Neutralino Dark Matter from Heavy Gravitino Decay

TL;DR

The paper addresses the problem that thermal neutralino dark matter often overproduces in light of WMAP data and that gravitino decays can disrupt BBN. It proposes a non-thermal mechanism in which a heavy modulus drives entropy production to dilute relics, while gravitinos produced in modulus decay later decay into neutralinos, setting the dark matter abundance via $Y_{3/2}$ rather than MSSM-spectrum details. Viable regions exist for a heavy gravitino with $m_{3/2} \sim 55-100$ TeV and a modulus mass $m_\phi \sim 10^2-4\times 10^3$ TeV, compatible with BBN constraints and $\Omega_{\rm LSP} h^2 \approx 0.11$, effectively solving the overproduction problem. The framework yields testable implications for collider phenomenology and DM searches, and suggests a SUSY-breaking pattern with mixed gravity and anomaly mediation.

Abstract

We propose a new scenario of non-thermal production of neutralino cold dark matter, in which the overproduction problem of lightest supersymmetric particles (LSPs) in the standard thermal history is naturally solved. The mechanism requires a heavy modulus field which decays mainly to ordinary particles releasing large entropy to dilute gravitinos produced just after inflation and thermal relics of LSPs. Significant amount of gravitinos are also pair-produced at the decay, which subsequently decay into the neutralinos. We identify the regions of the parameter space in which the requisite abundance of the neutralino dark matter is obtained without spoiling the big-bang nucleosynthesis by injection of hadronic showers from gravitino decay. The neutralino abundance obtained in this mechanism is insensitive to the details of the superparticle mass spectrum, unlike the standard thermal abundance. We also briefly mention the testability of the scenario in future experiments.

Figures (5)

• Figure 1: Upper bound on the yield variable $y_{3/2}=n_{3/2}/s$. For heavy gravitinos with their masses of $m_{3/2} > 10 {\rm TeV}$, the constraint mainly comes from the $^4$He overproduction. The thick solid line, which is denoted by "IT", comes from the observational value of $^4$He mass fraction by Izotov and Thuan (2003). The dotted strip indicates the region where the LSP abundance from the gravitino decay corresponds to the desired value $\Omega_{\rm LSP}h^2=0.0945-0.1287~(95\%~{\rm C.L.})$. The thin solid line, which is denoted by "OS", is the case that we adopted the most conservative observational value of $Y_p$ by Olive and Skillman (2004). Here we assumed that a gravitino can decay into all of the species of the chiral fermion and its scalar partner pairs ($\psi\tilde{\psi}$) and the gauge boson and the gaugino pairs ($g\tilde{g}$).
• Figure 2: Allowed regions for suitable observational value of $\Omega_{\rm LSP}h^2=0.0945-0.1287~(95\%~{\rm C.L.})$ in the $C$--$m_{\phi}$ plane. We plotted the strips for $m_{3/2}$ = 50, $10^2$, $5\times 10^2$, and $10^3$ TeV, respectively. We considered only two conditions that $T_R < m_{\rm LSP}/30$ (below the long dashed line), and $m_{\phi} > 2 m_{3/2}$. Here we took $N = 1$, and $m_{\rm LSP} = 100~ {\rm GeV}$.
• Figure 3: Various constraints on the $m_{3/2}$--$m_\phi$ plane, (i) BBN constraints (thick and thin solid lines), (ii) $T_R < m_{\rm LSP}/30$ (long dashed line), (iii) $T_R >1.2$ MeV (dashed line), and (iv) $m_{\phi} > 2 m_{3/2}$ (dot-dashed line) in the case $C=10^{-2}$ and $N=1$. Also depicted there are two strips where neutralino abundance from decaying gravitinos is in accord with the recently observed value $\Omega_{\rm LSP}h^2=0.0945-0.1287~(95\%~{\rm C.L.})$ with $m_{\rm LSP} = 100$ GeV. There is a region on this strip where all the constraints are satisfied simultaneously with $m_{3/2}\simeq 55-100$ TeV and $m_\phi\simeq (2-4)\times 10^3$ TeV. Since $N$ appears only in the form $N^{1/2} {m_{\phi}} ^{3/2}$ in all of the relevant expressions in Eqs. (\ref{['eq:TR']}), (\ref{['eq:thermal']}) and (\ref{['eq:direct']}), the constraints for $N$ other than $N = 1$ can easily be read off by replacing ${m_{\phi}}$ in the vertical axis by $N^{1/3} {m_{\phi}}$.
• Figure 4: How the results change as we take different values of $C$, which parameterizes the branching ratio of the modulus decay into the gravitino pair. We plot the cases (a) $C=10^{-4}$, (b) $C=10^{-3}$, (c) $C=10^{-2}$, and (d) $C=10^{-1}$, respectively. For the explanation of the various constraints, see the figure caption in Fig. \ref{['fig:two_grav_all_particle']}.
• Figure 5: Allowed region in the $m_{3/2}$--$m_\phi$ plane where $\Omega_{\rm LSP}h^2$ can take the observed value with $C\sim 10^{-4}-10^{-1}$. The vertical thick (thin) solid line represents the BBN constraint, which comes from the observational $^4$He mass fraction by Izotov and Thuan $Y_p(IT)$ ( Olive and Skillman $Y_p(OS)$). The long dashed line represents the boundary of $T_R < m_{\rm LSP}/30$ . This line for $N$ other than $N = 1$ can easily be read off by replacing ${m_{\phi}}$ in the vertical axis by $N^{1/3} {m_{\phi}}$. The dot-dashed line denotes the boundary of $m_{\phi} > 2 m_{3/2}$.