Gravitinos and hidden Supersymmetry at the LHC - Universität ...

2.5. THE MASSIVE GRAVITINO
keV which can enter thermal equilibrium and allow for arbitrary reheating temperature is
excluded by warm dark matter constraints [128].
In case of gravitino LSP, one has also to take care of the NLSP 2 decays, since the coupling
of the NLSP to the gravitino is also suppressed by the Planck scale. The NLSP lifetime is
given by
( m3/2
) 2
( ) 200 GeV 5
τ NLSP ≤ 2 months
≪ 1 s ∼ t BBN , (2.112)
100 GeV m NLSP
and one once again recovers potential tension with the predictions of the BBN [129]. Whether
the NLSP decay problem truly occurs or not, depends on the nature of the NLSP. The hadronic
decays of a neutralino NLSP typically dissociate the primordial light elements [130–132] and
also the stop NLSP is strongly constrained [133, 134]. A long lived stau NLSP can form a
bound state with 4 He and catalyze the production of 6 Li [135–138] but it is possible to obtain
a consistent cosmology with leptogenesis in some corners of its parameter space [139–141].
Also a sneutrino NLSP can allow for consistent cosmological scenarios due to its invisible
decays [142–144].
Although there are some regions in the parameter space of the theories allowing for consistent
cosmology, as presented above, there are also other mechanisms which can circumvent
the NLSP problem and lead to interesting consequences. The gravitino may be degenerate
in mass with the NLSP, so that its decay products are low-energetic and do not change the
predictions of BBN [141]. The gravitino could also have additional decay channels to hidden
sector particles and decay before the BBN [145,146]. Also a light gravitino with a super-light
neutralino is a possible spectrum solving all problems [147]. Furthermore, the number density
of the NLSPs can be diluted by late-time entropy production before the BBN [76, 137, 148].
A recent work exploring some of this ideas is [149].
In the present work we will mainly pursue another line of thought: Small violation of
R-parity is sufficient to cause the NLSP to decay into the SM particles before the onset of
BBN. In the next chapter we will extensively review R-parity violation and introduce the R-
parity violating couplings. In general, a gravitino coupling to the SM particles of the order of
10 −13 is sufficient to solve the NLSP decay problem [57]. We will review the upper bounds on
R-parity violating couplings from cosmology in Chapter 4, but we can state already here that
there is a several orders of magnitude wide range for the couplings allowed by all constraints.
The gravitino will also decay into SM particles but its decay is double suppressed due to
the Planck scale and the tiny R-parity violating couplings, and it therefore remains a viable
(decaying) dark matter candidate with a life-time exceeding the age of the universe [58].
The gravitino abundance in such scenario is determined only by the thermal production rate
and can explain the abundance of dark matter. Thus, small amount of R-parity breaking
renders supersymmetric cosmology consistent and allows additionally for interesting LHC
phenomenology involving long lived particles. In some cases the presence of R-parity violation
can significantly change supersymmetric signatures and hide SUSY from LHC searches. This
will be investigated in Section 5.2. Additionally, small violation of R-parity may also relax
cosmological constraints on the axion multiplet and therefore be connected with the solution
to the strong CP problem [150].
Summing up, we note that the presence of gravitino in the supersymmetric spectrum can
significantly change the course of the history of the universe. In order to achieve consistent
2 In the context of gravitino LSP, the NLSP is sometimes called LOSP - lightest ordinary supersymmetric
particle.
37