We report the detection of a possible gamma-ray counterpart of the accreting millisecond pulsar SAX J1808.4-3658. The analysis of ~6 years of data from the Large Area Telescope on board the Fermi Gamma-ray Space Telescope (Fermi-LAT) within a region of 15deg radius around the position of the pulsar reveals a point gamma-ray source detected at a significance of ~6 sigma (Test Statistic TS = 32), with position compatible with that of SAX J1808.4-3658 within 95% Confidence Level. The energy flux in the energy range between 0.6 GeV and 10 GeV amounts to (2.1 +- 0.5) x 10-12 erg cm-2 s-1 and the spectrum is well-represented by a power-law function with photon index 2.1 +- 0.1. We searched for significant variation of the flux at the spin frequency of the pulsar and for orbital modulation, taking into account the trials due to the uncertainties in the position, the orbital motion of the pulsar and the intrinsic evolution of the pulsar spin. No significant deviation from a constant flux at any time scale was found, preventing a firm identification via time variability. Nonetheless, the association of the LAT source as the gamma-ray counterpart of SAX J1808.4-3658 would match the emission expected from the millisecond pulsar, if it switches on as a rotation-powered source during X-ray quiescence.
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