Decaying gravitino dark matter and an upper bound on the gluino mass

The positron spectrum needed to explain the PAMELA excess is rather hard. If the positron fraction continues to rise above 100 GeV, the cosmic-ray electron flux as well may be significantly modified at high energies. Interestingly enough, the ATIC balloon experiment collaboration [8] has recently released the data, showing a clear excess in the total flux of electrons plus positrons peaked around 600 -700 GeV, in consistent with the PPB-BETS observation [9]. It is highly suggestive of the same origin for the PAMELA and ATIC/PPB-BETS anomalies, if both are to be accounted for by dark matter. As will be shown in Appendix, the decaying gravitino scenario can actually account for both excesses. We focus on this scenario in this letter.

The gravitino is assumed to be the lightest supersymmetric particle (LSP). In the presence of the R-parity violation, its longevity is due to a combination of the Planck-suppressed interactions and a tiny R-parity violating coupling. For the latter we assume the so-called bilinear R-parity violating coupling, which is parametrized by a dimensionless coupling κ i defined as the ratio of the vacuum expectation values (VEVs) of the sneutrinos to that of the standard-model like Higgs boson, where the subindex i(= 1, 2, 3) denotes the flavor dependence, e, µ and τ (see Ref. [10] for more details). We assume that the decay of an electron-type dominates over the others throughout this letter, i.e., κ 1 ≫ κ 2 , κ 3 , since one cannot fit well the sharp cut-off in the ATIC data otherwise. Then the mass and lifetime of the gravitino should be in the following range to account for the PAMELA and ATIC/PPB-BETS excesses:

Since all the other supersymmetric (SUSY) particles must be heavier than the gravitino, we expect a typical mass scale for the SUSY particles, especially the gluino, may be out of the reach of LHC. This would be quite discouraging for those who expect SUSY discovery at LHC. In this letter, however, we show that the gluino mass is bounded from above and is likely within the reach of LHC, if the baryon asymmetry is explained by the thermal leptogenesis scenario.

Let us first discuss the gravitino production in the early universe. The gravitino is produced by thermal scatterings, #1 and the abundance is given by [13,14,15]

where g 3 and M 3 are the SU(3) C gauge coupling and the gluino mass, respectively, and both are evaluated at a scale equal to the reheating temperature, T R , in Eq. ( 3). For simplicity we have dropped contributions involving the U(1) Y and SU(2) L gauge interactions, which are subdominant unless the bino and wino masses, M 1 and M 2 , are much larger than M 3 . Thus, the reheating temperature and the gluino mass are constrained from above for the gravitino abundance not to exceed the observed dark matter abundance, Ω DM h 2 ≃ 0.1143±0.0034 [16].

In Fig. 1 we have shown the upper bound on the gluino mass and the reheating temperature, where we have included contributions from U(1) Y and SU(2) L neglected in Eq. ( 3). We have imposed a requirement that the gravitino abundance should not exceed the 95% C.L. upper bound on the dark matter abundance. We used the code SuSpect2.41 [17] to calculate the gravitino abundance and the physical spectra for the superparticles, with the following Those parameters are chosen so that the gravitino is LSP #2 The origin of the baryon asymmetry is a big mystery of the modern cosmology. The thermal leptogenesis scenario [18] is appealing, and the reheating temperature must be higher than about 2 × 10 9 GeV [19] for the scenario to work. The precise value of the lower limit depends on flavor effects [20] and the mass spectrum of the right-handed neutrinos.

The detailed study showed the lower bound as T R 10 9 GeV, which is represented by the horizontal gray band in Fig. 1. We can see from Fig. 1 that the gluino mass is bounded #1 The inflaton decay may also contribute to the gravitino abundance [11,12]. We focus on the thermal production, since the non-thermal gravitino production depends on the inflation models. #2 In the case of m 3/2 = 1.4 TeV, the gravitino is LSP for M 3 600 GeV for the adopted parameters. This does not affect the following discussion. from above, M 3 1.5 TeV at the GUT scale, for T R to satisfy the lower bound #3 . This constraint can be translated into that the gluino mass should be lighter than about 3 TeV in the low energy, taking account of the renormalization group evolution. If we take a slightly tighter bound on T R , say, T R 1.4 × 10 9 Ge

…(Full text truncated)…