Determination of the HERA coherent diffractive $J/\psi$ production cross section via artificial neural network

An exclusive coherent diffractive $J/\psi$ production dataset from HERA, covering a large kinematic range in the photon virtuality $Q^2$, the squared momentum transfer $t$, and the photon-proton center-of-mass energy $W$, has been analyzed using various theoretical models with different approaches. In common model analyses, the inherent assumptions and limited kinematic applicability somewhat restrict the predictive power of the models, resulting in model-dependent prediction results. In this paper, we present our model-independent approach for the same reaction process and dataset, utilizing an artificial neural network (ANN) technique. The prediction of the best ANN model for the HERA differential cross-section dataset over a range of $W$, $Q^2$, and $t$ is obtained. We then extend the ANN model by combining the HERA and LHC data at various values of $W$ to predict the total photoproduction cross-section and demonstrate how to extract the exponential slope $b$. We find that the exponential slope $b$ strongly depends on $Q^2$ and $W$.