Lepton Flavor Violation and Cosmological Constraints on R-parity
  Violation
  In supersymmetric standard models R-parity violating couplings are severely
constrained, since otherwise they would erase the existing baryon asymmetry
before the electroweak transition. It is often claimed that this cosmological
constraint can be circumvented if the baryon number and one of the lepton
flavor numbers are sufficiently conserved in these R-parity violating
couplings, because B/3-L_i for each lepton flavor is separately conserved by
the sphaleron process. We discuss the effect of lepton flavor violation on the
B-L conservation, and show that even tiny slepton mixing angles \theta_{12}
\gsim {\cal O}(10^{-4}) and \theta_{23}, \theta_{13}\gsim {\cal O}(10^{-5})
will spoil the separate B/3-L_i conservation. In particular, if lepton flavor
violations are observed in experiments such as MEG and B-factories, it will
imply that all the R-parity violating couplings must be suppressed to avoid the
B-L erasure. We also discuss the implication for the decay of the lightest MSSM
particle at the LHC.
