Femtoscopy of $DN$ and $ar{D}N$ systems

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.

💡 Research Summary

The paper presents a comprehensive theoretical study of femtoscopic correlation functions for open‑charm mesons (D and (\bar D)) interacting with nucleons, motivated by recent capabilities of the ALICE (LHC) and STAR (RHIC) experiments to reconstruct D mesons in both small (pp) and large (AA) collision systems. The authors employ the Koonin‑Pratt (KP) formalism as the basic framework for femtoscopy, where the correlation function (C(k)) is obtained by folding the squared two‑particle wave function with a Gaussian source.

The strong interaction between the charmed meson and the nucleon is modeled using an effective Lagrangian based on vector‑meson exchange. In the zero‑range (ZR) approximation the tree‑level potential reduces to a Weinberg‑Tomozawa‑type interaction, Eq. (4), with universal coupling (g=m_V/(\sqrt{2}f)). The model includes all relevant coupled channels in the (C=+1) (D N) and (C=-1) ((\bar D) N) sectors, leading to 7–8 coupled channels for the D N case and a single channel for the (\bar D) N case.

To obtain the scattering amplitudes the Bethe‑Salpeter equation is solved both on‑shell (factorized) and off‑shell. The off‑shell T‑matrix is computed with the TROY (T‑matrix‑based Routine for hadrOn femtoscopy) formalism, which retains the full momentum dependence of the kernel and regularizes the ultraviolet divergence with a three‑momentum cutoff (k_{\rm max}). The cutoff is fixed by reproducing the dynamically generated (\Lambda_c(1295)) pole in the D N sector.

Two distinct methods for constructing the two‑particle wave function are compared. The first is the Lednický‑Lyuboshitz (LL) approximation, where the asymptotic wave function is used together with the effective‑range expansion of the scattering amplitude, including Coulomb corrections via the Gamow factor and the Sommerfeld parameter. This approach only incorporates the elastic channel and therefore neglects coupled‑channel dynamics.

The second method, the TROY approach, builds the full s‑wave component of the wave function directly from the half‑off‑shell T‑matrix, Eq. (23), and adds the appropriate Coulomb wave function when both particles are charged. Production weights (w_i) for each channel are estimated using a static fireball model with a temperature (T=171) MeV, following a thermal‑FIST prescription. This allows the correlation function to reflect realistic feed‑down contributions and relative abundances of the coupled channels.

Results show that the LL approximation yields smooth correlation functions governed solely by the scattering length (a_0) and effective range (d_0). In contrast, the TROY calculations exhibit pronounced structures at low relative momenta (30–80 MeV/c) arising from coupled‑channel effects, especially the influence of the (\Lambda_c(1295)) resonance and the opening of inelastic channels. Coulomb interactions produce the expected suppression (for like‑sign pairs) or enhancement (for opposite‑sign pairs) at the smallest (k) values, quantified by the Gamow factor. Sensitivity studies indicate that the source radius (r_0) (taken between 1 and 2 fm) significantly affects the width of the correlation peak, while the temperature choice mainly influences the channel weights.

The authors conclude that the TROY framework provides a more realistic description of D N and (\bar D) N femtoscopy than the traditional LL model, as it naturally incorporates coupled‑channel dynamics, Coulomb effects, and thermal production weights. The predictions presented for the four charge states (D⁺p, D⁻p, D⁰p, (\bar D^0)p) are ready to be confronted with forthcoming ALICE and STAR measurements, offering a novel avenue to extract low‑energy D‑N scattering parameters and to confirm the existence of dynamically generated charmed baryon resonances.