Thermal gravitino production and collider tests of leptogenesis

Considering gravitino dark matter scenarios, we obtain the full gauge-invariant result for the relic density of thermally produced gravitinos to leading order in the standard model gauge couplings. For the temperatures required by thermal leptogenesis, we find gaugino mass bounds which will be probed at future colliders. We show that a conceivable determination of the gravitino mass will allow for a unique test of the viability of thermal leptogenesis in the laboratory.

Figure 1

The relic gravitino density from thermal production, ${\Omega }_{\tilde{G}}^{\mathrm{TP}}{h}^2$, as a function of $T_{\mathrm{R}}$. The solid and dashed curves show the $\mathrm{SU}(3{)}_{\mathrm{c}}\times \mathrm{SU}(2{)}_{\mathrm{L}}\times \mathrm{U}(1{)}_{\mathrm{Y}}$ results for universal ($M_{1,2,3}=m_{1/2}$) and nonuniversal ($0.5M_{1,2}=M_3=m_{1/2}$) gaugino masses at $M_{\mathrm{GUT}}$, respectively. The dotted curves show our result of the $\mathrm{SU}(3{)}_{\mathrm{c}}$ contribution for $M_3=m_{1/2}$ at $M_{\mathrm{GUT}}$. The gray band indicates the dark matter density ${\Omega }_{\mathrm{DM}}{h}^2$.

Figure 2

Upper limits on the gaugino mass parameter $m_{1/2}$ from ${\Omega }_{\tilde{G}}^{\mathrm{TP}}\le {\Omega }_{\mathrm{DM}}^{\max }$ for the indicated values of $T_{\mathrm{R}}$. The solid and dashed curves show our $\mathrm{SU}(3{)}_{\mathrm{c}}\times \mathrm{SU}(2{)}_{\mathrm{L}}\times \mathrm{U}(1{)}_{\mathrm{Y}}$ results for universal ($M_{1,2,3}=m_{1/2}$) and nonuniversal ($0.5M_{1,2}=M_3=m_{1/2}$) gaugino masses at $M_{\mathrm{GUT}}$, respectively. The dotted curves show the $\mathrm{SU}(3{)}_{\mathrm{c}}$ limits for $M_3=m_{1/2}$ at $M_{\mathrm{GUT}}$.

Figure 3

Probing the viability of thermal leptogenesis. The solid curves show the limits on the gaugino mass parameter $m_{1/2}$ from ${\Omega }_{\tilde{G}}^{\mathrm{TP}}+{\Omega }_{\tilde{G}}^{\mathrm{NTP}}\le {\Omega }_{\mathrm{DM}}^{\max }$ for $T_{\mathrm{R}}={10}^9$, $3\times {10}^9$, and ${10}^{10}\mathrm{GeV}$. The dashed line indicates the $m_{1/2}$ value of the considered scenario. The vertical solid line is given by the ${\tilde{\tau }}_1$ NLSP mass which limits the gravitino LSP mass from above: $m_{\tilde{G}}<m_{{\tilde{\tau }}_1}=143.4\mathrm{GeV}$. The $m_{\tilde{G}}$ values at which temperatures above $3\times {10}^9\mathrm{GeV}$ and ${10}^9\mathrm{GeV}$ remain allowed are indicated by the dark-shaded and medium-shaded regions, respectively. The $m_{\tilde{G}}$ values within the light-shaded region are excluded by BBN constraints.