The \(\eta^{\prime}\)-carbon potential at low meson momenta

The production of \(\eta^{\prime}\) mesons in coincidence with forward-going protons has been studied in photon-induced reactions on 12C and on a liquid hydrogen (LH2) target for incoming photon energies of 1.3-2.6 GeV at the electron accelerator ELSA. The \(\eta^{\prime}\) mesons have been identified via the \(\eta^{\prime} \rightarrow \pi^{0} \pi^{0}\eta \rightarrow 6 \gamma\) decay registered with the CBELSA/TAPS detector system. Coincident protons have been identified in the MiniTAPS BaF2 array at polar angles of \(2^{\circ} \le \theta_{p} \le 11^{\circ}\). Under these kinematic constraints the \(\eta^{\prime}\) mesons are produced with relatively low kinetic energy (\(\approx 150\) MeV) since the coincident protons take over most of the momentum of the incident-photon beam. For the C-target this allows the determination of the real part of the \(\eta^{\prime}\)-carbon potential at low meson momenta by comparing with collision model calculations of the \(\eta^{\prime}\) kinetic energy distribution and excitation function. Fitting the latter data for \(\eta^{\prime}\) mesons going backwards in the center-of-mass system yields a potential depth of \(V = -(44 \pm 16(stat) \pm 15(syst))\) MeV, consistent with earlier determinations of the potential depth in inclusive measurements for average \(\eta^{\prime}\) momenta of \(\approx 1.1\) GeV/c. Within the experimental uncertainties, there is no indication of a momentum dependence of the \(\eta^{\prime}\)-carbon potential. The LH2 data, taken as a reference to check the data analysis and the model calculations, provide differential and integral cross sections in good agreement with previous results for \(\eta^{\prime}\) photoproduction off the free proton.