$\ddot{I}‰N$ scattering length from $\ddot{I}‰$ photoproduction on the proton near the threshold

Abstract

Photoproduction of the $\ddot{I}‰$ meson on the proton has been experimentally studied near the threshold. The total cross sections are determined at incident energies ranging from 1.09 to 1.15 GeV. The 1/2 and 3/2 spin-averaged scattering length $a_{\ddot{I}‰p}$ and effective range $r_{\ddot{I}‰p}$ between the $\ddot{I}‰$ meson and proton are estimated from the shape of the total cross section as a function of the incident photon energy: $a_{\ddot{I}‰p}=\left(-0.97_{-0.16_{\mathrm{stat}}}^{+0.16_{\mathrm{stat}}}{}_{-0.00_{\mathrm{syst}}}^{+0.03_{\mathrm{syst}}}\right)+i\left(0.07_{-0.14_{\mathrm{stat}}}^{+0.15_{\mathrm{stat}}}{}_{-0.09_{\mathrm{syst}}}^{+0.17_{\mathrm{syst}}}\right)$ fm and $r_{\ddot{I}‰p}=\left(+2.78_{-0.54_{\mathrm{stat}}}^{+0.68_{\mathrm{stat}}}{}_{-0.13_{\mathrm{syst}}}^{+0.11_{\mathrm{syst}}}\right)+i\left(-0.01_{-0.50_{\mathrm{stat}}}^{+0.46_{\mathrm{stat}}}{}_{-0.00_{\mathrm{syst}}}^{+0.07_{\mathrm{syst}}}\right)$ fm, resulting in a repulsive force. The real and imaginary parts for $a_{\ddot{I}‰p}$ and $r_{\ddot{I}‰p}$ are determined separately for the first time. A small $P$-wave contribution does not affect the obtained values.

6 pages, 4 figures