We study the average X-ray and soft \gamma -ray spectrum of Cyg X-1 in the hard spectral state , using data from INTEGRAL .
We compare these results with those from CGRO , and find a good agreement .
Confirming previous studies , we find the presence of a high-energy MeV tail beyond a thermal-Comptonization spectrum ; however , the tail is much softer and weaker than that recently published by Laurent et al .
In spite of this difference , the observed high-energy tail could still be due to the synchrotron emission of the jet of Cyg X-1 , as claimed by Laurent et al .

In order to test this possibility , we study optically-thin synchrotron and self-Compton emission from partially self-absorbed jets .
We develop formalisms for calculating both emission of the jet base ( which we define here as the region where the jet starts its emission ) and emission of the entire jet .
We require the emission to match that observed at the turnover energy .
The optically thin emission is dominated by that from the jet base , and it has to become self-absorbed within it at the turnover frequency .
We find this implies the magnetic field strength at the jet base of B _ { 0 } \propto z _ { 0 } ^ { 4 } , where z _ { 0 } is the distance of the base from the black-hole centre .
The value of B _ { 0 } is then constrained from below by the condition that the self-Compton emission is below an upper limit in the GeV range , and from above by the condition that the Poynting flux does not exceed the jet kinetic power .
This yields B _ { 0 } of the order of \sim 10 ^ { 4 } G and the location of the jet base at \sim 10 ^ { 3 } gravitational radii .
Using our formalism , we find the MeV tail can be due to jet synchrotron emission , but this requires the electron acceleration at a rather hard power-law index , p \simeq 1.3 –1.6 .
For acceleration indices of p \mathrel { \hbox { \raise 2.15 pt \hbox { $ > $ } \hbox to 0.0 pt { \lower 2.15 pt \hbox { $ \sim% $ } } } } 2 , the amplitude of the synchrotron component is much below that of MeV tail , and its origin is likely to be due to hybrid Comptonization in the accretion flow .