  LS 5039 is the only X-ray binary persistently detected at TeV energies by the
Cherenkov HESS telescope. It is moreover a gamma-ray emitter in the GeV and
possibly MeV energy ranges. To understand important aspects of jet physics,
like the magnetic field content or particle acceleration, and emission
processes, such as synchrotron and inverse Compton (IC), a complete modeling of
the multiwavelength data is necessary. LS 5039 has been detected along almost
all the electromagnetic spectrum thanks to several radio, infrared, optical and
soft X-ray detections. However, hard X-ray detections above 20 keV have been so
far elusive and/or doubtful, partly due to source confusion for the poor
spatial resolution of hard X-ray instruments. We report here on deep (300 ksec)
serendipitous INTEGRAL hard X-ray observations of LS 5039, coupled with
simultaneous VLA radio observations. We obtain a 20-40 keV flux of 1.1 +/- 0.3
mCrab (5.9 (+/-1.6) X 10^{-12} erg cm^{-2} s^{-1}), a 40-100 keV upper limit of
1.5 mCrab (9.5 x 10^{-12} erg cm^{-2}s^{-1}), and typical radio flux densities
of about 25 mJy at 5GHz. These hard X-ray fluxes are significantly lower than
previous estimates obtained with BATSE in the same energy range but, in the
lower interval, agree with extrapolation of previous RXTE measurements. The
INTEGRAL observations also hint to a break in the spectral behavior at hard
X-rays. A more sensitive characterization of the hard X-ray spectrum of LS 5039
from 20 to 100 keV could therefore constrain key aspects of the jet physics,
like the relativistic particle spectrum and the magnetic field strength. Future
multiwavelength observations would allow to establish whether such hard X-ray
synchrotron emission is produced by the same population of relativistic
electrons as those presumably producing TeV emission through IC.
