Nonfactorizable

Nonfactorizable refers to contributions in quantum field theory calculations that cannot be expressed as a simple product of independent factors associated with separate sub-processes. In this context, factorization implies that a complex amplitude can be decomposed into distinct, independent components—such as hard scattering kernels and universal parton distribution functions—that can be calculated or extracted separately. Nonfactorizable terms arise when interactions link these components in a way that prevents such a clean separation, often due to soft gluon exchanges or long‑distance effects that couple different parts of the diagram.

In the study of hadronic decays of heavy mesons, for instance, factorization theorems allow the decay amplitude to be written as a convolution of perturbatively calculable hard kernels with nonperturbative hadronic matrix elements. Nonfactorizable corrections appear when gluon exchanges between spectator quarks, or between the two final‑state mesons, introduce correlations that spoil this simple convolution. These terms are typically suppressed by powers of the hard scale, but can still be significant for precise predictions, especially in color‑suppressed decay modes. The calculation of nonfactorizable contributions often requires advanced techniques such as QCD sum rules, lattice QCD, or soft‑collinear effective theory to account for the complex interplay between short‑ and long‑distance dynamics.

In scattering processes, nonfactorizable effects manifest as color‑connected diagrams where color flow cannot be partitioned into independent sub‑processes. Recognizing and accurately estimating these contributions is crucial for reducing theoretical uncertainties in flavor physics and for testing the validity of factorization approaches in high‑energy experiments.