Leptogenesis via $LH_{u}$ flat direction with a gauged $U(1)_{B-L}$

We study the supersymmetric leptogenesis via $LH_{u}$ flat direction with a gauged $U(1)_{B-L}$ symmetry. We find that the resultant baryon asymmetry is enhanced compared with the case without a gauged $U(1)_{B-L}$ symmetry. The baryon asymmetry is proportional to the reheating temperature of inflation, but it is independent of the gravitino mass. If high reheating temperatures of inflation $T_{R}\sim 10^{10}\GEV$ are available, the mass of the lightest neutrino, $m_{\nu 1}\sim 10^{-4}\EV$, is small enough to explain the baryon asymmetry in the present universe. Furthermore, the gravitino mass independence of the produced baryon asymmetry allows us to explain the present baryon asymmetry even in low energy SUSY breaking scenarios such as gauge-mediation models. Our leptogenesis scenario is also very special in the sense that it is completely free from the serious Q-ball formation problem.