  We propose a scenario which can explain large lepton asymmetry and small
baryon asymmetry simultaneously. Large lepton asymmetry is generated through
Affleck-Dine (AD) mechanism and almost all the produced lepton numbers are
absorbed into Q-balls (L-balls). If the lifetime of the L-balls is longer than
the onset of electroweak phase transition but shorter than the epoch of big
bang nucleosynthesis (BBN), the large lepton asymmetry in the L-balls is
protected from sphaleron effects. On the other hand, small (negative) lepton
numbers are evaporated from the L-balls due to thermal effects, which are
converted into the observed small baryon asymmetry by virtue of sphaleron
effects. Large and positive lepton asymmetry of electron type is often
requested from BBN. In our scenario, choosing an appropriate flat direction in
the minimal supersymmetric standard model (MSSM), we can produce positive
lepton asymmetry of electron type but totally negative lepton asymmetry.
