Extraction of $\ddot{I}‰$n, $\ddot{I}‰$p and $\ddot{I}•$N scattering lengths from $\ddot{I}‰$ and $\ddot{I}•$ differential photoproduction cross sections on the deuterium target

Abstract

In this study, we try to extract $\ddot{I}‰n$, $\ddot{I}‰p$ and $\ddot{I}•$N scattering lengths from the differential cross-section data of near-threshold $\ddot{I}‰$ and $\ddot{I}•$ photoproductions not only to the energy at threshold t${}_{thr}$, but also in t to t = 0. The incoherent data of $\ddot{I}‰$ and $\ddot{I}•$ 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 $|\hat{I}{\pm }_{\ddot{I}‰n^{\ast }}|$ and $|\hat{I}{\pm }_{\ddot{I}‰p^{\ast }}|$ of loosely bound neutron and proton in the deuteron to be 0.709 $\pm$ 0.078 fm and 0.621 $\pm$ 0.022 fm respectively at threshold t${}_{thr}$ (1.258 $\pm$ 0.130 fm and 1.056 $\pm$ 0.032 fm respectively in t to t = 0) for the first time by fitting the near-threshold data of ${\hat{I}}^3$d $\to$ $\ddot{I}‰$n(p) and ${\hat{I}}^3$d $\to$ $\ddot{I}‰$p(n). For a comparison study, we also extracted the scattering length $|\hat{I}{\pm }_{\ddot{I}‰p}|$ of the free proton from the $\ddot{I}‰$ photoproduction on the hydrogen target by CBELSA/TAPS Collaboration. With the near-threshold and incoherent $\ddot{I}•$ photoproduction data of ${\hat{I}}^3$d $\to$ $\ddot{I}•$pn by LEPS Collaboration, we obtained scattering length $|\hat{I}{\pm }_{\ddot{I}•N}|$ of the bound nucleon inside the deuteron to be 0.109 $\pm$ 0.008 fm at threshold t${}_{thr}$ and 0.276 $\pm$ 0.010 fm in t to t = 0, respectively. The obtained $|\hat{I}{\pm }_{\ddot{I}‰p}|$ and $|\hat{I}{\pm }_{\ddot{I}•N}|$ are basically in agreement with the experimental indications and the theoretical predictions within the current uncertainties.

7 pages, 6 figures