively. The orange dotted curve shows the integrated solution obtained for $Y_{\tilde{b}}(x)=Y_{\tilde{b}}^{\mathrm{eq}}$. Right panel: Initial $\chi$ abundance set to the equilibrium abundance at relativistic temperatures, $Y_{\chi }(x)=Y_{\chi }^{\mathrm{eq}}(x\lesssim 1)$. The thick and thin orange solid curves denote the initial abundance and the following iterations, respectively. Only the decay term is considered. As in Fig. 7 the dashed curves denote the equilibrium abundances.

Figure 10

Relic density obtained from the iterative solution as a function of the iteration step for the three different initial abundances discussed here: $Y_{\chi }(x)=Y_{\chi }^{\mathrm{eq}}(x\lesssim 1)$ (red points, converging from above); $Y_{\tilde{b}}(x)=Y_{\tilde{b}}^{\mathrm{eq}}$ (blue points, converging from below); and $Y_{\tilde{b}}(x)$ set to the solution of the coupled integrated Boltzmann equation (green points, starting in the middle).