The $\bf{\Lambda p}$ interaction studied via femtoscopy in p + Nb reactions at $\mathbf{\sqrt{s_{NN}}=3.18} ~\mathrm{\bf{GeV}}

We report on the first measurement of p Lambda and pp correlations via the femtoscopy method in p + Nb reactions at root sNN = 3.18 GeV, studied with the High Acceptance Di-Electron Spectrometer (HADES). By comparing the experimental correlation function to model calculations, a source size for pp pairs of r(0,pp) = 2.02 +/- 0.01(stat)(-0.12)(+0.11)(sys) fm and a slightly smaller value for p Lambda pairs of r(0,Lambda p) = 1.62 +/- 0.02(stat)(-0.08)(+0.19)(sys) fm are extracted. Using the geometrical extent of the particle-emitting region, determined experimentally with pp correlations as reference together with a source function from a transport model, it is possible to study different sets of scattering parameters. The p Lambda correlation is proven to be sensitive to predicted scattering length values from chiral effective field theory. We demonstrate that the femtoscopy technique can be used as a valid alternative to the analysis of scattering data to study the hyperon-nucleon interaction.