  Disintegrating planets are ultra-short-period exoplanets that appear to have
a comet-like dust tail. They are commonly interpreted as low-mass planets whose
solid surface is evaporating and whose tail is made of recondensing minerals.
Transmission spectroscopy of the dust tails could thus allow us to directly
probe the elementary compositions of the planets. Previous work already
investigated the feasibility of such observations using the JWST mid-infrared
instrument. In this study, we explore if one can obtain a strong constrain on
the tail composition by adding spectroscopy at longer wavelengths using SPICA
mid-infrared instrument. We use a simple model for the spatial distribution of
the dust tails and produce their synthetic transmission spectra assuming
various dust compositions. We find that combined infrared spectra from JWST and
SPICA will allow us to diagnose various components of the dust tails. JWST will
be able to detect silicate and carbide absorption features with a
feature-to-noise ratio of $\gtrsim$ 3 in the tail transmission spectrum of a
disintegrating planet located within 100 pc from the Earth with a transit depth
deeper than 0.5%. SPICA can distinguish between Fe- and Mg-bearing crystalline
silicates for planets at $\lesssim$ 100 pc with a transit depth of $\gtrsim$
2%. Transit searches with current and future space telescopes (e.g., $TESS$ and
PLATO) will provide ideal targets for such spectroscopic observations.
