Thermal Gravitino Production and Collider Tests of Leptogenesis

TL;DR

This work provides a gauge-invariant, finite-temperature calculation of the relic density of thermally produced gravitino LSPs, $Ω_{\tilde G}^{TP}$, to leading order in SM gauge couplings and demonstrates how updated gaugino mass bounds arise as tests of thermal leptogenesis. By employing a full SU(3)×SU(2)×U(1) treatment and HTL-resummed rates, the authors show a ~30% enhancement in the SU(3) piece and significant electroweak contributions, tightening collider-based constraints on the gaugino spectrum. They connect cosmological requirements with laboratory probes, showing that LHC/ILC measurements of neutralinos, charginos, and NLSP decays to gravitinos can confirm or exclude standard thermal leptogenesis, particularly in scenarios with a long-lived charged slepton NLSP. The results imply that, given a measured gravitino mass, one can perform a decisive test of leptogenesis viability in the laboratory, and that entropy production after NLSP decoupling can relax some cosmological bounds while preserving the potential for collider tests.

Abstract

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.

Figures (3)

• Figure 1: The relic gravitino density from thermal production, $\Omega_{\widetilde{G}}^{\mathrm{TP}}h^2$, as a function of $T_{\mathrm{R}}$. The solid and dashed curves show the SU(3)$_\mathrm{c}\times$SU(2)$_\mathrm{L}\times$U(1)$_\mathrm{Y}$ results for universal ($M_{1,2,3}=m_{1/2}$) and non-universal ($0.5\, M_{1,2}=M_3=m_{1/2}$) gaugino masses at $M_{\mathrm{GUT}}$, respectively. The dotted curves show our result of the 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 $\Omega_{\widetilde{G}}^{\mathrm{TP}}\leq\Omega_{\mathrm{DM}}^{\max}$ for the indicated values of $T_{\mathrm{R}}$. The solid and dashed curves show our SU(3)$_\mathrm{c}\times$SU(2)$_\mathrm{L}\times$U(1)$_\mathrm{Y}$ results for universal ($M_{1,2,3}=m_{1/2}$) and non-universal ($0.5\, M_{1,2}=M_3=m_{1/2}$) gaugino masses at $M_{\mathrm{GUT}}$, respectively. The dotted curves show the 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 $\Omega_{\widetilde{G}}^{\mathrm{TP}}+\Omega_{\widetilde{G}}^{\mathrm{NTP}}\leq\Omega_{\mathrm{DM}}^{\max}$ 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 ${\widetilde{\tau}_1}$ NLSP mass which limits the gravitino LSP mass from above: $m_{\widetilde{G}}<m_{\tilde{\tau}_1}=143.4~\mathrm{GeV}$. The $m_{\widetilde{G}}$ values at which temperatures above $3\times 10^9~\mathrm{GeV}$ and $10^9~\mathrm{GeV}$ remain allowed are indicated by the dark-shaded (dark-green) and medium-shaded (light-green) regions, respectively. The $m_{\widetilde{G}}$ values within the light-shaded region are excluded by BBN constraints.