# H0LiCOW VIII. Weak lensing mass reconstruction of HE0435-1223.

The effectiveness of the quasar time-delay method in constraining the Hubble Constant H_{0} depends on the lens potential at the position of the quasar images and on the contribution of external galaxies along the line of sight. This external contribution, measured as the dimensionless projected mass κ_{ext}, can be estimated in various ways based, e.g. on N-body simulations or galaxy numbers counts. In this work we present a more direct measurement of κ_{ext} for the
quadruply imaged quasar HE0435-1223, using weak lensing measurement on deep r-band Subaru SuprimeCam images (r<26.5, seeing=0.7"). We reconstruct mass maps for the 0.5x0.5 deg^{2} field of view using several techniques including inpainting methods based on a sparse representation of the shear field. We show that there is no large mass distribution along the line of sight to HE0435-1223, and we set an upper limit of κ_{ext} at the position of the lensed quasar. Importantly, our mass maps do not show significant systematics, i.e. the B-modes are negligible. We also mock our data to infer the lowest detectable mass. We find that our data and method would have been able to detect any massive halo with a solid dectection probability. We conclude that the maximum possible bias on H_{0} due to line of sight contamination for HE0435-1223 is at most a few percents.