Nucleosynthesis constraints on a massive gravitino in neutralino dark matter scenarios

Abstract

The decays of massive gravitinos into neutralino dark matter particles and\nStandard Model secondaries during or after Big-Bang nucleosynthesis (BBN) may\nalter the primordial light-element abundances. We present here details of a new\nsuite of codes for evaluating such effects, including a new treatment based on\nPYTHIA of the evolution of showers induced by hadronic decays of massive,\nunstable particles such as a gravitino. We also develop an analytical treatment\nof non-thermal hadron propagation in the early universe, and use this to derive\nanalytical estimates for light-element production and in turn on decaying\nparticle lifetimes and abundances. We then consider specifically the case of an\nunstable massive gravitino within the constrained minimal supersymmetric\nextension of the Standard Model (CMSSM). We present upper limits on its\npossible primordial abundance before decay for different possible gravitino\nmasses, with CMSSM parameters along strips where the lightest neutralino\nprovides all the astrophysical cold dark matter density. We do not find any\nCMSSM solution to the cosmological Li7 problem for small m_{3/2}. Discounting\nthis, for m_{1/2} ~ 500 GeV and tan beta = 10 the other light-element\nabundances impose an upper limit m_{3/2} n_{3/2}/n_\\gamma < 3 \\times 10^{-12}\nGeV to < 2 \\times 10^{-13} GeV for m_{3/2} = 250 GeV to 1 TeV, which is similar\nin both the coannihilation and focus-point strips and somewhat weaker for tan\nbeta = 50, particularly for larger m_{1/2}. The constraints also weaken in\ngeneral for larger m_{3/2}, and for m_{3/2} > 3 TeV we find a narrow range of\nm_{3/2} n_{3/2}/n_\\gamma, at values which increase with m_{3/2}, where the Li7\nabundance is marginally compatible with the other light-element abundances.\n