Scattering data and correlation function for the $K f_1(1285)$ interaction

TL;DR

This work investigates the interaction of a kaon with the f_1(1285) resonance, treated as a KK^*–bar KK^* molecular state in an improved fixed center approximation that preserves elastic unitarity. By computing the three-body amplitude and threshold scattering parameters, the authors find a near-threshold resonance about 10 MeV below the K f_1 threshold with a width near 15 MeV, and predict a distinctive correlation function shape consistent with a bound state. The analysis distinguishes the molecular picture from an elementary f_1(1285), showing a strong attractive interaction only in the molecular scenario. The results provide experimentally accessible observables for ALICE and related experiments to test the f_1(1285) structure via particle–resonance correlations and multi-particle final-state analyses, potentially revealing a K f_1 bound state.

Abstract

We study the interaction of a kaon with the $f_1(1285)$ resonance, assuming that the $f_1(1285)$ is a molecular state generated by the $K \bar K^*, \bar K K^*$ interaction, evaluating the scattering amplitude, the scattering length and effective range of the $K f_1$ system. The scattering amplitude develops a resonant structure approximately $10$ MeV below the $K f_1$ threshold, with a width of around $15$ MeV. The corresponding correlation function has the distinctive shape of a system with a bound state close to threshold. We also show that the interaction of the $K f_1$ system is differs significantly from the one obtained assuming that the $f_1(1285)$ is an elementary particle. This provides motivation to continue the search for these observables, already initiated by the measurement of the $p f_1(1285)$ correlation function by the ALICE collaboration.

Figures (7)

• Figure 1: Diagrams entering the ordinary FCA approach for $K^+$ interacting with the cluster of $K^*\bar{K}$.
• Figure 2: Diagrams considering the elastic propagation of the $K^+$ and the cluster $f_1(1285)$ as a whole.
• Figure 3: Results for $T_{K^*\bar{K}}^{\,\mathrm{tot}}$ from Eq. \ref{['eq:1']}. The dashed line represents the real part, the dashed dotted line the imaginary part and the solid line the modulus of the scattering amplitude. The vertical line corresponds to the threshold mass, $M_{K^+}+M_c$.
• Figure 4: Correlation function of the component $K^*\bar{K}$ of the $f_1(1285)$ wave function.
• Figure 5: Result for $T^{\, \rm tot}$ of Eq. \ref{['eq:16']}, considering the two components $K^* \bar{K}$ and $\bar{K}^* K$ of the $f_1(1285)$ wave function.