Optimal use of deep-neural-network flexibility in TMD extraction

Determine how to harness the flexibility of deep-neural-network parametrizations for phenomenological transverse-momentum-dependent parton-distribution extraction while preserving a transparent separation between perturbatively calculable QCD contributions and genuine long-distance dynamics.

Background

The paper develops a physics-informed deep-neural-network extraction in which the perturbative W-term kernel, collinear PDFs, hard factor, matching coefficients, evolution, and Fourier–Bessel transform are fixed, while the neural network learns only the nonperturbative factor. This design is motivated by the risk that a fully unconstrained end-to-end network could obscure the distinction between perturbative and nonperturbative physics.

The authors identify the broader methodological question of how neural-network flexibility should be used in TMD phenomenology without sacrificing interpretability. The paper proposes one constrained FiLM-based construction, but does not claim to establish that it is the optimal way to balance data-driven flexibility and perturbative transparency.