Heavy-quark mass effects in off-light-cone distributions

We compute the one-loop correction to the forward matrix element of an off-light-cone bi-local quark correlator characterised by a space-like separation $z^2$ in the presence of heavy quarks with mass $m$. This calculation allows us to extract the one-loop matching kernel, necessary to connect quasi and pseudo-distributions to collinear parton distribution functions (PDFs), accounting for heavy-quark mass effects. Our result is exact in that it includes all powers of $z^2m^2$ at one loop in $α_s$. In the limit $z^2m^2\rightarrow 0$, it consistently reduces to the known massless result. We also carry out an implementation of our expression, which allows us to compute the charm pseudo-distribution of the proton given its PDF. We finally comment on the quantitative impact of heavy-quark mass corrections.