Weak lensing survey of galaxy clusters in the CFHTLS Deep

AIMS: We present a weak lensing search of galaxy clusters in the 4 deg2 of the CFHT Legacy Survey Deep. This work aims at building a mass-selected sample of clusters. METHODS: We use the deep i' band images to perform weak lensing mass reconstructions and to identify high convergence peaks. Thanks to the availability of deep ugriz exposures, sources are selected from their photometric redshifts. We also use lensing tomography to derive an estimate of the lens redshift. After considering the raw statistics of peaks we check whether they can be associated to a clear optical counterpart or to published X-ray selected clusters. RESULTS: Among the 14 peaks found above a signal-to-noise detection threshold nu=3.5, eight are secure detections with estimated redshift 0.15<zl<0.6 and a velocity dispersion 450<sigma\_v<600 km/s. This low mass range is accessible thanks to the high density of background sources. We also use photometric redshifts of sources to test the effect of contamination by source-lens clustering for clusters detection. This latter turns out to play a minor role in our cluster sample. We study the intersection between the shear-selected clusters and XMM/LSS X-ray clusters in the D1 field. [ABRIDGED]