$Λ_c N$ correlation functions with leading-order covariant chiral interactions

Abstract

The $Λ_c p$ momentum correlation functions are investigated using $Λ_c N$ interactions derived within the covariant chiral effective field theory. Our analysis reveals that the interaction is weakly attractive in the spin-singlet ${}^1S_0$ channel. In contrast, the ${}^3S_1$ channel exhibits a pronounced sensitivity to coupled-channel effects, i.e., the inclusion of $S$--$D$ mixing results in a repulsive $Λ_c p$ interaction; its absence leads to a weakly attractive one. Consequently, the spin-averaged correlation function -- dominated by the triplet state weight -- exhibits repulsive behavior when the $S$-- $D$ mixing is present. Furthermore, the source size dependence of the correlation functions is examined, demonstrating that the resulting variations remain experimentally resolvable within the precision of current femtoscopic measurements. A systematic comparison with non-relativistic chiral effective field theory and phenomenological models yields distinct discrepancies in the femtoscopic correlation functions. These findings underscore the capacity of femtoscopy to discriminate between different theoretical descriptions of the $Λ_c N$ interaction and provide useful references for upcoming experimental data.

Figures (5)

• Figure 1: $\Lambda_c N$$S$-wave phase shifts of the lattice QCD simulations in comparison with the ChEFT fits. Magenta and dark-blue dots correspond to the LQCD data Miyamoto:2017tjs at $m_{\pi}=410$ MeV and 570 MeV, respectively. Magenta and dark blue bands show the ChEFT fits with $\Lambda_F$ ranging from 500 to 600 MeV. Yellow and light-blue bands denote ChEFT predictions at $m_{\pi}=138$ MeV. The $\Lambda_c N$ interaction is obtained by fitting to the lattice QCD data only up to $E=30$ MeV.
• Figure 2: Effect of the Coulomb interaction on the $\Lambda_c p$ correlation function in the $^1S_0$ and $^3S_1$ partial waves. (a) The yellow (yellow shaded) band shows the results without (with) the Coulomb interaction. (b) Similar to panel (a), the $^{3}S_{1}$ results with $S-D$ mixing are shown. (c) Similar to panel (a), the $^{3}S_{1}$ results without $S-D$ mixing are shown.
• Figure 3: Spin-averaged $\Lambda_c p$ correlation functions for $R=1.2$ fm with the Coulomb interaction. The covariant ChEFT with $S-D$ mixing (blue) and without $S-D$ mixing (yellow) are shown. The dotted curve denotes the result obtained with the pure Coulomb interaction.
• Figure 4: The spin-averaged $\Lambda_c p$ correlation functions that include the Coulomb interaction are presented for three different source radii $R$. Predictions from the covariant ChEFT with $S$–$D$ mixing are presented. For reference, the results obtained with the pure Coulomb correlation are displayed as a dotted line.
• Figure 5: Spin-averaged $\Lambda_c p$ correlation functions including the Coulomb interaction for $R = 1.2$ fm. Results obtained from covariant ChEFT (blue band), non-relativistic ChEFT (green band) Haidenbauer:2020kwo, the simulation of the CTNN-d model (dashed line) Haidenbauer:2020kwo, and the pure Coulomb interaction (dotted line) are shown.