# $\omega N$ scattering length from $\omega$ photoproduction on the proton near the threshold

## TL;DR

This study measures the $oldsymbol{ ext{omega}}$ meson-proton scattering length near threshold using photoproduction data, providing the first separate determination of real and imaginary parts, indicating a repulsive interaction.

## Contribution

It presents the first separate determination of real and imaginary parts of the $oldsymbol{ ext{omega}}$-proton scattering length and effective range from photoproduction data near threshold.

## Key findings

- The scattering length $a_{\omega p}$ indicates a repulsive force.
- Total cross sections were measured at incident energies 1.09-1.15 GeV.
- Small P-wave contribution does not affect the results.

## 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.