We have obtained optical and near-infrared images of the field of the accreting millisecond X-ray pulsar XTE J1751-305. There are no stars in the 0.7 error circle (0.7 is the overall uncertainty arising from tying the optical and X-ray images and from the intrinsic uncertainty in the Chandra X-ray astrometric solution). We derive limiting magnitudes for the counterpart of R>23.1, I>21.6, Z>20.6, J>19.6, K>19.2. We compare these upper limits with the magnitudes one would expect for simple models for the possible donor stars and the accretion disk subject to the reddening observed in X-rays for XTE J1751-305 and when put at the distance of the Galactic Centre (8.5 kpc). We conclude that our non-detection does not constrain any of the models for the accretion disk or possible donor stars. Deep, near-infrared images obtained during quiescence will, however, constrain possible models for the donor stars in this ultra-compact system.
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