BAO + SNe + CFHTLS contour would thus descend along the WMAP5 + BAO + SNe one producing a positive lower bound for the neutrino mass. A similar effect appeared in Allen [et al. ]{}(2003), which also showed a preference for a non-zero neutrino mass from a combination of CMB, galaxy clustering and X-ray cluster data; that result was in fact caused by an underestimation of $\sigma_8$, as pointed out by Seljak [et al. ]{}(2005). Similarly, the joint constraint depends crucially on BAO data. Komatsu [et al. ]{}(2008) pointed out a tension between SNe and BAO results when the joint SDSS + 2dFGRS BAO sample is used. If BAO data overestimates the total matter density, then an unbiased WMAP5 + BAO + SNe contour in the $(\omega_\nu,\omega_{\mathrm{cdm}})$ plane (Fig. \[fig:joint\], left panel) will be shifted towards the bottom-left corner, weakening the preference for massive neutrinos.

Robustness of the constraints {#sec3c}
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We check here the robustness of our results against systematics of the cosmic shear data, that have not been included in the analysis so far. For this purpose, we first assume the data vector is biased as a consequence of an underestimation in the shear, as indicated by the 