  A search for $K^-pp$ bound state (the lightest kaonic nucleus) has been
performed using the $\gamma d \rightarrow K^+ \pi^- \rm{X}$ reaction at
E$_\gamma$=1.5-2.4 GeV at LEPS/SPring-8. The differential cross section of $K^+
\pi^-$ photo-production off deuterium has been measured for the first time in
this energy region, and a bump structure was searched for in the inclusive
missing mass spectrum. A statistically significant bump structure was not
observed in the region from 2.22 to 2.36 GeV/$c^2$, and the upper limits of the
differential cross section for the $K^-pp$ bound state production were
determined to be 0.1$-$0.7 $\mu$ b (95$%$ confidence level) for a set of
assumed binding energy and width values.
