18834 2204.03856 10.1007/JHEP08(2022)031 31 31 10.1007/JHEP12(2022)048 Definition and evolution of transverse momentum dependent distribution of twist-three Regular Article - Theoretical Physics 1 52 2022 8 2 2022 4 28 2022 6 22 2022 8 2 2022 12 9 An Erratum to this paper has been published: https://doi.org/10.1007/JHEP12(2022)048 The Author(s) 2022 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2022 2022 8 8 Simone Rodini simone.rodini@physik.uni-regensburg.de Alexey Vladimirov alexey.vladimirov@physik.uni-regensburg.de grid.7727.5 0000 0001 2190 5763 Institut für Theoretische Physik Universität Regensburg D-93040 Regensburg Germany grid.4795.f 0000 0001 2157 7667 Dpto. de Física Teórica & IPARCOS Universidad Complutense de Madrid E-28040 Madrid Spain Abstract We present an in-depth analysis of transverse momentum dependent (TMD) distributions of twist-three. In particular, we focus on evolution equations, symmetry relations, parameterization, interpretation, small-b asymptotic behaviour and the structure of singularities. The starting point of discussion are the correlators with the definite TMD-twist. By considering suitable combinations of these correlators, we introduce physical TMD distribution of twist-three that can be used for practical applications. We also establish relations with generic TMD distribution of twist-three, and demonstrate that their evolution equations are autonomous in the large-N c limit. Keywords Factorization Renormalization Group Parton Distributions ArXiv ePrint: 2204.03856 An Erratum to this article is available online at https://doi.org/10.1007/JHEP12(2022)048 .