$ωN$ scattering length from $ω$ photoproduction on the proton near the threshold

Abstract: Photoproduction of the $\omega$ 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 $a_{\omega p}$ and effective range $r_{\omega p}$ between the $\omega$ meson and proton are estimated from the shape of the total cross section as a function of the incident photon energy: $a_{\omega p} = \left(-0.97^{+0.16_{\rm stat}}{-0.16{\rm stat}}{}^{+0.03_{\rm syst}}{-0.00{\rm syst}}\right)+i \left(0.07^{+0.15_{\rm stat}}{-0.14{\rm stat}}{}^{+0.17_{\rm syst}}{-0.09{\rm syst}}\right)$ fm and $r_{\omega p}=\left(+2.78^{+0.68_{\rm stat}}{-0.54{\rm stat}}{}^{+0.11_{\rm syst}}{-0.13{\rm syst}}\right)+i\left(-0.01^{+0.46_{\rm stat}}{-0.50{\rm stat}}{}^{+0.07_{\rm syst}}{-0.00{\rm syst}}\right)$ fm, resulting in a repulsive force. The real and imaginary parts for $a_{\omega p}$ and $r_{\omega p}$ are determined separately for the first time. A small $P$-wave contribution does not affect the obtained values.