### The hyperon puzzle in neutron stars: Studying the hyperon-nucleon interactions in ALICE and HADES

One of the questions we are specifically addressing within our research group is the study of hyperon-nucleon and hyperon-nucleon-nucleon interactions in the vacuum. Indeed, already this basic piece of information is rather scarcely known. There are some scattering data with low statistics for the most common hyperon species as Λ and Σ and the measurements of Λ-hypernuclei of different size deliver information about the average interaction of this hyperon with nucleons but a detailed parametrization of the interaction as a function of the hadron distance and quantum numbers is not available and for hyperons as Ξ and Ω we do not even have quantitative information on average quantities.

This is where the **femtoscopy** technique can be useful.

The femtoscopy era was started in astronomy by measuring the (angular) size of stars by investigating the correlations between photons emitted from the latter. In particle physics the method was independently established to exploit the production of pions and introduce a symmetrization of the multiparticle wave function to describe the observed spectra. This (anti)symmetrization of the total wave function is a basic principle of quantum mechanics and influences particle pairs which are produced closely in phase-space and travels to the detector with a small relative momentum. Not only quantum statistics influences the final spectra but also final state interactions can play a role.

Femtoscopy normally focuses on the investigation of the size and time evolution of the region the particles are emitted from, which happens on the Femtometer scale (10−15 m). But since femtoscopy is also based on final state interactions one can use the method to study strong final state interactions of pairs where not much is known about the interaction and scattering experiments are difficult to realize. Our specific goal is to use p+p, p+A reactions at different energies ( GeV and TeV) to study the final state interaction of hyperon-nucleon and hyperon-nucleon-nucleon interactions. Indeed the source that generates the hadrons of interest in p+p and p+A reactions does not evolve in a sophisticated way as a function of time, no phase transitions occur and hence it can be modelled rather easily via simulation. If the source is known or at least well constrained, the measured correlation function provides the information about the final state interaction.

The figure here shows an example of the pp and Lambda-p correlation obtained as a function of the relative momentum k for the chosen particle pair measured in p+Nb fixed target collisions at beam kinetic energies of 3.5 GeV in HADES and the same analysis can be performed in p+p collisions at the LHC collider for energies equal to 7 TeV. The source produced in the two colliding system has a difference size, about 2 fm for the GeV energies and 1.2 fm for the TeV range, but the final state interaction among the outgoing hadrons is the same. An attractive interaction manifest itself as a correlation function larger than 1, while a negative interaction leads to values lower than 1. One can see that the effect of the attractive long range pp and Λ-p interaction and repulsive Coulomb interaction for pp. These plots show that the method works but the data collected so far, especially for the Λ-p case, are not sufficient to draw quantitative conclusions on the interaction yet. So more measurements are needed. This is also the reason why we are building a new faster detector components for the ALICE experiment at CERN, to be able to collect sufficient statistics during the RUN3 period starting in 2020 ( see our GEM-TPC project upgrade).