First measurement of the strong interaction scattering parameters for the $\mathbf{K^-d}$ and $\mathbf{K^+d}$ systems

Abstract

Charged kaon--deuteron interactions offer a sensitive probe of the strangeness sector of QCD at low energy, particularly through their scattering parameters. Despite available theoretical predictions, experimental constraints remain absent, particularly for the $\rm K^{-}d$ system. The first measurement of femtoscopic correlation functions for $\rm K^{-}d \oplus K^{+}\overline{d}$ and $\rm K^{+}d \oplus K^{-}\overline{d}$ particle pairs in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV recorded by ALICE at the LHC is presented. Correlation functions for both systems are analyzed in three centrality classes and fitted using the Lednický--Lyuboshitz model to extract the source size and strong interaction scattering lengths. The $\rm K^{-}d$ scattering length is found to be $\Re f_0 = -1.44 \pm 0.15\text{ (stat.)}^{+0.10}_{-0.10}$ (syst.) fm and $\Im f_0 = 1.34 \pm 0.33$ (stat.)$^{+0.21}_{-0.15}$ (syst.) fm, while for $\rm K^{+}d$ the value $\Re f_0 = -0.68 \pm 0.16$ (stat.)$^{+0.09}_{-0.09}$ (syst.) fm is obtained. These results provide the first constraints on the $\rm K^{\pm} d$ interaction modeling at low energy, delivering a long-awaited experimental benchmark for testing chiral QCD dynamics.

Figures (3)

• Figure 1: The $\rm K^{+}d$$\oplus$$\rm K^{-}\overline{d}$ (top pads of panels a, b, c), and $\rm K^{-}d$$\oplus$$\rm K^{+}\overline{d}$ (top pads of panels d, e, f), correlation functions in the three centrality classes 0$-$10$\%$, 10$-$30$\%$, 30$-$50$\%$ represented with markers. The vertical lines and gray boxes correspond to the statistical and systematic uncertainties, respectively. The light violet and orange bands corresponds to Lednický--Lyuboshits fits (denoted as L--L), including Coulomb and strong interactions. The width of the bands represents the systematic uncertainties of the fit. The bottom pads in all panels show the difference between the data and the L--L fit normalised by the statistical uncertainty of the data $\sigma_{\text{stat}}$.
• Figure 2: Scattering lengths of $\rm K^{-}d$: Lednický--Lyuboshits fit obtained in this study (red marker), available theoretical calculations using input data from SIDDHARTA and KEK experiments (blue markers) Duerinck:2025pbjLiu:2020focHoshino:2017mtyMizutaniShevchenko:2014uvaShevchenkoDoring. The full and empty ellipses correspond to systematic and statistical uncertainties of the ALICE measurement, respectively.
• Figure 3: Scattering lengths of $\rm K^{+}d$: Lednický--Lyuboshits fit obtained in this study (red marker), available theoretical calculations (blue marker) provided with the FCA Kamalov:2000iy with the KN scattering lengths from Ref. Aoki:2018wug and effective range fit (ER) PhysRevC.81.055204 to the cross section predictions at threshold anchored to the scattering data PhysRevC.81.055204. The full box and line correspond to systematic and statistical uncertainties of the ALICE measurement, respectively.