The $\psi^{(\ast)}p$ scattering length based on near-threshold charmoniums photoproduction

TL;DR

This paper estimates the scattering lengths of charmonium-proton interactions using theoretical models, providing new calculations for $ ext{ψ}(2S)$ and comparing results with existing predictions to guide future experimental research.

Contribution

The study introduces the first calculations of $ ext{ψ}(2S)$-proton scattering length within two gluon exchange and effective pomeron models, expanding understanding of vector meson-proton interactions.

Findings

Scattering length $ ext{J/ψ} p$ aligns with previous theoretical predictions.

Calculated $ ext{ψ}(2S)$-proton scattering lengths are 1.31±0.92 am and 3.24±0.63 am in two models.

Results highlight the need for precise experimental measurements.

Abstract

Under the framework of Vector Meson Dominance model, the value of scattering length can be expressed as a function of the ratio between total cross section $\sigma (W)$ and $R (W)$, where $R(W)$ is the ratio between final momentum $|{\bf p}_3 |$ and initial momentum $|{\bf p}_1|$ and positively correlated with the center-of-mass energy. Based on the theoretical study of charmoniums photoproduction within two gluon exchange model and effective pomeron model, we research the scattering lengths of vector mesons and proton interaction in this work. Results show that the scattering length $\left|\alpha_{J/\psi p}\right|$ obtained from the two models are close and basically in agreement with the theoretical prediction of Strakovsky and co-workers. Additionally, we first calculate the scattering length of $\psi(2S) $-proton interaction in two gluon exchange model and effective pomeron model as $ 1.31\pm 0.92$ am (1 am = $10^{-3}$ fm) and $ 3.24 \pm 0.63$ am, respectively. This is a little bit different from the two models and requires precise measurements from subsequent experiments. In short, our results will provide a theoretical reference for future studies on characterizing the vector meson-proton scattering length.