Functional form of nonperturbative fragmentation functions

Determine the exact functional form of nonperturbative fragmentation functions at the initial factorization scale without relying on a presumed phenomenological parametrization.

Background

Fragmentation functions are nonperturbative quantities whose scale dependence is calculable through DGLAP evolution, while their dependence on the momentum fraction must be inferred from data. Global analyses therefore specify an assumed functional form at an initial scale and fit its parameters to experimental measurements.

The chapter notes that polynomial parametrizations and neural networks are alternative strategies, each introducing different assumptions or sources of flexibility. The underlying exact functional form is not established from first principles, leaving a central unresolved issue for extracting fragmentation functions and quantifying their uncertainties.