Lifetime Limit of LSP from Cosmological Light Elements

From the present cosmic abundance of the light elements, one can obtain a lifetime bounds of LSP. From the consideration of deuterium, we obtain τχ ≥ 10 6 s [1]. INTRODUCTION More than 20 years have passed since the Lee-Weinberg bound on the stable heavy neutrino was proposed [2]. It applies to an absolutely stable particle which needs a conserved quantum number. The decaying particle cosmology was propsed around the same time [3]. But the decaying particle cosmology has been extensively applied for the gravitino [4]. In this talk, we focus on the decay of the lightest supersymmetric particle (LSP), χ. For χ to decay, the R-parity must be broken. In supergravity, there can be nonrenormalizable interactions for the R-parity violation, but we neglect these compared to the renormalizable ones. There can be also R-violating bilinear terms, of the form LiH2, which can be rotated away at the superpotential level. However, in the presence of soft terms some bilinear terms cannot be rotated away. But for decay processes, this subtle point is not important. Thus we consider the R-violating trilinear terms, W = 1 2 λijkL LE + λ′ijkL QD + 1 2 λDDD (1) which are allowed by (i) supersymmetry and (ii) gauge symmetry. Therefore, it is reasonable to consider the phenomenology of R-parity violation. With the above superpotential present, the lepton number and/or baryon number are broken. That 1) Talk presented at cosmo-98, Asilomar, Monterey, CA, November 16–20, 1998. This work is supported in part by KOSEF, MOE through BSRI 98-2468, and Korea Research Foundation. is the reason for requiring the R = (−1) conservation. Anyway, with the Rparity violation, we expect neutrino oscillation, proton decay, and other abnormal processes. From laboratory experiments, the single bounds on the couplings are not very strong, e.g. λ121 < 0.05, λ122 < 0.05, λ ′ 111 < 0.001, λ ′ 112 < 0.02, λ ′′ 112 < 10 , and λ 113 < 10 . However, a combined bound from lower limit of the proton decay lifetime is very strong λλ < 10. (2) If a universal strength for the R-violating couplings are assumed, then these couplings are very small. For example, if a singlet scalar field φ carrying odd R-parity develops a VEV, < φ >≡ ǫMP , then the R-parity is spontaneously broken. At low energy, these effects are represented by λ, λ, and λ couplings which carry negative R-parity. These may arise from nonrenormalizable interactions containing φ field. In this case, these couplings can be of the same order. Thus, to allow reasonably large R-violating couplings, one usually fobid λ or λ completely. In general, laboratory experiments give upper bounds on the couplings. However, the cosmological bounds depend on the region of couplings. It is schematically shown in Fig. 1. In this talk, I am interested in the region τχ ∼ 10 −6 s.