Kaon-deuteron femtoscopy from unitarized chiral interactions

Abstract

We have performed a theoretical study of the correlation functions of $K^- d$ and $K^+ d$ pairs and compared them with those provided by the ALICE Collaboration from Pb-Pb collisions, and also from high-multiplicity p-p collisions in the case of $K^+ d$. In addition to implementing the effect of the Coulomb force, the $K^- d$ and $K^+ d$ wave functions are derived from the corresponding strong scattering amplitudes that are built employing a unitarized chiral model for the elementary $K^- N$ and $K^+ N$ interactions. We present results for the impulse approximation, which accounts for single-scattering processes of the kaon with the nucleons of the deuteron, as well as for the solution of the Faddeev equations in the so-called fixed center approximation, which includes multiple rescattering effects. The $K^- d$ correlation function is shown to be very sensitive to both the size of the source and the relative momentum of the interacting pair, with large deviations from the Coulomb baseline and sizable multi-step scattering contributions, effects that are tied to a ${\bar K}N$ strong interaction that is dominated by the influence of the subthreshold resonance $Λ(1405)$. In contrast, the $K^+ d$ correlation function only differs appreciably from the Coulomb one for relatively small sources, reflecting the mildly repulsive and elastic behavior of the $KN$ strong force. The calculated correlation functions are found to nicely reproduce the experimental data of the ALICE collaboration. Our study serves to reinforce the validity of the theoretical models employed and demonstrates the value of femtoscopy as a powerful tool for probing hadronic interactions involving strangeness.

Figures (9)

• Figure 1: Diagrams contributing to the $K^-d$ Faddeev equations in the fixed-center approximation. The three rows correspond to the Faddeev partitions denoted as $T_p^-$ (top), $T_n^-$ (middle) and $T_n^\mathrm{x}$ (bottom).
• Figure 2: Diagrams contributing to the $K^+d$ Faddeev equations in the fixed-center approximation. The three rows correspond to the Faddeev partitions denoted as $T_p^+$ (top), $T_n^+$ (middle) and $T_p^\mathrm{x}$ (bottom) scatterings.
• Figure 3: (a) Scattering amplitude $T_{K^- d}$ for $K^- d \to K^- d$ around and below the $K^- d$ threshold. The solid lines represent the real part and the dashed lines the imaginary part. The red lines correspond to the IA and the blue lines to the FCA. (b) Squared modulus of the scattering amplitude $|T_{K^- d}|^2$. The $K^-pn$ and $\bar{K}^0nn$ thresholds are indicated with vertical dashed lines.
• Figure 4: (a) Scattering amplitude $T_{K^+ d}$ for the process $K^+ d \to K^+ d$ around and below the $K^+ d$ threshold. The solid lines represent the real part and the dashed lines the imaginary part. The red lines correspond to the IA and the blue lines to the FCA. (b) Squared modulus of the scattering amplitude $|T_{K^+ d}|^2$. The $K^+ np$ and the $K^0pp$ thresholds are indicated with vertical dashed lines.
• Figure 5: Correlation function $C(k^*)$ of $K^-d$ pairs for three different values of the radius $R_{Kd}$ of the Gaussian source. The green line accounts only for the Coulomb interaction, while the additional effects of the strong $K^-d$ amplitude are implemented within the IA (red line) or the FCA (black line).