Gravitino Dark Matter in the CMSSM With Improved Constraints from BBN

TL;DR

This paper reevaluates gravitino dark matter within the CMSSM by jointly considering thermal and non-thermal gravitino production and by applying refined BBN and CMB constraints. Using a detailed treatment of electromagnetic and hadronic energy injections from NLSP decays, the authors map out the regions of parameter space that yield the observed cold dark matter abundance, finding neutralino NLSP regions largely excluded while substantial stau NLSP regions remain viable, typically requiring a sizeable reheating temperature. The analysis highlights tension with thermal leptogenesis due to an upper bound on TR, and reveals that many viable stau NLSP scenarios correspond to a true vacuum that is color- and charge-breaking, with potential LHC signatures in the form of long-lived charged tracks. An erratum corrects the TP production formula and a numerical alpha_s issue, shifting the viable regions to smaller m1/2 and tightening TR bounds to a few ×10^8 GeV, thereby reinforcing the study's core conclusions about gravitino CDM in the CMSSM.

Abstract

In the framework of the Constrained MSSM we re--examine the gravitino as the lightest superpartner and a candidate for cold dark matter in the Universe. Unlike in other recent studies, we include both a thermal contribution to its relic population from scatterings in the plasma and a non--thermal one from neutralino or stau decays after freeze--out. Relative to a previous analysis [1] we update, extend and considerably improve our treatment of constraints from observed light element abundances on additional energy released during BBN in association with late gravitino production. Assuming the gravitino mass in the GeV to TeV range, and for natural ranges of other supersymmetric parameters, the neutralino region is excluded, while for smaller values of the gravitino mass it becomes allowed again. The gravitino relic abundance is consistent with observational constraints on cold dark matter from BBN and CMB in some well defined domains of the stau region but, in most cases, only due to a dominant contribution of the thermal population. This implies, depending on the gravitino mass, a large enough reheating temperature. If $\mgravitino>1$ GeV then $T_R>10^7$ GeV, if allowed by BBN and other constraints but, for light gravitinos, if $\mgravitino>100$ keV then $T_R>3\times 10^3$ GeV. On the other hand, constraints mostly from BBN imply an upper bound $T_R \lsim {a few}x 10^8\times10^9$ GeV which appears inconsistent with thermal leptogenesis. Finally, most of the preferred stau region corresponds to the physical vacuum being a false vacuum. The scenario can be partially probed at the LHC.

Figures (6)

• Figure 1: The plane ($m_{1/2},m_0$) for $\tan\beta=10$, $m_{\widetilde{G}}=m_0$ (left window) and $\tan\beta=50$, $m_{\widetilde{G}}=0.2m_0$ (right window) and for $A_0=0$, $\mu>0$. 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 region labelled "$b\to s\gamma$" is excluded assuming minimal flavor violation. The dark grey region below the dashed line is labelled "TACHYONIC" because of some sfermion masses becoming tachyonic and is also excluded. In the rest of the grey region (above the dashed line) the stau mass bound $m_{{\tilde{\tau}}_1}>87\,\hbox{GeV}$ is violated. In the region "No EWSB" the conditions of EWSB are not satisfied. Magenta lines mark contours of the NLSP lifetime $\tau_{X}$ (in seconds). The dotted line is the boundary of neutralino ($\chi$) or stau ($\tilde{\tau}$) NLSP.
• Figure 2: The same as in fig. \ref{['fig:lifetime']} but with constraints from BBN and CMB superimposed. The regions excluded by the various BBN constraint are denoted in violet. The region disallowed by $D+Y_p$ and additional regions excluded by ${^3}{\! He}$ and ${^6}{\! Li}$ are denoted accordingly by their respective names. A solid magenta curve labelled "CMB" delineates the region (on the side of label) inconsistent with the CMB spectrum. In both windows, the dark green bands labelled "$T_R=10^7 \,\hbox{GeV}$" and "$10^8$" denote the total relic abundance of the gravitino from both thermal and non--thermal production with denoted reheating temperature is in the favored range, while in the light green regions (marked "NTP") the same is the case for the relic abundance from NTP processes alone.
• Figure 3: The same as fig. \ref{['fig:newbbn']} but with UFB constraints (solid blue line and UFB label plus a big arrow) added. For $m_{1/2}\mathrel{\hbox{$\sim$} \hbox{$<$}}5\,\hbox{TeV}$ and small $m_0$ the UFB constraints disfavor the stau NLSP region that has remained allowed after applying the BBN and CMB constraints.
• Figure 4: The same as fig. \ref{['fig:bbn+ufb']} but for fixed gravitino mass, $m_{\widetilde{G}}=10\,\hbox{GeV}$ and $\tan\beta=10$ (left window) and $m_{\widetilde{G}}=100\,\hbox{GeV}$ and $\tan\beta=50$ (right window).
• Figure 5: Left window: The total gravitino relic abundance $\Omega_{\widetilde{G}}h^2$ (solid lines) as a function of the gravitino mass $m_{\widetilde{G}}$ for $\tan\beta=10$, $A_0=0$, $\mu>0$ and for the point $m_{1/2}=500\,\hbox{GeV}$, $m_0=200\,\hbox{GeV}$ ($\chi$ NLSP). Thermal production contribution (dot--dashed lines) to $\Omega_{\widetilde{G}}h^2$ is shown for different choices of the reheating temperature ($T_{\rm R}=10^9,\ 10^7, 10^5\,\hbox{GeV}$), while the non--thermal production one (dotted line) is marked by NTP. The horizontal green band shows the preferred range for $\Omega_{{\rm CDM}} h^2$ (marked WMAP). Right window: The highest reheating temperature (blue line) versus $m_{\widetilde{G}}$ such that the relic density constraint is satisfied for the same choice of parameters as in the left window. The colored regions are excluded by BBN (violet), CMB (right side of magenta line), and the gravitino not being the LSP. We can see that the sub--GeV gravitino, $T_{\rm R}$ as small as $10^5\,\hbox{GeV}$ are sufficient to provide the expected amount of DM in the Universe.