Exclusive diffractive vector meson production: A comparison between the dipole model and the leading twist shadowing approach

Abstract

With the imminent construction of an electron-ion collider in the USA, both saturation physics and nuclear shadowing physics will be important for the same processes for the first time. In particular for exclusive production of vector mesons, such as the J/$ψ$. In this paper we investigate the underlying assumptions commonly made when phenomenologically investigating this process from a shadowing and saturation perspective respectively. We use the bSat model which is commonly used to describe saturation physics, and a calculation by M.G. Ryskin which is commonly used when describing nuclear shadowing at leading twist. It is expected that the bSat model is equivalent to Ryskin's result in the hard scattering and non-relativistic limits. By explicitly taking these limits we show that the bSat model does indeed become equivalent to Ryskin's result. However, two more approximations are needed for this result. Firstly, the factorisation and renormalisation scales in the bSat model has to be independent of the dipole radius, and secondly, we need to omit a term in the overlap between the vector meson and virtual photon wave functions. We show that for the typical dipole radius of the J/$ψ$, the different approximations off-set each other and the bSat model agrees very well with Ryskin's calculation in hard-scattering and non-relativistic limits.