We present the analysis of the high-energy emission of the Galactic black hole binary GX 339-4 in a low/hard state at the beginning of its 2004 outburst. The data from 273 ks of INTEGRAL observations, spread over 4 weeks, are analyzed, along with the existing simultaneous RXTE HEXTE and PCA data. During this period, the flux increases by a factor of ~=3, while the spectral shape is quite unchanged, at least up to 150 keV. The high-energy data allow us to detect the presence of a high-energy cutoff, generally related to thermal mechanisms, and to estimate the plasma parameters in the framework of the Comptonization models. We found an electron temperature of 60-70 keV and an optical depth of around 2.5, with a rather low reflection factor (0.2-0.4). In the last observation, we detected a high-energy excess above 200 keV with respect to thermal Comptonization, while at lower energies the spectrum is practically identical to the previous one taken just 2 days before. This suggests that the low- and high-energy components have a different origin
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