Definition and evolution of transverse momentum dependent distribution of twist-three

A bstract 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.