Gravitino Dark Matter in the CMSSM and Implications for Leptogenesis and the LHC

TL;DR

This paper analyzes gravitino dark matter in the CMSSM, accounting for both thermal production in the early plasma and non-thermal production from NLSP decays, while rigorously applying BBN, CMB, and collider constraints. By computing the gravitino relic density as the sum of TP and NTP contributions and evaluating NLSP decays into gravitinos, the authors map viable regions in the CMSSM parameter space, distinguishing neutralino and stau NLSP scenarios. They find that reheating temperatures up to about $5\times10^9$ GeV can be compatible with gravitino DM in some cases, which is favorable for thermal leptogenesis, but many regions are tightly squeezed by EM/HAD and CMB bounds; the LHC could probe parts of the favored parameter space, notably through long-lived stau signatures. Overall, the work delineates a viable gravitino DM framework in the CMSSM, highlights the sensitivity to BBN/CMB inputs, and outlines testable collider phenomenology that could validate or falsify gravitino CDM and associated leptogenesis scenarios.

Abstract

In the framework of the CMSSM we study the gravitino as the lightest supersymmetric particle and the dominant component of cold dark matter in the Universe. We include both a thermal contribution to its relic abundance from scatterings in the plasma and a non--thermal one from neutralino or stau decays after freeze--out. In general both contributions can be important, although in different regions of the parameter space. We further include constraints from BBN on electromagnetic and hadronic showers, from the CMB blackbody spectrum and from collider and non--collider SUSY searches. The region where the neutralino is the next--to--lightest superpartner is severely constrained by a conservative bound from excessive electromagnetic showers and probably basically excluded by the bound from hadronic showers, while the stau case remains mostly allowed. In both regions the constraint from CMB is often important or even dominant. In the stau case, for the assumed reasonable ranges of soft SUSY breaking parameters, we find regions where the gravitino abundance is in agreement with the range inferred from CMB studies, provided that, in many cases, a reheating temperature $\treh$ is large, $\treh\sim10^{9}\gev$. On the other side, we find an upper bound $\treh\lsim 5\times 10^{9}\gev$. Less conservative bounds from BBN or an improvement in measuring the CMB spectrum would provide a dramatic squeeze on the whole scenario, in particular it would strongly disfavor the largest values of $\treh\sim 10^{9}\gev$. The regions favored by the gravitino dark matter scenario are very different from standard regions corresponding to the neutralino dark matter, and will be partly probed at the LHC.

Figures (4)

• Figure 1: The plane ($m_{1/2},m_0$) for $\tan\beta=10$ (left window) and $\tan\beta=50$ (right window) and for $A_0=0$ and $\mu>0$. The light brown regions labelled "LEP $\chi^+$" and "LEP Higgs" are excluded by unsuccessful chargino and Higgs searches at LEP, respectively. In the right window the darker brown regions labelled "$b\to s\gamma$" and the dark grey region labelled "TACHYONIC" are also excluded. In the dark green band labelled "$\Omega_{\widetilde{G}}h^2$" the total relic abundance of the gravitino from both thermal and non--thermal production is in the favored range, while in the light green regions which are denoted "NTP" the same is the case for the relic abundance from NTP processes alone. Regions excluded by applying conservative bounds on electromagnetic showers from $D/H+Y_p+{^7}{\! Li}$ obtained with inputs (\ref{['cefodeutinput:eq']})--(\ref{['cefoliinput:eq']}) are denoted in orange and labelled "EM". Regions excluded by imposing less conservative bounds on hadronic showers from $D/H+Y_p$ derived assuming $B_{had}=1$ and input (\ref{['kkmdeutinput:eq']})--(\ref{['kkmypinput:eq']}) are denoted in blue and labelled "HAD". (The overlapping EM/HAD--excluded regions appear as light violet.) A solid magenta curve labelled "CMB" delineates the region (on the side of the label) inconsistent with the CMB spectrum. The cosmologically favored (green) regions are ruled out when we apply bounds from $D/H+Y_p$ derived with (\ref{['kkmdeutinput:eq']})--(\ref{['kkmypinput:eq']}) as input, as described in the text.
• Figure 2: The same as in fig. \ref{['fig:tr1x9mg02mhalf']} but for $m_{\widetilde{G}}=0.2m_0$ (top row) and $m_{\widetilde{G}}=m_0$ (bottom row). In the light grey areas the gravitino is not the LSP. Applying bounds from $D/H+Y_p$ derived with (\ref{['kkmdeutinput:eq']})--(\ref{['kkmypinput:eq']}) as input rules out most of the cosmologically favored regions, except for small patches for $\tan\beta=50$ in the $m_{\widetilde{G}}=0.2m_0$ and $m_0$ windows, as described in the text.
• Figure 3: Left panel: A comparison of the relative energy $\xi^X_{i}$ ($X=\chi,{\tilde{\tau}}_1$ and $i={em},\, {had}$) with BBN constraints for the case $\tan\beta=10$, $\mu>0$ and $m_{\widetilde{G}}=m_0=62.85\,\hbox{GeV}$. The black long--dashed curves corresponds to $\xi^X_{em}$ and should be compared with the red thick (thin) solid line denoting the upper bounds from $D/H+Y_p$ on the relative energy release from electromagnetic showers of Cyburt, et al., cefo02 (Kawasaki, et al., kkm04), as explained in the text. Clearly, the excluded ranges of $\tau_{X}$ strongly depend on the assumed experimental bounds. The magenta short--dashed curves corresponds to $\xi^X_{had}$ and should be compared with the thick blue solid curve denoting the upper bounds from $D/H+Y_p$ on the relative energy release from hadronic showers only (no photo-dissociation) of kkm04, as explained in the text.
• Figure 4: The same as in fig. \ref{['fig:tr1x9mg02mhalf']} but for $T_{\rm R}=5\times 10^9\,\hbox{GeV}$ and $\tan\beta=10$ and $m_{\widetilde{G}}=m_0$ (left window) and $\tan\beta=10$ and $m_{\widetilde{G}}=0.2m_{1/2}$ (right window). Applying bounds from $D/H+Y_p$ derived with (\ref{['kkmdeutinput:eq']})--(\ref{['kkmypinput:eq']}) as input rules out the cosmologically favored regions, as described in the text.