$J/\psi$-$p$ Scattering Length from the Total and Differential Photoproduction Cross Sections

TL;DR

This paper estimates the $J/\psi$-proton scattering length from near-threshold photoproduction data using the VMD model, finding values significantly lower than theoretical predictions and analyzing the impact of data extrapolation methods.

Contribution

It provides a systematic analysis of the $J/\psi$-p scattering length extraction from experimental data, highlighting the influence of different cross section measurements and extrapolation techniques.

Findings

Estimated $|\alpha_{J/\psi p}|$ range: 0.003 to 0.025 fm

Lower experimental values compared to theoretical predictions

Impact of data extrapolation methods on the results

Abstract

The $J/\psi$-$p$ scattering length, $\alpha_{J/\psi p}$, can be extracted from the $J/\psi$ photoproduction cross section near threshold using the Vector Meson Dominance (VMD) model to relate the reaction $\gamma p \to J/\psi p$ to $J/\psi p \to J/\psi p$. Such estimates based on experimental data result in values for $|\alpha_{J/\psi p}|$, which are much lower than most of the theoretical predictions. In this work, we study the relations between the different results, depending on the use of the total or the differential cross sections, and the method of extrapolating the data to threshold in the case of a low-statistics data sample, such as the near threshold $J/\psi$ photoproduction dataset. We estimate a range for $|\alpha_{J/\psi p}|$ of $0.003$ to $0.025$~fm as extracted from experimental data within the VMD model and discuss possible reasons for such lower values compared to the theoretical results.