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Possible Fermi Detection of the Accreting Millisecond Pulsar Binary SAX J1808.4-3658

We report the Fermi Large Area Telescope (LAT) detection of a $γ$-ray source at the position of SAX J1808.4$-$3658. This transient low-mass X-ray binary contains an accreting millisecond puslar, which is only seen during its month-long outbursts and likely switches to be rotation powered during its quiescent state. Emission from the $γ$-ray source can be described by a power law with an exponential cutoff, the characteristic form for pulsar emission. Folding the source's 2.0--300 GeV photons at the binary orbital period, a weak modulation is seen (with an H-test value of $\sim$17). In addition, three sets of archival XMM-Newton data for the source field are analyzed, and we find only one X-ray source with 3--4$σ$ flux variations in the 2$σ$ error circle of the $γ$-ray source. However based on the X-ray properties, this X-ray source is not likely a background AGN, the major class of Fermi sources detected by LAT. These results support the possible association between the $γ$-ray source and SAX J1808.4$-$3658 and thus the scenario that the millisecond pulsar is rotation powered in the quiescent state. Considering a source distance of 3.5 kpc for SAX J1808.4$-$3658, the 0.1--300 GeV luminosity is 5.7$\times 10^{33}$ erg s$^{-1}$, implying a $γ$-ray conversion efficiency of 63\% for the pulsar in this binary.