This article presents the first measurement of the interaction between charm hadrons and nucleons. The two-particle momentum correlations of $\mathrm{pD^-}$ and $\mathrm{\overline{p}D}^+$ pairs are measured by the ALICE Collaboration in high-multiplicity pp collisions at $\sqrt{s} = 13~\mathrm{TeV}$. The data are compatible with the Coulomb-only interaction hypothesis within (1.1-1.5)$\sigma$. The level of agreement slightly improves if an attractive nucleon(N)$\overline{\mathrm{D}}$ strong interaction is considered, in contrast to most model predictions which suggest an overall repulsive interaction. This measurement allows for the first time an estimation of the 68% confidence level interval for the isospin $\mathrm{I}=0$ inverse scattering length of the $\mathrm{N\overline{D}}$ state ${f_{0,~\mathrm{I}=0}^{-1} \in [-0.4,0.9]~\mathrm{fm^{-1}}}$, assuming negligible interaction for the isospin $\mathrm{I}=1$ channel.
$\mathrm{pD^-}$ $\oplus$ $\mathrm{\overline{p}D^+}$ momentum correlation function as a function of the relative momentum in the particle-pair rest frame $k^*$ in high-multiplicity (0-0.17%) pp collisions at $\sqrt{s}=13$ TeV.
$1\sigma$ confidence interval for the $\mathrm{N\overline{D}}$ inverse scattering length for the isospin $\mathrm{I}=0$ channel, $f_{0,~\mathrm{I}=0}^{-1}$, as a function of the effective source radius $R_\mathrm{eff}$.
Best fit for the $\mathrm{N\overline{D}}$ inverse scattering length for the isospin $\mathrm{I}=0$ channel, $f_{0,~\mathrm{I}=0}^{-1}$, as a function of the effective source radius $R_\mathrm{eff}$.
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