  We present ground-based broad-band photometry of two transits in the WASP-44
planetary system obtained simultaneously through four optical (Sloan g', r',
i', z') and three near-infrared (NIR; J, H, K) filters. We achieved low
scatters of 1-2 mmag per observation in the optical bands with a cadence of 48
s, but the NIR-band light curves present much greater scatter. We also observed
another transit of WASP-44 b by using a Gunn-r filter and telescope
defocussing, with a scatter of 0.37 mmag per point and an observing cadence
around 135 s. We used these data to improve measurements of the time of
mid-transit and the physical properties of the system. In particular, we
improved the radius measurements of the star and planet by factors of 3 and 4,
respectively. We find that the radius of WASP-44 b is 1.002 R_Jup, which is
slightly smaller than previously thought and differs from that expected for a
core-free planet. In addition, with the help of a synthetic spectrum, we
investigated the theoretically-predicted variation of the planetary radius as a
function of wavelength, covering the range 370-2440 nm. We can rule out extreme
variations at optical wavelengths, but unfortunately our data are not precise
enough (especially in the NIR bands) to differentiate between the theoretical
spectrum and a radius which does not change with wavelength.
