Explain the anomalous Gaussian-truncation evolution of the singlet gluon–gluon operator

Explain why the Gaussian-truncation prediction for the singlet gluon–gluon operator Omega_{gg}^{1} evolves more slowly than the full JIMWLK simulation data, despite the singlet representation having smaller dimension and quadratic Casimir than the adjoint representation, and determine the origin of this violation of the observed representation-dependent ordering.

Background

The paper compares the rapidity evolution of gluon–gluon building-block operators Omega_{gg}^{omega} obtained from full numerical JIMWLK evolution with predictions from the Gaussian truncation, using the adjoint dipole to determine the two-point correlation function. For most representations, including omega=27 and omega=10+\overline{10}, the Gaussian truncation evolves more slowly than the JIMWLK data, and the discrepancy generally appears to increase with the representation's dimension or color charge. The adjoint channels omega=8_a and omega=8_s are comparatively well described.

The singlet channel omega=1 is anomalous: its Gaussian-truncation evolution is also slower than the data, even though the singlet has both smaller dimension and smaller quadratic Casimir than the adjoint representation. This contradicts the naive expectation that the singlet prediction should evolve faster and undermines a simple rescaling of rapidity by representation dimension or charge. The authors explicitly leave the origin of this behavior unresolved.