We study the big-bang nucleosynthesis (BBN) with the long-lived exotic particle, called $X$. If the lifetime of $X$ is longer than $\ensuremath{\sim}0.1\text{ }\text{ }\mathrm{sec}$, its decay may cause nonthermal nuclear reactions during or after the BBN, altering the predictions of the standard BBN scenario. We pay particular attention to its hadronic decay modes and calculate the primordial abundances of the light elements. Using the result, we derive constraints on the primordial abundance of $X$. Compared to the previous studies, we have improved the following points in our analysis: The JETSET 7.4 Monte Carlo event generator is used to calculate the spectrum of hadrons produced by the decay of $X$; the evolution of the hadronic shower is studied taking into account the details of the energy-loss processes of the nuclei in the thermal bath; we have used the most recent observational constraints on the primordial abundances of the light elements; in order to estimate the uncertainties, we have performed the Monte Carlo simulation which includes the experimental errors of the cross sections and transferred energies. We will see that the nonthermal productions of D, $^{3}\mathrm{He}$, $^{4}\mathrm{He}$, and $^{6}\mathrm{Li}$ provide stringent upper bounds on the primordial abundance of a late-decaying particle, in particular, when the hadronic branching ratio of $X$ is sizable. We apply our results to the gravitino problem, and obtain an upper bound on the reheating temperature after inflation.

Big-bang nucleosynthesis and hadronic decay of long-lived massive particles