  We investigate the cold nuclear matter effects on $J/\psi$ production, whose
understanding is fundamental to study the quark-gluon plasma. Two of these
effects are of particular relevance: the shadowing of the parton distributions
and the nuclear absorption of the $c\bar{c}$ pair. If $J/\psi$'s are not
produced {\it via} a $2 \to 1$ process as suggested by recent theoretical
works, one has to modify accordingly the way to compute the nuclear shadowing.
This naturally induces differences in the absorption cross-section fit to the
data. A careful analysis of these differences however requires taking into
account the experimental uncertainties and their correlations, as done in this
work for $d$Au collisions at $\sqrtsNN=200\mathrm{GeV}$, using several
shadowing parametrisations.
