  Understanding the mechanisms of accretion-ejection during X-ray binaries
outbursts has been a problem for several decades. It is still not clear yet
what controls the spectral evolution of these objects from the hard to the soft
states and then back to the hard states at the end of the outburst, tracing the
well-known hysteresis cycle in the hardness-intensity diagram. Moreover, the
link between the spectral states and the presence/absence of radio emission is
still highly debated. In a series of papers, we developed a model composed of a
truncated outer standard accretion disk (SAD, from the solution of Shakura and
Sunyaev) and an inner jet emitting disk (JED). In this paradigm, the JED plays
the role of the hot corona while simultaneously explaining the presence of a
radio jet. Our goal is to apply for the first time direct fitting procedures of
the JED-SAD model to the hard states of four outbursts of GX 339-4 observed
during the 2000-2010 decade by RXTE, combined with simultaneous or quasi
simultaneous ATCA observations. We built JED-SAD model tables usable in Xspec
as well as a reflection model table based on the Xillver model. We apply our
model to the 452 hard state observations obtained with RXTE/PCA. We were able
to correctly fit the X-ray spectra and simultaneously reproduce the radio flux.
We show that the functional dependency of the radio emission on the model
parameters (mainly the accretion rate and the transition radius between the JED
and the SAD) is similar between all the rising phases of the different
outbursts of GX 339-4. But it is significantly different from the functional
dependency obtained in the decaying phases. This result strongly suggests a
change in the radiative and/or dynamical properties of the ejection between the
beginning and the end of the outburst. We discuss possible scenarios that could
explain these differences.
