Color-entanglement logarithms from multiple soft-gluon emissions

Determine whether multiple soft-gluon emissions in QCD generate additional logarithms associated with color entanglement, and develop a resummation incorporating those logarithms together with the full QCD evolution of the Qiu–Sterman functions.

Background

The paper derives a fixed-order enhancement of the double-Sivers asymmetry caused by crossed coherent-gluon attachments in a photon-exchange model. It then proposes a heuristic resummation for photon radiation, where the color-blind photon exponent acts on the joint coefficient rather than on two independent Sivers functions.

Extending this construction to QCD is unresolved because soft-gluon radiation can mix color structures. The authors specifically identify the need to determine whether such radiation produces additional logarithms tied to color entanglement and, if so, to resum them consistently with Qiu–Sterman evolution.

References

Extending this ansatz to QCD is less straightforward because soft-gluon radiation, unlike photon radiation, can mix color structures. Whether it also generates additional logarithms associated with color entanglement remains an open question.

— Quantifying TMD factorization breaking at tree level  (2610.11258 - Zhou, 8 Oct 2026) in Section 3, immediately following Eq. (joint-photon-resummation)

Beyond the perturbative region considered here, it remains unclear whether the nonperturbative effects of color entanglement at small $q_T$ admit a controlled quantitative description.

— Quantifying TMD factorization breaking at tree level  (2610.11258 - Zhou, 8 Oct 2026) in Section 4, Summary