  We investigate the mid-infrared properties of the largest (42 objects) sample
of radio-loud narrow-line Seyfert 1 (RL NLS1) collected to date, using data
from the Wide-field Infrared Survey Explorer (WISE). We analyse the mid-IR
colours of these objects and compare them to what is expected from different
combinations of AGN and galaxy templates. We find that, in general, the
host-galaxy emission gives an importan contribution to the observed mid-IR flux
in particular at the longest wavelengths (W3, at 12micron, and W4, at
22micron). In about half of the sources (22 objects) we observe a very red
mid-IR colour (W4-W3>2.5) that can be explained only using a starburst galaxy
template (M82). Using the 22micron luminosities, corrected for the AGN
contribution, we have then estimated the star-formation rate for 20 of these
"red" RL NLS1, finding values ranging from 10 to 500 Msun/y. For the RL NLS1
showing bluer colours, instead, we cannot exclude the presence of a
star-forming host galaxy although, on average, we expect a lower star-formation
rate. Studying the radio (1.4GHz) to mid-IR (22micron) flux ratios of the RL
NLS1 in the sample we found that in ~10 objects the star-forming activity could
represent the most important component also at radio frequencies, in addition
(or in alternative) to the relativistic jet. We conclude that both the mid-IR
and the radio emission of RL NLS1 are a mixture of different components,
including the relativistic jet, the dusty torus and an intense star-forming
activity.
