Measurement of Differential Cross Sections and Integrated Luminosity using Proton-Proton Elastic Scattering with HADES at T = 4.53 GeV and T = 1.60 GeV
This work presents an investigation of elastic proton-proton scattering based on data collected with the recently upgraded HADES detector using beams of protons with kinetic energies of $T = 4.53$ GeV and $T = 1.60$ GeV impinging on a liquid hydrogen target. This is the first measurement emerging from the upgraded detector setup, including a Forward Detector with straw-tube tracking planes designed for the PANDA experiment. The well-constrained two-body kinematic relations of elastic scattering have been exploited to study the detector alignment, the beam alignment, and to provide the final measurement of the beam energy. In addition, the recorded luminosity of the experiment has been determined by normalizing the HADES data in a range of the squared four-momentum transfer $t$ that overlaps with measurements by previous experiments worldwide. Furthermore, the differential cross sections have been determined over a large range of $t$ from which the slope parameter $B$ is extracted, yielding $B = 8.98 \pm 0.3$ (GeV/$c$)$^{-2}$ and $7.3 \pm 0.1$ (GeV/$c$)$^{-2}$ at $T = 4.53$ GeV and $1.60$ GeV, respectively. This contribution to the world database on elastic proton-proton scattering provides input to theoretical modeling and serves as a reference for luminosity determinations by future experiments in the same energy range.