  We present a theoretical prediction on random close packing factor \phi_RCP^b
of binary granular packings based on the hard-sphere fluid theory. An
unexplored regime is unravelled, where the packing fraction \phi_RCP^b is
smaller than that of the mono-sized one \phi_RCP^m, i.e., the so-called loose
jamming state. This is against our common perception that binary packings
should always reach a denser packing than mono-sized packings at the jamming
state. Numerical evidence further supports this prediction and confirms the
regime location in the size ratio and mole fraction (R_r-X_s) space, where the
size ratio R_r is close to 1, and the mole fraction of the smaller sphere X_s
close to 0. This extreme regime remains unreported in existing literature, yet
significant for our fundamental understanding of binary packing systems.
