Stau-catalyzed ⁶Li production in big-bang nucleosynthesis

If the gravitino mass is in the region from a few GeV to a few 10's GeV, the scalar lepton X such as stau is most likely the next lightest supersymmetry particle. The negatively charged and long-lived X^- may form a Coulomb bound state (A X^-) with a nucleus A and may affect the big-bang nucleosynthesis through catalyzed fusion process. We calculate a production cross section of ⁶Li from the catalyzed fusion (⁴He X^-) + d → ⁶Li + X^- by solving the Schrödinger equation exactly for three-body system of ⁴He, d and X. We utilize the state-of-the-art coupled-channel method, which is known to be very accurate to describe other three-body systems in nuclear and atomic reactions. The importance of the use of appropriate nuclear potential and the exact treatment of the quantum tunneling in the fusion process are emphasized. We find that the astrophysical S-factor at the Gamow peak corresponding to T = 10 keV is 0.038 MeV barn. This leads to the ⁶Li abundance from the catalyzed process as ⁶Li |_CBBN ≃ 4.3 × 10^-11 (D / 2.8 × 10^-5) ([n_X- / s] / 10^-16) in the limit of long lifetime of X. Particle physics implication of this result is also discussed.