Context :

Aims : Various studies have shown a lensing bias in the mass-concentration relation of cluster-scale structures due to alignment of the major axis and the line of sight .
In this paper , we aim to study this lensing bias through the mass-concentration relation of galaxy groups , thus extending observational constraints to dark matter haloes of mass \sim 10 ^ { 13 } -10 ^ { 14 } \mathrm { M _ { \odot } } .

Methods : Our work is based on the stacked weak-lensing analysis of a sample of 80 strong-lensing galaxy groups .
By combining several lenses , we increase significantly the signal-to-noise ratio of the lensing signal , thus providing constraints on the mass profile that can not be obtained for individual objects .
The resulting shear profiles are fitted with various mass models , among them the NFW profile , which provides an estimate of the total mass and concentration of the composite galaxy groups .

Results : The main results of our analysis are the following : ( i ) the lensing signal does not allow us to firmly reject a simple singular isothermal sphere mass distribution compared to the expected NFW mass profile ; ( ii ) we obtain an average concentration c _ { 200 } = 8.6 _ { -1.3 } ^ { +2.1 } that is much higher than the expected value from numerical simulations for the corresponding average mass M _ { 200 } = 0.73 _ { -0.10 } ^ { +0.11 } \times 10 ^ { 14 } \mathrm { M _ { \odot } } ; ( iii ) the combination of our results with those at larger mass scales gives a mass-concentration relation c ( M ) over nearly two decades in mass , with a slope in disagreement with predictions from numerical simulations using unbiased populations of dark matter haloes ; ( iv ) our combined c ( M ) relation matches results from simulations using only haloes with a large strong-lensing cross section , i.e .
elongated with a major axis close to the line of sight ; ( v ) for the simplest case of prolate haloes , we estimate with a toy model a lower limit on the minor : major axis ratio a / c = 0.5 for the average SARCS galaxy group .

Conclusions : Our analysis based on galaxy groups confirmed the results obtained at larger mass scales : strong lenses present apparently too large concentrations , which can be explained by triaxial haloes preferentially oriented with the line of sight .
Because more massive systems already have large lensing cross sections , they do not require a large elongation along the line of sight , contrary to less massive galaxy groups .
Therefore , it is natural to observe larger lensing ( projected ) concentrations for such systems , resulting in an overall mass-concentration relation steeper than that of non-lensing haloes .