Transverse Momentum Moments

We establish robust relations between Transverse Momentum Dependent distributions (TMDs) and collinear functions. We define weighted integrals of TMDs which we call Transverse Momentum Moments (TMMs). We demonstrate that TMMs are related to collinear distributions via calculable scheme-coefficients

and we derive expressions for them up

to three loops. We prove that TMMs obey the same evolution equations as the corresponding collinear quantities. We discuss in details the zeroth, the first, and the second TMMs and provide phenomenological results for those based on the current extractions of TMDs. Results of this paper open new avenues for theoretical and phenomenological investigation of the three-dimensional and collinear hadron structures.