Femtoscopy of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:move

The capability of the ALICE@LHC and STAR@RHIC experiments to reconstruct <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>D</a:mi> </a:math> mesons has enabled femtoscopic correlation measurements of open-charm mesons in both small and large systems. In this work, we present a theoretical calculation of the correlation functions of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>D</c:mi> </c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mover accent="true"> <e:mi>D</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> </e:math> mesons with nucleons, based on the Koonin-Pratt formalism. We employ an effective Lagrangian to model the interaction between charmed mesons and baryons and apply the TROY formalism to obtain the off-shell <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>T</i:mi> </i:math> -matrix in coupled channels, incorporating the effect of the Coulomb interaction when the pair involves two charged particles. The resulting full coupled-channel wave function is inserted into the Koonin-Pratt equation with channel weights derived from a thermal model. Additionally, we compute the correlation functions using the Lednický-Lyuboshitz approximation with low-energy scattering parameters extracted from the unitarized amplitudes. We compare these two approaches and provide predictions for different correlated pairs. Our results can be tested against current and future experimental data from the ALICE and STAR Collaborations in both proton-proton and heavy-ion collisions.