Extraction of con, cop, and phi N scattering lengths from co and phi differential photoproduction cross sections on a deuterium target

In this study, we try to extract omega n, omega p, and phi N scattering lengths from the differential cross-section data of near-threshold omega and phi photoproductions at threshold tthr. The incoherent data of omega and phi photoproductions on deuterium target for scattering length extractions are provided by the CBELSA/TAPS Collaboration and LEPS Collaboration, respectively, where the deuteron is usually approximated as a weakly bound state of a quasifree neutron plus a quasifree proton. Under the vector meson dominance model and the assumption of energy independence of the differential cross section, we obtained the |alpha omega n* | and |alpha omega p* | of loosely bound neutron and proton in the deuteron to be 0.709 +/- 0.078 fm and 0.621 +/- 0.022 fm, respectively, at threshold tthr for the first time by fitting the near-threshold data of gamma d -> omega n(p) and gamma d -> omega p(n). For a comparison study, we also extracted the scattering length |alpha omega p| of the free proton from the omega photoproduction on the hydrogen target by the CBELSA/TAPS Collaboration. With the near-threshold and incoherent phi photoproduction data of gamma d -> phi pn by the LEPS Collaboration, we obtained scattering length |alpha phi N| of the bound nucleon inside the deuteron to be 0.109 +/- 0.008 fm at threshold tthr. The obtained |alpha omega p| and |alpha phi N | are basically in agreement with the experimental indications and the theoretical predictions within the current uncertainties.