  The spectrum of the radio halo in the Coma cluster is measured over almost
two decades in frequency. The current radio data show a steepening of the
spectrum at higher frequencies, which has implications for models of the radio
halo origin. There is an on-going debate on the possibility that the observed
steepening is not intrinsic to the emitted radiation, but is instead caused by
the SZ effect. Recently, the Planck satellite measured the SZ signal and its
spatial distribution in the Coma cluster allowing to test this hypothesis.
Using the Planck results, we calculated the modification of the radio halo
spectrum by the SZ effect in three different ways. With the first two methods
we measured the SZ-decrement within the aperture radii used for flux
measurements of the halo at the different frequencies. First we adopted the
global compilation of data from Thierbach et al. and a reference aperture
radius consistent with those used by the various authors. Second we used the
available brightness profiles of the halo at different frequencies to derive
the spectrum within two fixed apertures, and derived the SZ-decrement using
these apertures. As a third method we used the quasi-linear correlation between
the y and the radio-halo brightness at 330 MHz discovered by Planck to derive
the modification of the radio spectrum by the SZ-decrement in a way that is
almost independent of the adopted aperture radius. We found that the spectral
modification induced by the SZ-decrement is 4-5 times smaller than that
necessary to explain the observed steepening. Consequently a break or cut-off
in the spectrum of the emitting electrons is necessary to explain current data.
We also show that, if a steepening is absent from the emitted spectrum, future
deep observations at 5 GHz with single dishes are expected to measure a halo
flux in a 40 arcmin radius that would be 7-8 times higher than currently seen.
