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 (AX−) 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 (He4X−)+d→Li6+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=10keV is 0.038 MeV barn. This leads to the 6Li abundance from the catalyzed process as Li6|CBBN≃4.3×10−11(D/2.8×10−5)([nX−/s]/10−16) in the limit of long lifetime of X. Particle physics implication of this result is also discussed.