Femtoscopy of $DN$ and $\bar{D}N$ systems

TL;DR

This work develops a comprehensive framework to compute femtoscopic correlation functions for $DN$ and $\bar{D}N$ systems in proton-proton and heavy-ion collisions. It combines a vector-meson-exchange, WT/zero-range meson-baryon interaction with both on-shell and off-shell T-matrix formalisms (LL and TROY), including Coulomb effects and a thermal-weighted channel decomposition within the Koonin-Pratt equation. The LL and full off-shell TROY approaches yield complementary insights, revealing significant coupled-channel and near-threshold resonance effects (e.g., $\Lambda_c(2595)$, $\Sigma_c(2800)$) that shape the correlation functions, particularly for $D^+p$ and $D^0p$. The results provide predictions for current and future ALICE and STAR measurements and emphasize the need to account for inelastic channels and Coulomb interactions in open-charm femtoscopy.

Abstract

The capability of the ALICE@LHC and STAR@RHIC experiments to reconstruct $D$ 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 $D$ and $\bar{D}$ 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 $T$-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.

Figures (10)

• Figure 1: $D^+p$ correlation function as function of the relative momentum. Our results with the ZR approximation are shown in black, in comparison with other works. All of them were calculated using the LL model, Eq. (\ref{['eq:CLLC']}), with the low-energy scattering parameters from each paper.
• Figure 2: $D^-p$ correlation function as function of the relative momentum. Our results with the ZR approximation are shown in black, in comparison with other works. All of them were calculated using the LL model, Eq. (\ref{['eq:CLLC']}), with the low-energy scattering parameters from each paper.
• Figure 3: $\bar{D}^0 p$ correlation function as function of the relative momentum for a source size of $r_0=1$ fm. We show the full TROY result with the ZR kernel (solid black line), the LL model (short-dashed red line), and the correlation function obtained with the on-shell version of the $T$-matrix (dash-dotted blue line).
• Figure 4: $D^-p$ correlation function as function of the relative momentum for a source size of $r_0=1$ fm. We show the full TROY result with the ZR kernel (solid black line), the elastic contribution to the TROY result (dashed green line), the LL model (short-dashed red line), and the correlation function obtained with the on-shell version of the $T$-matrix (dash-dotted blue line). The dotted blue line displays the Coulomb-only result.
• Figure 5: $D ^0p$ correlation function as function of the relative momentum for a source size of $r_0=1$ fm. We show the full TROY result with the ZR kernel (solid black line), the elastic contribution to the TROY result (dashed green line), the LL model (short-dashed red line), and the correlation function obtained with the on-shell version of the $T$-matrix (dash-dotted blue line).