Nonlinear extension of the rapidity-only TMD factorization scheme

Extend the rapidity-only TMD factorization scheme that interpolates between CSS and small-x evolution from the dilute regime to the nonlinear saturation regime.

Background

Rapidity-only factorization provides a unified description of high-energy and Sudakov evolution and has been developed using background-field methods. The existing scheme can go beyond the collinear limit and capture BFKL dynamics, but its applicability to nonlinear Wilson-line dynamics in the saturation region has not been established.

References

Extending this TMD factorization scheme to the non-linear regime remains an open task.

— Transverse momentum dependent parton distributions at small $x$  (2610.26004 - Caucal et al., 19 Oct 2026) in Section 3.2.1, paragraph beginning “Several further developments”

For forward two-particle production in proton-nucleus collisions, it remains an open question whether TMD factorisation, supplemented by CSS resummation for each TMD distribution and fragmentation function, can be consistently matched to an NLO small-x calculation.

— Transverse momentum dependent parton distributions at small $x$  (2610.26004 - Caucal et al., 19 Oct 2026) in Section 3.2.2, paragraph beginning “For forward two-particle production”