Are the total mass density and the low-mass end slope of the IMF anti-correlated?

We conduct a detailed lensing, dynamics and stellar population analysis of nine massive lens early-type galaxies (ETGs) from the X-Shooter Lens Survey (XLENS). Combining gravitational lensing constraints from HST imaging with spatially-resolved kinematics and line-indices constraints from VLT X-Shooter (XSH) spectra, we infer the low-mass slope and the low cut-off mass of the stellar Initial Mass Function (IMF): $x_{250}=2.37^{+0.12}_{-0.12}$ and $M_{{\rm low}, 250}= 0.131^{+0.023}_{-0.026}\, M_{\odot}$, respectively, for a reference point with $\sigma \equiv 250\, {{\rm kms}}^{-1}$ and R$_{{\rm eff}} \equiv 10$ kpc. All the XLENS systems are consistent with an IMF slope steeper than Milky Way-like. We find no significant correlations between IMF slope and any other quantity, except for an anti-correlation between total dynamical mass density and low-mass IMF slope at the 87% CL [$dx/d\log(\rho)$ = $ -0.19^{+0.15}_{-0.15}$]. This anti-correlation is consistent with the low redshift lenses found by Smith et al. (2015) that have high velocity dispersions and high stellar mass densities but surprisingly shallow IMF slopes.