We searched for isolated planetary-mass T-dwarfs in the 3Myr old Serpens Core cluster. We performed a deep imaging survey of the central part of this cluster using the WIRCam camera at the CFHT. Observations were performed through the narrow-band CH4_off and CH4_on filters, to identify young T-dwarfs from their 1.6micr methane absorption bands, and the broad-band JHK filters, to better characterize the selected candidates. We complemented our WIRCam photometry with optical imaging data from MegaCam at CFHT and Suprime-Cam at the Subaru telescope and mid-IR flux measurements from the Spitzer c2d Legacy Survey. We report four faint T-dwarf candidates in the direction of the Serpens Core with CH4_on-CH4_off above 0.2 mag, estimated visual extinction in the range 1-9 mag and spectral type in the range T1-T5 based on their dereddened CH4_on-CH4_off colors. Comparisons with T-dwarf spectral models and optical to mid-IR color-color and color-magnitude diagrams, indicate that two of our candidates (ID1 and 2) are background contaminants (most likely heavily reddened low-redshift quasars). The properties of the other two candidates (ID3 and 4) are consistent with them being young members of the Serpens Core cluster, although our analysis can not be considered conclusive. In particular, ID3 may also be a foreground T-dwarf. It is detected by the Spitzer c2d survey but only flux upper limits are available above 5.8 microns and, hence, we can not assess the presence of a possible disk around this object. However, it presents some similarities with other young T-dwarf candidates (SOri70 in the Sigma Ori cluster and CFHTJ0344+3206 in the direction of IC348). If ID3 and 4 belong to Serpens, they would have a mass of a few Jupiter masses and would be amongst the youngest, lowest mass objects detected in a star-forming region so far.
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