  We derive the phase factor proposed by Beisert, Eden and Staudacher for the
S-matrix of planar N=4 Super Yang-Mills, from the all-loop Bethe ansatz
equations without the dressing factor. We identify a configuration of the Bethe
roots, from which the closed integral formula of the phase factor is reproduced
in the thermodynamic limit. This suggests that our configuration describes the
``physical vacuum'' in the sense that the dressing phase is nothing but the
effective phase for the scattering of fundamental excitations above this
vacuum, providing an interesting clue to the physical origin of the dressing
phase.
