Big-Bang Nucleosynthesis with Unstable Gravitino and Upper Bound on the Reheating Temperature

TL;DR

This work assesses how unstable gravitinos influence big-bang nucleosynthesis by performing a meticulous calculation of gravitino decay channels, resulting hadron spectra, and their ensuing hadro- and photo-dissociation effects on light-element abundances. By combining detailed MSSM spectra from four mSUGRA benchmark points with Boltzmann-type production yields and Monte-Carlo decay chains, the authors derive upper bounds on the reheating temperature $T_{\rm R}$ that depend on the gravitino mass and MSSM spectrum. The results demonstrate that hadronic cascades are especially constraining for $m_{3/2}$ of a few TeV, while heavier gravitinos relax bounds and observational uncertainties, particularly from $^4$He. They also discuss implications for Li-7 and potential regions where Li-7 could be reconciled with observations, as well as non-thermal LSP production and CMB distortion constraints, highlighting the model-dependence of the bounds and outlining directions for future work including gravitino LSP scenarios.

Abstract

We study the effects of the unstable gravitino on the big-bang nucleosynthesis. If the gravitino mass is smaller than \sim 10 TeV, primordial gravitinos produced after the inflation are likely to decay after the big-bang nucleosynthesis starts, and the light element abundances may be significantly affected by the hadro- and photo-dissociation processes as well as by the p n conversion process. We calculate the light element abundances and derived upper bound on the reheating temperature after the inflation. In our analysis, we calculate the decay parameters of the gravitino (i.e., lifetime and branching ratios) in detail. In addition, we performed a systematic study of the hadron spectrum produced by the gravitino decay, taking account of all the hadrons produced by the decay products of the gravitino (including the daughter superparticles). We discuss the model-dependence of the upper bound on the reheating temperature.

Figures (11)

• Figure 1: Feynman diagrams for the process $\psi_\mu\rightarrow q\bar{q}\chi_1^0$. The "blobs" are from the gravitino-supercurrent interaction. For (d), there is also CP-conjugated diagram (with the replacements $q\leftrightarrow\bar{q}$ and $\tilde{q}^*\rightarrow\tilde{q}$).
• Figure 2: Width for the process $\psi_\mu\rightarrow q\bar{q}\chi_1^0$ as a function of $m_{3/2}-m_{\chi^0_1}$ (solid line). We adopt the mSUGRA parameters for the Case 1. For comparison, the decay rate $\Gamma (\psi_\mu\rightarrow Z\chi_1^0)\times {\rm Br}(Z\rightarrow q\bar{q})$ is also shown in the dashed line.
• Figure 3: Lifetime of the gravitino as a function of the gravitino mass.
• Figure 4: Branching ratios of the decay of the gravitino as functions of the gravitino mass. The thick solid line is for the final states $\chi^0_1$$+$ anything, dot-dashed line for lepton-slepton pairs, dotted line for $\chi^0_i$ ($i = 2-4$) or chargino $+$ anything, dashed line for gluon-gluino pair, and thin solid line for quark-squark pair final states.
• Figure 5: Distributions of the nucleons (i.e., (a) proton and (b) neutron) from the decay of a single gravitino as functions of the kinetic energy. Here we take the mSUGRA parameters for the Case 1, and $m_{3/2}=1$TeV.