Mixed axion/gravitino dark matter from SUSY models with heavy axinos

We examine dark matter production rates in supersymmetric (SUSY) axion models typified by the mass hierarchy $m_{3/2}\ll m(\text{neutralino})\ll m(\text{axino})$. In such models, one expects the dark matter to be composed of an axion/gravitino admixture. After presenting motivation for how such a mass hierarchy might arise, we examine dark matter production in the SUSY Kim-Shifman-Vainshtein-Zakharov (KSVZ) model, the SUSY Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model and a hybrid model containing contributions from both KSVZ and DFSZ. Gravitinos can be produced thermally and also nonthermally from axino, saxion or neutralino decay. We obtain upper bounds on $T_R$ due to overproduction of gravitinos including both the thermal and nonthermal processes. For $T_R$ near the upper bound, dark matter tends to be gravitino dominated, but for $T_R$ well below the upper bounds, axion domination is more typical although in many cases we find a comparable mixture of both axions and gravitinos. In this class of models, we ultimately expect detection of relic axions but no weakly interacting massive particle signal, although SUSY should ultimately be discovered at colliders.

Figure 1

Axino branching fractions versus $f_a$ for $m_{\tilde{a}}=10\mathrm{TeV}$ (left) and versus $m_{\tilde{a}}$ for $f_a=10^{11}\mathrm{GeV}$ (right) in the KSVZ model. The sparticle mass spectrum is taken from the SUA benchmark point of Ref. [28].

Figure 2

Relic abundance of gravitinos from various sources versus $f_a$ with $m_s=2m_{\tilde{a}}$ (left) and $m_s=m_{\tilde{a}}$ (right) for the SUA benchmark point in the KSVZ model.

Figure 3

Relic abundance of gravitinos from various sources versus $f_a$ with $m_s=2m_{\tilde{a}}$ (left) and $m_s=m_{\tilde{a}}$ (right) for the SOA benchmark point in the KSVZ model.

Figure 4

The upper bound of $T_R$ calculated from thermal and nonthermal production of gravitinos as a function of $f_a$ (left) and $m_{\tilde{a}}$ (right) for SUA (red) and SOA (blue) in the KSVZ model. The region above the curves is disallowed by overproduction of gravitinos.

Figure 5

The upper bound of $T_R$ calculated from thermal and nonthermal production of gravitinos as a function of $m_{3/2}$ for SUA (red) and SOA (blue) in the KSVZ model. The region above the curves is disallowed by overproduction of gravitinos.

Figure 6

Relic abundance of gravitinos from various sources versus $f_a$ with $m_s=2m_{\tilde{a}}$ (left) and $m_s=m_{\tilde{a}}$ (right) for the SUA benchmark point in the DFSZ model.

Figure 7

Relic abundance of gravitinos from various sources versus $f_a$ with $m_s=2m_{\tilde{a}}$ (left) and $m_s=m_{\tilde{a}}$ (right) for the SOA benchmark point in the DFSZ model.

Figure 8

The upper bound of $T_R$ calculated from thermal and nonthermal production of gravitinos as a function of $f_a$ (left) and $m_{\tilde{a}}$ (right) for SUA (red) and SOA (blue) in the DFSZ model. The region above the curves is disallowed by overproduction of gravitinos.

Figure 9

The upper bound of $T_R$ calculated from thermal and nonthermal production of gravitinos as a function of $m_{3/2}$ for SUA (red) and SOA (blue) in the DFSZ model. The region above the curves is disallowed by overproduction of gravitinos.

Figure 10

The upper bound of $T_R$ calculated from thermal and nonthermal production of gravitinos as a function of $f_a$ (left) and $m_{\tilde{a}}$ (right) for SUA (red) and SOA (blue) in the $\mathrm{KSVZ}+\mathrm{DFSZ}$ model. The region above the curves is disallowed by overproduction of gravitinos.

Figure 11

The upper bound of $T_R$ calculated from thermal and nonthermal production of gravitinos as a function of $m_{3/2}$ for SUA (red) and SOA (blue) in the $\mathrm{KSVZ}+\mathrm{DFSZ}$ model. The region above the curves is disallowed by overproduction of gravitinos.