ω N scattering length from ω photoproduction on the proton near the reaction threshold

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.