Using a two-orbital model of the superconducting phase of the pnictides, we
compute the spectrum of the Leggett mode -- a collective excitation of the
phase of the superconducting gap known to exist in multi-gap superconductors --
for different possible symmetries of the superconducting order parameter.
Specifically, we identify the small regions of parameter space where the
Leggett mode lies below the two-particle continuum, and hence should be visible
as a sharp resonance peak. We discuss the possible utility of the Leggett mode
in distinguishing different momentum dependencies of the superconducting gap.
We argue that the observation of a sharp Leggett mode would be consistent with
the presence of strong electron-electron correlations in iron-based
superconductors. We also emphasize the importance of the orbital character of
the Leggett mode, which can result in an experimental observation of the mode
in channels other than A1gβ
