Native transverse-momentum evolution and matching for TMD factorization and extraction

@misc{keller2026native,
  title = {{Native transverse-momentum evolution and matching for TMD factorization and extraction}},
  author = {Dustin Keller},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03712},
  eprint = {2611.03712},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03712},
}

TY  - UNPB
TI  - Native transverse-momentum evolution and matching for TMD factorization and extraction
AU  - Dustin Keller
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.03712
UR  - https://arxiv.org/abs/2611.03712
AB  - We present a native transverse-momentum realization of the Collins/CSS2 leading-power transverse-momentum-dependent (TMD) factorization framework. The construction connects fixed-order distributional matching, origin contacts, unexpanded two-scale evolution, and a differentiable interface for hadronic structure. An endpoint-independent canonical scale with a specified infrared completion generates a Collins--Soper kernel on a common invariant domain. Complete canonical legs are bounded and admit constructive momentum-space evaluation through resolvent convolutions or elliptic solves. We give contact and finite-bin error bounds, parent-to-momentum-boundary translations, ordered flavor recurrences, and an all-order argument for the four exponent towers of N^3LL evolution. Localized joint-(x,k_T) inputs, nonperturbative rapidity broadening, regulated moments and the full-spectrum subtraction are formulated as distinct parts of the prescription. The physical realization uses sourced four-loop beta/cusp and three-loop noncusp/Collins--Soper ingredients with strict-NLO hard/OPE boundaries. Non-Gaussian continuum tests and three-scale physical-PDF comparisons validate ordinary legs, contacts, individual insertions and analytic input derivatives. Including a declared bound on the continuation above a finite PDF table, physical bin discrepancies remain below 4.27×10^−5 of the peak reference bin. A qualified proton--proton Drell--Yan and neural-closure demonstration connects the method to inverse use. Higher-order boundary assembly and matched observables are specified without claiming an implemented N^3LL' spectrum or a completed global extraction.
ER  -