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We consider one of the most fundamental sets of hadronic matrix elements,namely the generalized transverse momentum distributions (GTMDs), and arguethat their existing definitions lack proper evolution properties. By exploitingthe similarity of GTMDs with the much better understood transverse momentumdistributions, we argue that the existing definitions of GTMDs have to includean additional dependence on soft gluon radiation in order to render themproperly defined. With this, we manage to obtain the evolution kernel of all(un)polarized quark and gluon GTMDs, which turns out to be spin independent. Asa byproduct, all large logarithms can be resummed up tonext-to-next-to-leading-logarithmic accuracy with the currently knownperturbative ingredients.

Proper definition and evolution of generalized transverse momentum distributions