<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">ϒ</mml:mi></mml:math> photoproduction on the proton at the Electron-Ion Collider
Oleksii Gryniuk, S. Joosten, Z.-E. Meziani, Marc Vanderhaeghen
Abstract
We present a dispersive analysis with the aim to extract the $\mathrm{\ensuremath{\Upsilon}}\text{\ensuremath{-}}p$ scattering length from $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}p$ experiments. In this framework, the imaginary part of the $\mathrm{\ensuremath{\Upsilon}}\text{\ensuremath{-}}p$ forward scattering amplitude is obtained from $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}p$ cross section measurements and is constrained at high energies from existing HERA and LHC data. Its real part is calculated through a once-subtracted dispersion relation, and the subtraction constant is proportional to the $\mathrm{\ensuremath{\Upsilon}}\text{\ensuremath{-}}p$ scattering length. We perform a feasibility study for $\mathrm{\ensuremath{\Upsilon}}$ photoproduction experiments at an Electron-Ion Collider and discuss the sensitivity and precision that can be reached in the extraction of the $\mathrm{\ensuremath{\Upsilon}}\text{\ensuremath{-}}p$ scattering length.