<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>?</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mo>*</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:msup><mml:mi>p</mml:mi></mml:mrow></mml:math> scattering length based on near-threshold charmonium photoproduction

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