Extraction of $ω$n, $ω$p and $ϕ$N scattering lengths from $ω$ and $ϕ$ differential photoproduction cross sections on the deuterium target

Abstract

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 not only to the energy at threshold t thr , but also in t to t = 0. The incoherent data of ω and φ photoproductions on deuterium target for scattering length extractions are provided by CBELSA/TAPS Collaboration and LEPS Collaboration respectively, where the deuteron is usually approximated as a weakly bound state of a quasi-free neutron plus a quasi-free proton. Under the Vector Meson Doninance 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 ± 0.078 fm and 0.621 ± 0.022 fm respectively at threshold t thr (1.258 ± 0.130 fm and 1.056 ± 0.032 fm respectively in t to t = 0) 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 CBELSA/TAPS Collaboration. With the near-threshold and incoherent φ photoproduction data of γd → φpn by LEPS Collaboration, we obtained scattering length |α φN | of the bound nucleon inside the deuteron to be 0.109 ± 0.008 fm at threshold t thr and 0.276 ± 0.010 fm in t to t = 0, respectively. The obtained |αωp| and |α φN | are basically in agreement with the experimental indications and the theoretical predictions within the current uncertainties.