A femtoscopic Correlation Analysis Tool using the Schr\"odinger equation (CATS)

We present a new analysis framework called "Correlation Analysis Tool using the Schr\"odinger equation" (CATS) which computes the two-particle femtoscopy correlation function $C(k)$, with $k$ being the relative momentum for the particle pair. Any local interaction potential and emission source function can be used as an input and the wave function is evaluated exactly. In this paper we present a study on the sensitivity of $C(k)$ to the interaction potential for different particle pairs: p-p, p-$\mathrm{\Lambda}$, $\mathrm{K^-}$-p, $\mathrm{K^+}$-p, p-$\mathrm{\Xi}^-$ and $\mathrm{\Lambda}$-$\mathrm{\Lambda}$. For the p-p Argonne $v_{18}$ and Reid Soft-Core potentials have been tested. For the other pair systems we present results based on strong potentials obtained from effective Lagrangians such as $\chi$EFT for p-$\mathrm{\Lambda}$, J\"ulich models for $\mathrm{K(\bar{K})}$-N and Nijmegen models for $\mathrm{\Lambda}$-$\mathrm{\Lambda}$. For the p-$\mathrm{\Xi}^-$ pairs we employ the latest lattice results from the HAL QCD collaboration. Our detailed study of different interacting particle pairs as a function of the source size and different potentials shows that femtoscopic measurements can be exploited in order to constrain the final state interactions among hadrons. In particular, small collision systems of the order of 1~fm, as produced in pp collisions at the LHC, seem to provide a suitable environment for quantitative studies of this kind.