Document Type


Publication Date




Publication Title

Physical Review D




094029 (1-24)


Parametrizing TMD parton densities and fragmentation functions in ways that consistently match their large transverse-momentum behavior in standard collinear factorization has remained notoriously difficult. We show how the problem is solved in a recently introduced set of steps for combining perturbative and nonperturbative transverse momentum in TMD factorization. Called a “bottom-up” approach in a previous article, here we call it a “hadron structure oriented” (HSO) approach to emphasize its focus on preserving a connection to the TMD parton model interpretation. We show that the associated consistency constraints improve considerably the agreement between parametrizations of TMD functions and their large-kT behavior, as calculated in collinear factorization. The procedure discussed herein will be important for guiding future extractions of TMD parton densities and fragmentation functions and for testing TMD factorization and universality. We illustrate the procedure with an application to semi-inclusive deep inelastic scattering (SIDIS) structure functions at an input scale Q0, and we show that there is improved consistency between different methods of calculating at moderate transverse momentum. We end with a discussion of plans for future phenomenological applications.


Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Original Publication Citation

Gonzalez-Hernandez, J. O., Rainaldi, T., & Rogers, T. C. (2023). Resolution to the problem of consistent large transverse momentum in TMDS. Physical Review D, 107(9), 1-24, Article 094029.


0000-0002-8342-6765 (Rainaldi), 0000-0002-0762-0275 (Rogers)