  The Raman response in a superconductor is a powerful probe to investigate the
symmetry of the superconducting gap. Here we show that in a multiband
superconductor it also offers the unique opportunity to establish if the
driving pairing interaction has an intraband or interband character. In the
model with one hole and one electron band the full gauge-invariant Raman
response, obtained by accounting for the fluctuations of both the density and
superconducting phase degrees of freedom, is always dominated by the Leggett
mode, regardless its nature. However, while in the case of intra-band dominated
pairing the Josephson-like phase fluctuations of the two condensates identify a
well-defined peak, as observed in MgB$_2$, for dominant interband pairing the
Leggett resonance is pushed at twice the largest gap, resembling apparently a
pair-breaking peak. The latter case is in very good agreement with experimental
data in iron-based superconductors, suggesting that an interband pairing
mechanism should be at play in these systems. These results have also
interesting implications for the non-linear optical response probed by means of
intense THz fields.
