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

Taufiq Iqbal Baihaqi, Chalis Setyadi, Zulkaida Akbar, Parada T. P. Hutauruk, Apriadi Salim Adam

TL;DR

The paper tackles the challenge of modeling exclusive coherent diffractive $J/\psi$ production by introducing a data-driven ANN that learns the multidimensional mapping from $(Q^2,W,t,y)$ to $d\sigma/dt$ with quantified uncertainties, trained on HERA data and extended to total cross sections using HERA–LHC data. The model uses a heteroscedastic loss to capture aleatoric uncertainty and a deep ensemble to capture epistemic uncertainty, achieving $\chi^2/\mathrm{ndf} \approx 1$ and well-behaved pull distributions. It reproduces the $t$- and $W$-dependencies and provides a consistent extraction of the exponential slope $b$, while highlighting regions with larger uncertainties due to data scarcity and collider differences. The results illustrate that a data-driven framework can complement traditional QCD-based dipole models by reducing reliance on specific theoretical assumptions and enabling robust interpolation for current and future vector-meson measurements, including those at EIC facilities.

Abstract

An exclusive coherent diffractive $J/ψ$ 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 $W$.

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

TL;DR

The paper tackles the challenge of modeling exclusive coherent diffractive production by introducing a data-driven ANN that learns the multidimensional mapping from to with quantified uncertainties, trained on HERA data and extended to total cross sections using HERA–LHC data. The model uses a heteroscedastic loss to capture aleatoric uncertainty and a deep ensemble to capture epistemic uncertainty, achieving and well-behaved pull distributions. It reproduces the - and -dependencies and provides a consistent extraction of the exponential slope , while highlighting regions with larger uncertainties due to data scarcity and collider differences. The results illustrate that a data-driven framework can complement traditional QCD-based dipole models by reducing reliance on specific theoretical assumptions and enabling robust interpolation for current and future vector-meson measurements, including those at EIC facilities.

Abstract

An exclusive coherent diffractive production dataset from HERA, covering a large kinematic range in the photon virtuality , the squared momentum transfer , and the photon-proton center-of-mass energy , 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 , , and is obtained. We then extend the ANN model by combining the HERA and LHC data at various values of to predict the total photoproduction cross-section and demonstrate how to extract the exponential slope . We find that the exponential slope strongly depends on and .
Paper Structure (11 sections, 7 equations, 7 figures)

This paper contains 11 sections, 7 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Exclusive coherent diffractive $J/\psi$ production
  3. ANN model framework
  4. HERA Dataset and pre-processing
  5. Model Architecture and Uncertainty Quantification
  6. Heteroscedastic Architecture (Aleatoric Uncertainty)
  7. Loss Function (Gaussian NLL)
  8. Deep Ensemble (Epistemic Uncertainty)
  9. Training and Evaluation Metrics
  10. Numerical result and discussion
  11. Summary and conclusion

Figures (7)

  • Figure 1: Results for the NLL for the training and validation losses as a function of epoch.
  • Figure 2: Differential cross section of the exclusive coherent diffractive $J/\psi$ production at fixed $<W > =$ 90 GeV with different $<Q^2>$ in comparison with the H1 dan ZEUS data as a function of $t$.
  • Figure 3: Differential cross section of the exclusive coherent diffractive $J/\Psi$ production at fixed $<Q^2> =$ 0.05 GeV$^2$ for different $t$ as a function of $W$.
  • Figure 4: Center of mass energy ($W$) dependence of the differential cross-section of the exclusive $J/\psi$ electroproduction at fixed $<Q^2> =$ 8.9 GeV$^2$ for the values of $t=$ 0.05, 0.19, and 0.64 GeV$^2$.
  • Figure 5: Total cross-section of $\gamma^{(*)} p \rightarrow J/\psi \, p$ at fixed $W=$ 90 GeV as a function of $Q^2$, in comparison with H1 (triangle point) and ZEUS (circle point) data. The experimental data of the H1 and ZEUS collaborations are taken from Refs. H1:2005dtpZEUS:2004yeh.
  • ...and 2 more figures