Extraction of <math><mrow><mi>ω</mi><mi>n</mi></mrow></math>, <math><mrow><mi>ω</mi><mi>p</mi></mrow></math>, and <math><mrow><mi>ϕ</mi><mi>N</mi></mrow></math> scattering lengths from <math><mi>ω</mi></math> and <math><mi>ϕ</mi></math> differential photoproduction cross sections on a deuterium target

In this study, we try to extract ωn, ωp, and ϕN scattering lengths from the differential cross-section data of near-threshold ω and ϕ photoproductions at threshold tthr. The incoherent data of ω and ϕ 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 |αωn*| and |αωp*| of loosely bound neutron and proton in the deuteron to be 0.709 &#177; 0.078 fm and 0.621 &#177; 0.022 fm, respectively, at threshold tthr for the first time by fitting the near-threshold data of γd → ωn(p) and γd → ωp(n). For a comparison study, we also extracted the scattering length |αωp| of the free proton from the ω photoproduction on the hydrogen target by the CBELSA/TAPS Collaboration. With the near-threshold and incoherent ϕ photoproduction data of γd → ϕpn by the LEPS Collaboration, we obtained scattering length |αϕN| of the bound nucleon inside the deuteron to be 0.109 &#177; 0.008 fm at threshold tthr. The obtained |αωp| and |αϕN| are basically in agreement with the experimental indications and the theoretical predictions within the current uncertainties.