Determination of the initial condition for the Balitsky-Kovchegov equation with transformers
In the high-energy limit of QCD, scattering off nucleons and nuclei can be described in terms of Wilson-line correlators whose energy dependence is perturbative. The energy dependence of the two-point correlator, called the dipole amplitude, is governed by the Balitsky-Kovchegov (BK) equation. The initial condition for the BK equation can be fitted to the experimental data, which requires evolving the dipole amplitude for a large set of different parameter values. In this work, we train a transformer model to learn the energy dependence of the dipole amplitude, skipping the time-consuming numerical evaluation of the BK equation. The transformer predicts the learned dipole amplitude and the leading order inclusive deep inelastic scattering cross section very accurately, allowing for efficient fitting of the initial condition to the experimental data. Using this setup, we fit the initial condition of the BK equation to the inclusive deep inelastic scattering data from HERA and consider two different starting points $x_0$ for the evolution. We find better agreement with the experimental data for a smaller $x_0$. This work paves the way for future studies involving global fits of the dipole amplitude at leading order and beyond.